# Activity cycles in RS-CVn Stars

C. I. Martínez1,2, P. J. D. Mauas3,4, A. P. Buccino3,4

1Observatorio Astronómico Félix Aguilar, Universidad Nacional de San Juan, Av.
Benavides 8175 oeste, CP 5400 San Juan, Argentina.
2Instituto de Ciencias Astronómicas de la Tierra y el Espacio (CONICET-UNSJ),
Av. España 1512 sur, San Juan, Argentina.
3Instituto de Astronomía y Física del Espacio (CONICET-UBA), C.C. 67 Sucursal
28, C1428EHA-Buenos Aires, Argentina.
4Departamento de Física. Facultad de Ciencias Exactas y Naturales -
Universidad de Buenos Aires, Buenos, Argentina.
Contact e-mail<EMAIL_ADDRESS>e-mail<EMAIL_ADDRESS>
###### Abstract

We compile a list of 121 RS CVn type stars from the bibliography in southern
hemisphere, to search for activity cycles, covering a large range of
luminosities and rotation periods. For each system of the list, we obtain
photometric data from the All Sky Automated Survey (ASAS), and we complement
it with our own photometry, obtained with the Optical Robotic Observatory
(ORO). We analyze this data with the Generalized Lomb–Scargle periodogram to
determine the rotation period and possible activity cycles for each system. We
found rotation periods for 102 systems and activity cycles for 91 systems.
From the statistical analysis of the results, we found that giant stars behave
differently than subgiants and main-sequence stars, and that there is a good
correlation between rotation periods and luminosities.

###### keywords:

stars: activity - stars: rotation - stars: binaries: spectroscopic.

††pubyear: 2021††pagerange: Activity cycles in RS-CVn Stars–Activity cycles in
RS-CVn Stars

##  1 Introduction

RS CVn stars are close binaries where the hottest component, the primary, is a
subgiant or giant star of spectral type between F and K, and the coolest
component, the secondary, is a dwarf or subgiant of spectral type from G to M
(Biermann & Hall, 1976). The prototypical example, which gives its name to the
group, is the eclipsing binary RS Canum Venaticorum. As a result of the much
fainter luminosity of the coolest star, most of these systems are of the SB1
type.

These stars are fast rotators tidally synchronized, and are therefore more
active than single stars with the same characteristics (Hall, 1972; Dempsey et
al., 1993), and they usually show strong H$\alpha$, Ca II, X-ray, and
microwave emissions. This activity is dominated by the hottest component,
which exhibits a high rotational rate (Weiler, 1978). In the optical band, the
most prominent feature is the periodic photometric variability, much larger
than in individual stars with the same spectral type (Dempsey et al., 1993).
This variability is due to the rotational modulation by large starspots,
covering almost 10% of the stellar surface (Vogt et al., 1999).

Walter et al. (1978) determined that RS CVn are also strong X-ray sources,
with fluxes between $10^{26}$ and $10^{31.5}$ erg s-1, and Dempsey et al.
(1993) found that the temporal variations in X-rays are of the order of the
starspot life-time. Singh et al. (1996) proposed that the X-ray variability is
related to the tidally induced rotation that enhances the dynamo activity,
since they did not found clear evidence that it might be due to mass
transference between the components.

On the other hand, many of these systems show long-term chromospheric activity
variations and activity cycles (Hall et al., 1991; Berdyugina & Henry, 2007;
Messina, 2008; Buccino & Mauas, 2009; Martínez et al., 2019). To study these
cycles is key to understand the connection between stellar rotation and long-
term activity (see for example Rodono et al. 1986; Berdyugina et al. 1999),
and it is relevant to constrain the mechanism responsible for the generation
and maintenance of the stellar magnetic fields (Weiler, 1978). With this goal,
we have studied the long-term activity of different main-sequence stars, and
we have detected cycles in many of them (Cincunegui et al., 2007; Díaz et al.,
2007; Buccino et al., 2011, 2014; Flores et al., 2017; Ibañez Bustos et al.,
2019a; Ibañez Bustos et al., 2019b).

From statistical studies of activity in late-type stars with rotation periods
between 22 and 48 days, Noyes et al. (1984) found a possible correlation
between the activity-cycle period $P_{\mathrm{cyc}}$ and the Rossby number
$Ro=P_{\mathrm{rot}}/\tau_{\mathrm{c}}$, where $\tau_{\mathrm{c}}$ is the
convective turnover time near the bottom of the convection zone.

Later, Saar & Baliunas (1992) reported that stellar activity cycles form two
distinct branches when plotted as a function of the rotation period, a fact
that was later confirmed by Saar & Brandenburg (1999); Böhm-Vitense (2007) and
Brandenburg et al. (2017). Brandenburg et al. (1998) found that the ratio
$P_{\mathrm{cyc}}$/$P_{\mathrm{rot}}$ is proportional to the $\alpha$-effect
in the mean field dynamo theory. Tuominen et al. (1988) found that this ratio
decreases systematically with increasing thickness of the convection zone.
Outside the main-sequence, evolved stars can develop increasingly thick
convective envelopes and their convective turnover time increases (Gilliland,
1985). Simultaneously, the rotation period of the giant stars will also
increase due to rotational braking (Skumanich, 1972). Therefore, studying
activity cycles in evolved stars should help understand the dynamo mechanisms
responsible for stellar activity.

In this work, we look for activity cycles on a large set of RS CVn-type stars,
using photometric data obtained by the All Sky Automated Survey (ASAS,
Pojmanski 2002), and our own photometry obtained with the Optical Robotic
Observatory (ORO). In Section 2 we present our stellar list and the
observations dataset. In Section 3 we describe the method used to study the
temporal evolution of the data, the correlation between the stellar variables
that characterize our targets and the statistical analysis. Finally, in
Section 4 we discuss the results.

##  2 Observations and Data collection

###  2.1 Target list

To our knowledge, there is not available a reliable list of RS CVn-type stars
in the southern hemisphere. Therefore, it is important to build a list as
complete as possible of confirmed RS CVn stars. In first approach, we obtained
a preliminary classification from an exhaustive search in the bibliography of
bright southern stars ($V\leq 14$ and $Dec<0$).

We first explored the southern brighter stars catalog of Bidelman & MacConnell
(1973) together with the southern RS CVn candidate list of Weiler & Stencel
(1979). We confirm the targets as RS CVn-type using the catalogs of active
binary stars published by Rodono et al. (1986), Strassmeier et al. (1988),
Pallavicini et al. (1992) and Strassmeier et al. (1993); the RS CVn binaries
catalog of Morris & Mutel (1988) for radio sources and Fleming et al. (1989)
for X-ray sources; and the stellar classification catalogs given by Berdnikov
& Pastukhova (2008) and Drake et al. (2014). We also included all the stars
individually classified by Pollard et al. (1989), Pandey et al. (2005),
Strassmeier (2000), Drake (2006), Gálvez et al. (2009) and López-Santiago et
al. (2012).

Finally, we added a few stars following the criteria established by Hall
(1976)111 This classification describes the main features of the RS CVn stars:
spectral types between F-M with one or both evolved components, high rotation
rate, chromospheric and X-ray emission.. The spectral type of the stars were
obtained from the classification catalogs of Houk (1982), Stocke et al.
(1991), Pourbaix et al. (2004), Torres et al. (2006) and Skiff (2014); the
catalogs of chromospherically active stars by Fekel et al. (1986), Popper
(1991), Randich et al. (1993), Thatcher & Robinson (1993), Fekel & Henry
(2005), Bernhard et al. (2010) and Boro Saikia et al. (2018); and the of X-ray
emission sources by Cutispoto et al. (1996), Kang et al. (1996), Cutispoto et
al. (1999), Hünsch et al. (1999), Fuhrmeister & Schmitt (2003), Shtykovskiy &
Gilfanov (2005), Haakonsen & Rutledge (2009) and Kiraga (2012).

In total, our final list, presented in Table 1, includes 121 sources.

A statistic exploratory analysis allowed us to characterize our target list
and estimate the distribution of different stellar parameters, also listed in
Table 1. These quantities were obtained from the next catalogs:

  * •

The Hipparcos Catalogue (Perryman et al., 1997): $V$ y $B$ magnitudes, $B-V$
color index.

  * •

ASAS Photometry of ROSAT Sources (Kiraga, 2012): $V$ magnitude.

  * •

The Tycho-2 catalogue (Høg et al., 2000): $V$ and $B$ magnitudes, $B-V$ color
index.

  * •

The International Variable Star Index (Watson et al., 2006): rotation periods.

  * •

The PASTEL catalogue, 2016 version (Soubiran et al., 2016): effective
temperature $T_{\mathrm{eff}}$.

  * •

Gaia Data Release 2 (Gaia Collaboration, 2018): $G$ (330-1050 nm), $G_{BP}$
(330-680 nm) and $G_{RP}$ (630–1050 nm) apparent magnitudes,
$T_{\mathrm{eff}}$ and luminosity $\log L$.

In Fig. 1 we show the histograms for the colours $B-V$ and $G_{BP}-G_{RP}$,
the effective temperature $T_{\mathrm{eff}}$ and the luminosity $\log L$. In
each graph $N$ is the number of sources for which the specific quantity was
available.

###  2.2 Observations

We used photometric data provided by the ASAS-3 database, which is available
for our 121 stars. We only used observations qualified as A or B in the
database (best or mean quality according to the ASAS definition).

We also carried out photometric observations from February 2017 to January
2019 using the three 16” MEADE telescopes that are part of the Optical Robotic
Observatory (ORO) installed at the Estación en Altura Carlos U. Cesco, located
in San Juan, Argentina. We observed 8-10 objects per night in non-consecutive
nights to have a nearly uniform sample throughout their expected rotation
periods. The image calibration and aperture differential photometry were
optimally performed using our package killastro, developed under the
IRAF222The Image Reduction and Analysis Facility (IRAF) is distributed by the
Association of Universities for Research in Astronomy (AURA), Inc., under
contract to the National Science Foundation platform. This package tries 10
different apertures, ranging from 0.7 to 4 FWHM, and chooses the aperture
which minimizes the flux dispersion. We then performed differential photometry
on these images, using as reference stars between 2 and 4 stars which do not
show variability in the ASAS database. Finally, we intercalibrate with ASAS
using the ASAS magnitude of the brightest reference star in the field (for
details, see Martínez et al. 2019).

Figure 1: Distribution of the stellar parameters in our list. The shaded
region shows the results for the whole sample, and the coloured lines the
clustering groups described in Sect. 3

##  3 Activity cycles analysis

The Lomb–Scargle (LS) periodogram (Horne & Baliunas, 1986) has been widely
used to search for stellar activity cycles. Zechmeister & Kürster (2009)
proposed a modification which has certain advantages in comparison to the
classic LS periodogram: the Generalized Lomb–Scargle (GLS) periodogram.
Namely, it takes into account a varying zero point, it does not require
bootstrap or Monte Carlo algorithms to compute the significance of a signal,
reducing the computational cost, and it is less susceptible to aliasing than
the LS periodogram. In this study, we used the Python libraries developed by
Czesla et al. (2019).

First, we applied to the light curves of all the sources the GLS periodogram
in the 0.1 to 150 days range, to determine the rotation period of each target.
This range was selected according to the maximum and minimum orbital periods
of RS CVn-type systems found by Strassmeier et al. (1993). However, we usually
found weak peaks that could not be distinguished from noise, or with high
levels of FAP. In fact, the photometric modulation attributed to rotation is
usually not persistent throughout the entire data set. The absence of a well-
defined photometric modulation at different epochs could be the result of
longitudinal distributions of spots which are more or less homogeneous
(Murdoch et al., 1995). Therefore, we looked in the periodogram for long-term
variations associated with possible activity cycles, choosing periods longer
than 150 days, and we obtained significant periods for 91 stars.

Then, we fitted the light curves with a sinusoidal function for the period
found, we applied the GLS to the residuals for the period range between 0.1
and 150 days, and we found rotation periods for 102 sources. In several cases,
marked with a $\bigstar$ in Table 1, we found that the amplitude of the
rotational modulation changes during the activity cycle, due to the different
filling factor of spots and active regions.

We complemented this analysis with periods for 13 sources found in The
International Variable Star Index (VSX, Watson et al. 2006). For the eclipsing
binaries, indicated with a $\dagger$ in Table 1, we used the phase dispersion
minimization algorithm (PDM, Stellingwerf 1978) provided in IRAF, and we list
the orbital period instead. All the periods obtained are listed in Table 1,
and the phase curves are shown in Figure 6. It can be seen in this figure that
in a few cases the phase coverage of the observations in not adequate. We plan
to complete the coverage with future observations.

We also applied to the data set the hierarchical agglomerative clustering with
Ward linkage and Euclidean distance described by Ward (1963), considering the
variables $P_{\mathrm{rot}}$, $P_{\mathrm{cyc}}$, $A_{\mathrm{cyc}}$,
$T_{\mathrm{eff}}$ and $\log L$. In fact, we found that the sample can be
separated in two different clusters. In Fig. 2 we show our stars in the HR
diagram, with both clusters indicated with different colours. It can be seen
that the stars marked in blue are giant stars, while those marked in red are
closer to the main-sequence.

Figure 2: HR diagram: Luminosity vs. effective temperature. The clustering we
found is shown in red and blue. The size of each point is proportional to the
rotation period. The theoretical main-sequence is represented by a black
dotted line.

In Fig. 3 we show the distribution of our results for the whole sample and for
both clusters. We plot $P_{\mathrm{rot}}$, $P_{\mathrm{cyc}}$ and the activity
cycle amplitude $A_{\mathrm{cyc}}$, expressed as percentage of the mean
magnitude $V$ (% mmag). It can be seen that the red group has shorter rotation
periods and cycles both longer and with larger amplitudes. This last result
can also be seen in Fig. 4, where we plot the activity period
$P_{\mathrm{cyc}}$ as a function of the rotation period $P_{\mathrm{rot}}$ for
each agglomerate.

For the cluster #2 (blue color), associated to giant stars, we found that
${P_{\mathrm{cyc}}}/{P_{\mathrm{rot}}}=75\pm 38$ and
$\log({P_{\mathrm{cyc}}}/{P_{\mathrm{rot}}})=1.81\pm 0.26$. For comparison,
Böhm-Vitense (2007), in a study of main-sequence stars, obtained
$\log({P_{\mathrm{cyc}}}/{P_{\mathrm{rot}}})=1.95$ for the inactive branch.

Figure 3: Distribution of the GLS results: $P_{\mathrm{rot}}$ in two different
scales, $P_{\mathrm{cyc}}$ and its amplitude $A_{\mathrm{cyc}}$. The shaded
regions show the results for the whole sample, and the coloured lines
represent the clustering groups; there are 56 objects in cluster 1 (red) and
27 objects in cluster 2 (blue). Figure 4: Rotation vs. activity periods. The
two groups found in the clustering are shown in red and blue. The position of
the Sun is indicated by the yellow star.

Finally, to look for correlations between the stellar properties in our target
list, we used the non-parametrical Spearman correlation coefficient $r_{ij}$
(Conover, 1999), which can be applied to variables with non-Gaussian
distributions. The quantities we analyzed form a variable vector $\mathbf{v}$,
given by:

$\mathbf{v}=\left[\begin{matrix}P_{\mathrm{rot}}&P_{\mathrm{cyc}}&A_{\mathrm{cyc}}&T_{\mathrm{eff}}&\log
L\\\ \end{matrix}\right],$ (1)

and the results can be summarized by a matrix $\mathbf{R}$. In this matrix,
the elements $r_{ij}$ below the main diagonal represent the correlation
between the i-th y j-th variables, and the elements $p_{ij}$ above the main
diagonal represent the probability that the i-th and j-th variables are
independent.

The $r_{ij}$ coefficients indicate if the correlation is perfect ($\lvert
1\rvert$), excellent ($\lvert 0.9-1\rvert$), acceptable ($\lvert
0.75-0.9\rvert$), regular ($\lvert 0.5-0.75\rvert$), weak ($\lvert
0.25-0.5\rvert$) or absent ($<0.25$). $r_{ij}$ is positive for a direct
correlation and negative for an inverse one.

The result we obtained is:

$\mathbf{R}=\left[\begin{matrix}1&0.64&0.1&\ast&\ast\\\
-0.05&1&\ast&0.51&0.59\\\ 0.18&0.63&1&0.01&0.83\\\ -0.36&-0.07&-0.26&1&\ast\\\
0.76&-0.06&0.02&-0.35&1\\\ \end{matrix}\right].$ (2)

The matrix elements pointed out with a $\ast$ represent probability values
lower than 0.0005. From these results, it seems that there is a good positive
correlation between rotation period $P_{\mathrm{rot}}$ and luminosity $\log
L$, and a regular correlation between the activity period $P_{\mathrm{cyc}}$
and its amplitude $A_{\mathrm{cyc}}$.

Figure 5: $\log(P_{\mathrm{rot}})$ versus $\log(L/L_{\odot})$. The clustering
is shown with the same colour code than in the other figures. The $R$-spearman
coefficient for this correlation is 0.76.

We therefore plot the rotation periods $P_{\mathrm{rot}}$ in logarithmic scale
as a function of the luminosity $L/L_{\odot}$ in Fig. 5. The correlation found
in (2), with $R_{s}=0.76$, is apparent. The two groups seen in Fig. 2 are
separated by luminosity. Fitting this correlation, we obtain that:

$P_{\mathrm{rot}}\approx 3.16\ \left(\frac{L}{L_{\odot}}\right)^{3/5}.$ (3)

##  4 Conclusions

In this work we present a list of 121 bona fide RS CVn southern stars with
$V\leq 14$. For this list, we compiled the main stellar parameters: the colour
index $B-V$, the effective temperature $T_{\mathrm{eff}}$ and the luminosity
$L$ (see 1)

We also analyzed the activity of these systems in different time scales.
Applying the Generalized Lomb-Scargle periodogram (GLS) to photometric data
obtained from the publicly available ASAS-3 database and our own observations
obtained with ORO, we found rotation periods for 102 systems, which we
completed with results from the literature for 13 more. We also obtained
activity cycles for 91 systems. In many cases, we observed that the amplitude
variation due to the rotation is modulated by the activity cycle, due to the
different area covered by starspots.

We applied a hierarchical agglomerative clustering method to our data and
found that giant stars are separated from subgiants and main-sequence stars.

We also found a good correlation between the rotation period
$P_{\mathrm{rot}}$ and the luminosity $\log L$, and a fair one between the
activity period $P_{\mathrm{cyc}}$ and the percent amplitude variation
$A_{\mathrm{cyc}}$.

##  5 Acknowledgments

We are grateful to the personal of the Observatorio Astronómico Félix Aguilar
for their invaluable help with the operation of the Optical Robotic
Observatory.

##  6 Data availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

## References

  * Berdnikov & Pastukhova (2008) Berdnikov L. N., Pastukhova E. N., 2008, Peremennye Zvezdy, 28, 9
  * Berdyugina & Henry (2007) Berdyugina S. V., Henry G. W., 2007, ApJ, 659, L157
  * Berdyugina et al. (1999) Berdyugina S. V., Berdyugin A. V., Ilyin I., Tuominen I., 1999, A&A, 350, 626
  * Bernhard et al. (2010) Bernhard K., Lloyd C., Frank P., 2010, Berliner Arbeitsgemeinschaft fuer Veraenderliche Sterne - Mitteilungen, 210, 1
  * Bidelman & MacConnell (1973) Bidelman W. P., MacConnell D. J., 1973, AJ, 78, 687
  * Biermann & Hall (1976) Biermann P., Hall D. S., 1976, in Eggleton P., Mitton S., Whelan J., eds, IAU Symposium Vol. 73, Structure and Evolution of Close Binary Systems. p. 381
  * Böhm-Vitense (2007) Böhm-Vitense E., 2007, ApJ, 657, 486
  * Boro Saikia et al. (2018) Boro Saikia S., et al., 2018, A&A, 616, A108
  * Brandenburg et al. (1998) Brandenburg A., Saar S. H., Turpin C. R., 1998, ApJ, 498, L51
  * Brandenburg et al. (2017) Brandenburg A., Mathur S., Metcalfe T. S., 2017, ApJ, 845, 79
  * Buccino & Mauas (2009) Buccino A. P., Mauas P. J. D., 2009, A&A, 495, 287
  * Buccino et al. (2011) Buccino A. P., Díaz R. F., Luoni M. L., Abrevaya X. C., Mauas P. J. D., 2011, AJ, 141, 34
  * Buccino et al. (2014) Buccino A. P., Petrucci R., Jofré E., Mauas P. J. D., 2014, ApJ, 781, L9
  * Cincunegui et al. (2007) Cincunegui C., Díaz R. F., Mauas P. J. D., 2007, A&A, 461, 1107
  * Conover (1999) Conover W. J., 1999, Practical Nonparametric Statistics. Ed. John Wiley & Sons, Inc.
  * Cutispoto et al. (1996) Cutispoto G., Tagliaferri G., Pallavicini R., Pasquini L., Rodono M., 1996, A&AS, 115, 41
  * Cutispoto et al. (1999) Cutispoto G., Pastori L., Tagliaferri G., Messina S., Pallavicini R., 1999, A&AS, 138, 87
  * Czesla et al. (2019) Czesla S., Schröter S., Schneider C. P., Huber K. F., Pfeifer F., Andreasen D. T., Zechmeister M., 2019, PyA: Python astronomy-related packages (ascl:1906.010)
  * Dempsey et al. (1993) Dempsey R. C., Linsky J. L., Fleming T. A., Schmitt J. H. M. M., 1993, ApJS, 86, 599
  * Díaz et al. (2007) Díaz R. F., González J. F., Cincunegui C., Mauas P. J. D., 2007, A&A, 474, 345
  * Drake (2006) Drake A. J., 2006, The Astronomical Journal, 131, 1044
  * Drake et al. (2014) Drake A. J., et al., 2014, ApJS, 213, 9
  * Fekel & Henry (2005) Fekel F. C., Henry G. W., 2005, AJ, 129, 1669
  * Fekel et al. (1986) Fekel F. C., Moffett T. J., Henry G. W., 1986, ApJS, 60, 551
  * Fleming et al. (1989) Fleming T. A., Gioia I. M., Maccacaro T., 1989, AJ, 98, 692
  * Flores et al. (2017) Flores M. G., Buccino A. P., Saffe C. E., Mauas P. J. D., 2017, MNRAS, 464, 4299
  * Fuhrmeister & Schmitt (2003) Fuhrmeister B., Schmitt J. H. M. M., 2003, A&A, 403, 247
  * Gaia Collaboration (2018) Gaia Collaboration 2018, A&A, 616, A1
  * Gálvez et al. (2009) Gálvez M. C., Montes D., Fernández-Figueroa M. J., De Castro E., Cornide M., 2009, AJ, 137, 3965
  * Gilliland (1985) Gilliland R. L., 1985, ApJ, 299, 286
  * Haakonsen & Rutledge (2009) Haakonsen C. B., Rutledge R. E., 2009, ApJS, 184, 138
  * Hall (1972) Hall D. S., 1972, PASP, 84, 323
  * Hall (1976) Hall D. S., 1976, Astrophysics and Space Science Library, 60, 287
  * Hall et al. (1991) Hall D. S., et al., 1991, J. Astrophys. Astron., 12, 281
  * Høg et al. (2000) Høg E., et al., 2000, A&A, 355, L27
  * Horne & Baliunas (1986) Horne J. H., Baliunas S. L., 1986, ApJ, 302, 757
  * Houk (1982) Houk N., 1982, Michigan Catalogue of Two-dimensional Spectral Types for the HD stars. Volume 3. Declinations -40 to -26. Department of Astronomy, University of Michigan
  * Hünsch et al. (1999) Hünsch M., Schmitt J. H. M. M., Sterzik M. F., Voges W., 1999, A&AS, 135, 319
  * Ibañez Bustos et al. (2019a) Ibañez Bustos R. V., Buccino A. P., Flores M., Martinez C. I., Maizel D., Messina S., Mauas P. J. D., 2019a, MNRAS, 483, 1159
  * Ibañez Bustos et al. (2019b) Ibañez Bustos R. V., Buccino A. P., Flores M., Mauas P. J. D., 2019b, A&A, 628, L1
  * Kang et al. (1996) Kang Y. W., Guinan E. F., Guedel M., Margheim S., 1996, in American Astronomical Society Meeting Abstracts. p. 44.14
  * Kiraga (2012) Kiraga M., 2012, Acta Astron., 62, 67
  * López-Santiago et al. (2012) López-Santiago J., Stelzer B., Saxton R., 2012, PASP, 124, 682
  * Martínez et al. (2019) Martínez C. I., González J. F., Buccino A., Ibañez Bustos R., Mauas P. J. D., 2019, MNRAS, 490, 5832
  * Messina (2008) Messina S., 2008, A&A, 480, 495
  * Morris & Mutel (1988) Morris D. H., Mutel R. L., 1988, AJ, 95, 204
  * Murdoch et al. (1995) Murdoch K. A., Hearnshaw J. B., Kilmartin P. M., Gilmore A. C., 1995, MNRAS, 276, 836
  * Noyes et al. (1984) Noyes R. W., Weiss N. O., Vaughan A. H., 1984, ApJ, 287, 769
  * Pallavicini et al. (1992) Pallavicini R., Randich S., Giampapa M. S., 1992, A&A, 253, 185
  * Pandey et al. (2005) Pandey J. C., Singh K. P., Sagar R., Drake S. A., 2005, Bulletin of the Astronomical Society of India, 33, 373
  * Perryman et al. (1997) Perryman M. A. C., et al., 1997, A&A, 500, 501
  * Pojmanski (2002) Pojmanski G., 2002, Acta Astronom., 52, 397
  * Pollard et al. (1989) Pollard K. R., Hearnshaw J. B., Gilmore A. C., Kilmartin P. M., 1989, J. Astrophys. Astron., 10, 139
  * Popper (1991) Popper D. M., 1991, AJ, 101, 220
  * Pourbaix et al. (2004) Pourbaix D., et al., 2004, A&A, 424, 727
  * Randich et al. (1993) Randich S., Gratton R., Pallavicini R., 1993, A&A, 273, 194
  * Rodono et al. (1986) Rodono M., et al., 1986, A&A, 165, 135
  * Saar & Baliunas (1992) Saar S. H., Baliunas S. L., 1992, in Harvey K. L., ed., Astronomical Society of the Pacific Conference Series Vol. 27, The Solar Cycle. pp 150–167
  * Saar & Brandenburg (1999) Saar S. H., Brandenburg A., 1999, ApJ, 524, 295
  * Shtykovskiy & Gilfanov (2005) Shtykovskiy P., Gilfanov M., 2005, A&A, 431, 597
  * Singh et al. (1996) Singh K. P., Drake S. A., White N. E., 1996, AJ, 111, 2415
  * Skiff (2014) Skiff B. A., 2014, VizieR Online Data Catalog,
  * Skumanich (1972) Skumanich A., 1972, ApJ, 171, 565
  * Soubiran et al. (2016) Soubiran C., Le Campion J.-F., Brouillet N., Chemin L., 2016, A&A, 591, A118
  * Stellingwerf (1978) Stellingwerf R. F., 1978, ApJ, 224, 953
  * Stocke et al. (1991) Stocke J. T., Morris S. L., Gioia I. M., Maccacaro T., Schild R., Wolter A., Fleming T. A., Henry J. P., 1991, ApJS, 76, 813
  * Strassmeier (2000) Strassmeier K. G., 2000, A&A, 357, 608
  * Strassmeier et al. (1988) Strassmeier K. G., Hall D. S., Zeilik M., Nelson E., Eker Z., Fekel F. C., 1988, ApJS, 72, 291
  * Strassmeier et al. (1993) Strassmeier K. G., Hall D. S., Fekel F. C., Scheck M., 1993, A&AS, 100, 173
  * Thatcher & Robinson (1993) Thatcher J. D., Robinson R. D., 1993, MNRAS, 262, 1
  * Torres et al. (2006) Torres C. A. O., Quast G. R., da Silva L., de La Reza R., Melo C. H. F., Sterzik M., 2006, A&A, 460, 695
  * Tuominen et al. (1988) Tuominen I., Rüdiger G., Brandenburg A., 1988, Observational Constraints for Solar-Type Dynamos. D. Reidel Publishing Company, p. 13
  * Vogt et al. (1999) Vogt S. S., Hatzes A. P., Misch A. A., Kürster M., 1999, ApJS, 121, 547
  * Walter et al. (1978) Walter F., Charles P., Bowyer S., 1978, ApJ, 225, L119
  * Ward (1963) Ward J. H., 1963, American Statistical Associationt, 58, 236
  * Watson et al. (2006) Watson C. L., Henden A. A., Price A., 2006, Society for Astronomical Sciences Annual Symposium, 25, 47
  * Weiler (1978) Weiler E. J., 1978, MNRAS, 182, 77
  * Weiler & Stencel (1979) Weiler E. J., Stencel R. E., 1979, AJ, 84, 1372
  * Zechmeister & Kürster (2009) Zechmeister M., Kürster M., 2009, A&A, 496, 577

Figure 6: Phase curves for the activity cycles we detected ($P$ is expressed
in years). (continued) (continued). Table 1: The complete list of our targets,
including our results. The different columns list (from left to right) the
star ID, the $V$ magnitude, the $B-V$ colour index, the effective temperature
of the binary system, the luminosity in logarithm scale, the short-period
associated to the stellar rotation, the error in the short-period
determination, the FAP corresponding to the short-period, the long-period
associated to the stellar activity cycle, the long-period amplitude, the error
in the long-period determination and the FAP corresponding to the long-period.
$\maltese$ rotation period obtained from The International Variable Star Index
(VSX). $\bigstar$ stars having a rotation amplitude which varies during the
activity cycle. $\dagger$ eclipsing binaries.

ID $V$ $B-V$ $T_{\mathrm{eff}}$ $\log L$ $P_{\mathrm{rot}}$ FAP
($P_{\mathrm{rot}}$) $P_{\mathrm{cyc}}$ $A_{\mathrm{cyc}}$ FAP
($P_{\mathrm{cyc}}$) [K] [$L_{\odot}$] [d] [yr] [%] *42 Cap 5.18 0.65 5682
0.99 - - $7.22\pm 2.39$ 1.79 $10^{-4}$ del Eri 3.54 0.92 5023 0.60 - - - - -
1E2157.6-1016 12.54 - 4395 0.36 $7.108\pm 0.001$ - - - - BD-19 2531 10.51 0.69
4984 0.44 $6.984\pm 0.001$ $<10^{-15}$ $7.50\pm 0.16$ 0.42 $<10^{-15}$ CD-35
4072 10.93 0.83 4738 0.50 $2.373\pm 0.0001$ $<10^{-15}$ $7.20\pm 0.18$ 0.49
$<10^{-15}$ CD-38 336 $\bigstar$ 10.59 1.26 4744 0.80 $20.521\pm 0.006$
$<10^{-15}$ $3.49\pm 0.03$ 0.53 $<10^{-15}$ CD-40 4808 $\bigstar$ 9.00 1.13
4699 1.45 $55.552\pm 0.055$ $<10^{-15}$ $17.23\pm 0.96$ 0.77 $<10^{-15}$ CD-42
130 10.55 1.68 4989 0.72 $16.941\pm 0.007$ - - - - CD-42 5265 $\bigstar$ 11.44
1.16 4397 0.83 $9.998\pm 0.002$ $<10^{-15}$ $10.61\pm 0.91$ 0.44 $<10^{-15}$
CD-43 2399 $\bigstar$ 10.58 0.83 4742 1.97 $31.369\pm 0.007$ $<10^{-15}$
$4.44\pm 0.28$ 0.24 $0.08$ CD-46 5148 10.40 0.93 4978 0.50 $20.127\pm 0.006$
$<10^{-15}$ $22.58\pm 2.06$ 0.93 $10^{-14}$ CD-49 1808 11.67 1.09 4959 0.75
$11.259\pm 0.002$ $<10^{-15}$ $3.34\pm 0.07$ 0.25 $<10^{-15}$ CD-50 245 10.11
0.77 5339 -0.30 $2.566\pm 0.0002$ $<10^{-15}$ $6.94\pm 0.08$ 0.51 $<10^{-15}$
CD-50 2604 9.74 0.63 5336 1.70 $24.289\pm 0.011$ - - - - CD-50 4879 $\bigstar$
10.94 0.98 4843 0.51 $4.547\pm 0.0003$ $<10^{-15}$ $6.99\pm 0.14$ 0.51
$<10^{-15}$ CD-55 2324 10.00 2.02 4373 2.00 $52.133\pm 0.050$ $<10^{-15}$
$13.10\pm 0.20$ 0.78 $<10^{-15}$ CD-56 1450 $\bigstar$ 9.55 0.97 4729 1.41
$17.948\pm 0.019$ $10^{-7}$ $13.21\pm 0.49$ 0.92 $<10^{-15}$ CD-58 860 10.01
0.80 5615 -0.07 $2.615\pm 0.0002$ $<10^{-15}$ $17.39\pm 0.78$ 0.55 $<10^{-15}$
CPD-43 1859 11.45 0.98 4873 0.68 $6.830\pm 0.001$ $<10^{-15}$ $16.99\pm 0.82$
0.75 $<10^{-15}$ CPD-57 1131 9.95 0.75 5196 0.92 $7.414\pm 0.001$ $<10^{-15}$
$11.17\pm 0.30$ 0.33 $<10^{-15}$ CRTS J031335.7-002032 12.70 - 4522 0.41
$7.704\pm 0.001$ $<10^{-15}$ $6.86\pm 0.59$ 0.74 $10^{-6}$ CRTS
J205535.2-153510 12.88 - 4760 1.08 $10.650\pm 0.004$ - - - - CRTS
J225004.4-075247 13.16 - 4897 0.96 $42.112\pm 0.054$ - - - - GSC 08054-00859
$\bigstar$ 11.71 1.09 4742 0.63 $13.257\pm 0.002$ $<10^{-15}$ $9.90\pm 0.94$
0.71 $10^{-10}$ GSC 08550-01650 11.43 0.90 4802 -0.39 $4.618\pm 0.001$
$10^{-9}$ $4.67\pm 0.10$ 0.49 $<10^{-15}$ Haro 5-72 13.86 - 4310 -0.25
$5.929\pm 0.002$ - - - - HD 214169 8.38 0.96 5431 0.92 $5.796\pm 0.001$
$10^{-9}$ $3.26\pm 0.21$ 0.09 $0.001$ HD 29597 $\bigstar$ 8.40 0.82 5044 1.15
$76.253\pm 0.084$ $<10^{-15}$ $4.77\pm 0.15$ 0.32 $<10^{-15}$ HD 65358
$\bigstar$ 8.85 1.40 4638 1.93 $85.266\pm 0.139$ $<10^{-15}$ $25.84\pm 4.94$
0.70 $<10^{-15}$ HD 155555 6.72 0.78 5129 0.28 $1.687\pm 0.0002$ - - - - HD
17925 6.05 0.86 5235 -0.39 $6.710$ - - - - MACHO 7.7422.10 11.88 - 4897 0.73
$3.161\pm 0.0001$ $<10^{-15}$ $11.37\pm 0.77$ 0.40 $<10^{-15}$ TYC 4743-662-1
$\bigstar$ 11.25 1.44 4517 0.25 $1.784\pm 0.00004$ $<10^{-15}$ $5.78\pm 0.36$
0.40 $10^{-8}$ TYC 8380-1953-1 10.45 1.06 4517 1.21 $3.076\pm 0.0002$ - - - -
UCAC3 173-22790 12.80 - 4388 0.04 $5.144\pm 0.0005$ $<10^{-15}$ $10.10\pm
1.11$ 0.41 $10^{-8}$ V* AB Lep - 4944 1.50 $6.425\pm 0.001$ $10^{-13}$
$11.28\pm 0.95$ 0.62 $<10^{-15}$ V* AD Cap $\maltese$ $\dagger$ 9.77 1.00 4968
0.95 $2.959\pm 0.089$ - $10.09\pm 1.53$ 0.56 $10^{-15}$ V* AE Men 8.26 1.11
4635 1.71 $12.038\pm 0.002$ $<10^{-15}$ $3.95\pm 0.31$ 0.12 $0.001$ V* AF Lep
$\dagger$ 6.30 0.54 6496 0.25 $1.000$ - $10.73\pm 0.60$ 0.62 $<10^{-15}$ V* AG
Dor $\bigstar$ 8.60 0.90 4851 -0.29 $2.534\pm 0.0001$ $<10^{-15}$ $5.28\pm
0.09$ 0.42 $<10^{-15}$ V* AH Ant 8.40 1.20 4460 2.07 $75.671\pm 0.104$
$<10^{-15}$ $3.17\pm 0.20$ 0.38 $0.2$ V* AI Lep 8.95 0.63 5728 0.03 $2.281\pm
0.0002$ $10^{-7}$ $4.67\pm 0.12$ 0.27 $<10^{-15}$ V* AK Vol 8.60 0.99 4739
1.83 $31.792\pm 0.017$ - - - - V* AR Mon $\dagger$ 8.79 1.05 4709 1.84
$21.211$ - - - - V* AS Cap $\bigstar$ 7.69 1.06 4815 1.55 $60.625\pm 0.050$
$<10^{-15}$ $10.95\pm 4.07$ 0.49 $0.02$ V* AT Cap $\maltese$ $\dagger$ 8.87
1.28 4649 1.92 $23.193$ - $6.09\pm 0.29$ 0.30 $<10^{-15}$ V* AU Cap 8.01 1.21
4551 1.86 $17.196\pm 0.012$ $10^{-12}$ $3.95\pm 0.25$ 0.13 $10^{-5}$ V* AZ Psc
$\bigstar$ - 4781 1.44 $91.920\pm 0.221$ $<10^{-15}$ $3.85\pm 0.24$ 0.56
$0.01$ V* BC Phe $\dagger$ 8.92 0.71 5240 0.55 $0.657$ - $6.79\pm 0.30$ 0.39
$<10^{-15}$ V* BD Cet $\bigstar$ 7.98 1.11 4541 1.68 $34.593\pm 0.026$
$10^{-14}$ $6.43\pm 0.68$ 0.24 $10^{-6}$ V* BH Ind 9.12 1.04 4762 1.48
$22.117\pm 0.020$ $10^{-7}$ $4.20\pm 0.09$ 0.30 $<10^{-15}$

(continued)

ID $V$ $B-V$ $T_{\mathrm{eff}}$ $\log L$ $P_{\mathrm{rot}}$ FAP
($P_{\mathrm{rot}}$) $P_{\mathrm{cyc}}$ $A_{\mathrm{cyc}}$ FAP
($P_{\mathrm{cyc}}$) [K] [$L_{\odot}$] [d] [yr] [%] V* BH Vir $\dagger$ 9.68
0.61 5876 0.43 $0.817$ - - - - V* BI Ind 7.67 1.22 4604 2.02 $29.775\pm 0.017$
$<10^{-15}$ $6.01\pm 0.10$ 0.44 $<10^{-15}$ V* BM Mic $\bigstar$ 8.29 0.77
5050 1.01 $14.382\pm 0.007$ $<10^{-15}$ $4.32\pm 0.08$ 0.19 $<10^{-15}$ V* BN
Mic 7.76 1.11 4699 1.39 $55.149\pm 0.047$ $<10^{-15}$ $8.69\pm 1.42$ 0.22
$10^{-4}$ V* BQ Hyi 9.12 0.72 4797 1.53 $18.430\pm 0.005$ $<10^{-15}$ $7.84\pm
0.52$ 0.41 $<10^{-15}$ V* BY Cet $\bigstar$ 9.60 0.77 5188 -0.17 $2.580\pm
0.0002$ $10^{-12}$ $2.47\pm 0.05$ 0.33 $<10^{-15}$ V* BZ Scl 9.68 0.64 5804
-0.05 $3.053\pm 0.0002$ $10^{-14}$ $14.17\pm 3.16$ 0.20 $<10^{-15}$ V* CF Oct
7.93 1.07 4881 1.62 $20.376\pm 0.010$ - - - - V* CF Scl 9.93 0.70 4835 1.40
$27.292\pm 0.012$ $<10^{-15}$ $20.04\pm 0.49$ 2.13 $<10^{-15}$ V* CF Tuc
$\maltese$ $\dagger$ 7.90 0.41 5157 0.80 $2.798$ - $7.41\pm 0.71$ 0.34
$<10^{-15}$ V* EI Eri 7.04 0.67 5513 0.59 - - $13.51\pm 4.31$ 0.50 $<10^{-15}$
V* EL Eri $\bigstar$ 8.19 1.10 4780 1.78 $49.614\pm 0.065$ $10^{-15}$
$18.77\pm 1.44$ 3.09 $<10^{-15}$ V* ER Eri 9.85 1.10 4666 0.69 $5.920\pm
0.001$ - - - - V* ES Eri 10.63 0.98 5078 -0.18 - - $3.20\pm 0.06$ 0.22
$<10^{-15}$ V* EZ Eri 10.17 1.03 4970 0.85 $8.824\pm 0.001$ $<10^{-15}$
$9.67\pm 0.70$ 0.28 $<10^{-15}$ V* FF Oct - 4462 0.18 $3.114\pm 0.0002$
$<10^{-15}$ $15.26\pm 11.32$ 0.49 $10^{-5}$ V* GX Lib 7.35 1.04 4836 1.36
$11.139\pm 0.001$ $<10^{-15}$ $8.69\pm 0.73$ 0.35 $<10^{-15}$ V* HU Vir 8.71
0.98 4517 0.74 $10.438\pm 0.002$ - - - - V* IL Hya $\bigstar$ 7.37 1.01 4856
1.23 $12.755\pm 0.003$ $<10^{-15}$ $13.41\pm 2.01$ 0.72 $<10^{-15}$ V* IN Vel
$\bigstar$ 9.08 1.18 4569 1.39 $62.611\pm 0.068$ $<10^{-15}$ $13.62\pm 0.51$
0.99 $<10^{-15}$ V* IN Vir 9.13 1.20 4436 0.75 $8.129\pm 0.001$ - - - - V* IR
Eri $\dagger$ 8.45 0.85 5296 0.02 $8.050$ - $2.06\pm 0.05$ 0.10 $10^{-8}$ V*
IS Vir $\dagger$ 8.43 1.07 4720 1.61 $23.500$ - $4.52\pm 0.10$ 0.52
$<10^{-15}$ V* LO Eri $\bigstar$ 10.76 0.89 5105 0.74 $9.318\pm 0.001$
$<10^{-15}$ $7.42\pm 0.73$ 0.19 $10^{-10}$ V* LS TrA $\bigstar$ 8.14 1.04 4735
1.22 $44.997\pm 0.041$ $<10^{-15}$ $8.25\pm 0.20$ 0.69 $<10^{-15}$ V* LU Hya
7.35 0.95 4999 0.47 $37.474\pm 0.050$ $10^{-10}$ $6.77\pm 0.71$ 0.11 $10^{-6}$
V* LZ Vel $\bigstar$ 7.19 1.27 4420 3.39 $92.791\pm 0.306$ $<10^{-15}$
$5.14\pm 0.05$ 0.41 $<10^{-15}$ V* NR Lib 11.34 0.93 4571 0.30 $2.683\pm
0.0001$ - - - - V* QQ Lib $\dagger$ 11.89 0.56 5051 -0.64 $0.577$ - $9.86\pm
0.40$ 0.84 $<10^{-15}$ V* QY Lib 10.41 0.81 5245 0.88 $1.050\pm 0.00002$
$<10^{-15}$ $4.57\pm 0.21$ 0.16 $<10^{-15}$ V* RV Lib $\dagger$ 9.17 1.09 4708
1.41 $10.721$ - - - - V* RZ Eri $\dagger$ 7.88 0.65 5324 1.49 $39.282$ - - - -
V* SZ Pic 7.91 0.75 5089 1.39 $4.988\pm 0.001$ $<10^{-15}$ $5.30\pm 0.17$ 0.30
$10^{-4}$ V* TW Lep 7.47 1.05 4805 1.71 $27.752\pm 0.025$ - - - - V* TX Pic
6.10 1.16 4559 2.13 $20.914\pm 0.033$ - - - - V* TY Col 9.60 0.68 5603 -0.14
$1.363\pm 0.0001$ $10^{-6}$ $10.64\pm 0.83$ 0.37 $<10^{-15}$ V* TY Pic
$\bigstar$ 7.70 0.99 4723 2.18 $49.378\pm 0.037$ $<10^{-15}$ $9.18\pm 0.51$
0.65 $<10^{-15}$ V* TY Pyx $\dagger$ 6.87 0.69 5669 0.67 $3.199$ - - - - V* TZ
Col 9.08 0.59 5907 0.26 $2.843\pm 0.0003$ - - - - V* TZ Pic 7.74 1.05 4673
1.34 $13.839\pm 0.008$ $10^{-5}$ $12.50\pm 0.35$ 0.78 $<10^{-15}$ V* UU Lep
6.94 1.11 4674 1.88 - - $5.36\pm 0.21$ 0.31 $<10^{-15}$ V* UV For $\bigstar$
8.06 0.99 4814 0.97 $66.447\pm 0.135$ $10^{-11}$ $8.54\pm 0.23$ 0.71
$<10^{-15}$ V* UX Col 10.59 1.03 5076 - $0.970\pm 0.00002$ $<10^{-15}$
$11.35\pm 1.20$ 0.33 $<10^{-15}$ V* UX For 8.06 0.72 5281 -0.04 $22.035\pm
0.016$ $10^{-7}$ $8.93\pm 0.31$ 0.42 $<10^{-15}$ V* UY For $\bigstar$ 8.25
1.15 4541 1.98 $16.144\pm 0.010$ $10^{-9}$ $8.51\pm 0.42$ 0.20 $<10^{-15}$ V*
V1017 Sco $\bigstar$ 7.99 1.16 4896 2.06 $66.356\pm 0.152$ $<10^{-15}$
$13.42\pm 0.23$ 1.17 $<10^{-15}$ V* V1257 Cen $\bigstar$ 11.68 1.01 4308 -0.48
$2.761\pm 0.0003$ $<10^{-15}$ $18.14\pm 0.91$ 1.05 $<10^{-15}$ V* V1265 Cen
11.01 - 4361 0.86 $3.533\pm 0.0001$ - - - - V* V1335 Cen 10.06 0.59 5863 0.26
$1.695\pm 0.0001$ $10^{-11}$ $7.35\pm 0.16$ 0.20 $<10^{-15}$ V* V1355 Ori
$\bigstar$ 9.19 0.86 4856 0.62 $3.863\pm 0.0002$ $<10^{-15}$ $10.08\pm 1.30$
0.66 $<10^{-15}$ V* V2253 Oph $\bigstar$ 8.49 1.17 4767 1.66 $21.544\pm 0.009$
$<10^{-15}$ $19.37\pm 2.27$ 0.50 $<10^{-15}$ V* V344 Pup 6.89 1.06 4778 1.45
$11.757\pm 0.001$ - - - - V* V354 Lib $\bigstar$ 11.34 1.23 4439 0.37
$5.623\pm 0.0004$ $<10^{-15}$ $13.30\pm 1.36$ 1.19 $<10^{-15}$

(continued)

ID $V$ $B-V$ $T_{\mathrm{eff}}$ $\log L$ $P_{\mathrm{rot}}$ FAP
($P_{\mathrm{rot}}$) $P_{\mathrm{cyc}}$ $A_{\mathrm{cyc}}$ FAP
($P_{\mathrm{cyc}}$) [K] [$L_{\odot}$] [d] [yr] [%] V* V356 Pup $\maltese$
$\dagger$ 8.21 1.21 4445 2.12 $37.306$ - $4.20\pm 0.08$ 0.30 $10^{-13}$ V*
V4091 Sgr 8.45 1.16 4527 1.56 $16.932\pm 0.011$ - - - - V* V4138 Sgr
$\bigstar$ 6.74 1.02 4713 1.18 $61.933\pm 0.067$ $<10^{-15}$ $5.35\pm 0.09$
0.92 $<10^{-15}$ V* V4139 Sgr 8.45 1.17 4363 1.66 $44.828\pm 0.018$ - - - - V*
V414 Hya $\bigstar$ 8.90 1.06 4586 1.39 $18.750\pm 0.004$ $<10^{-15}$ $5.51\pm
0.31$ 0.41 $10^{-12}$ V* V592 Pup 7.86 0.61 6023 0.45 $1.967\pm 0.0001$ - - -
- V* V764 Cen 8.91 1.37 4541 1.52 $22.519\pm 0.019$ $<10^{-15}$ $12.43\pm
0.53$ 1.25 $<10^{-15}$ V* V789 Mon 9.39 0.96 4648 -0.50 $1.401\pm 0.0001$
$<10^{-15}$ $13.47\pm 1.65$ 0.53 $<10^{-15}$ V* V829 Cen 7.84 0.93 4614 1.32
$11.707\pm 0.003$ $<10^{-15}$ $10.30\pm 0.30$ 0.41 $<10^{-15}$ V* V841 Cen
$\bigstar$ 8.57 1.06 4588 0.60 $5.997\pm 0.001$ $<10^{-15}$ $4.32\pm 0.52$
0.23 $10^{-4}$ V* V851 Cen 7.80 0.94 4700 0.74 $12.225\pm 0.007$ $10^{-9}$
$13.60\pm 0.17$ 1.33 $<10^{-15}$ V* V858 Cen 10.45 0.88 4939 -0.41 $1.037\pm
0.00002$ $<10^{-15}$ $20.05\pm 0.96$ 0.91 $<10^{-15}$ V* V965 Sco $\bigstar$
8.57 0.95 4707 1.81 $30.544\pm 0.025$ $<10^{-15}$ $4.51\pm 0.04$ 0.43
$<10^{-15}$ V* V991 Sco $\dagger$ 9.69 0.68 5498 0.28 $3.300$ - $5.97\pm 0.17$
0.23 $<10^{-15}$ V* VV Mon $\dagger$ 9.40 0.81 4978 1.05 $6.051$ - - - - V* VX
Pyx 6.37 0.95 5046 1.77 - - $9.43\pm 0.48$ 0.33 $<10^{-15}$ V* YZ Men
$\bigstar$ 7.77 1.08 4594 1.50 $19.216\pm 0.006$ $<10^{-15}$ $16.99\pm 2.38$
1.31 $<10^{-15}$


# Agreement Tracking for Multi-Issue Negotiation Dialogues

Amogh Mannekote
University of Florida
<EMAIL_ADDRESS>
&Bonnie J. Dorr
University of Florida
<EMAIL_ADDRESS>
&Kristy Elizabeth Boyer
University of Florida
<EMAIL_ADDRESS>Amogh Mannekote,1 Bonnie J. Dorr,1 Kristy Elizabeth Boyer1
1University of Florida Correspondence: {amogh.mannekote, bonniejdorr,
<EMAIL_ADDRESS>
###### Abstract

Automated negotiation support systems aim to help human negotiators reach more
favorable outcomes in multi-issue negotiations (e.g., an employer and a
candidate negotiating over issues such as salary, hours, and promotions before
a job offer). To be successful, these systems must accurately track agreements
reached by participants in real-time. Existing approaches either focus on
task-oriented dialogues or produce unstructured outputs, rendering them
unsuitable for this objective. Our work introduces the novel task of agreement
tracking for two-party multi-issue negotiations, which requires continuous
monitoring of agreements within a structured state space. To address the
scarcity of annotated corpora with realistic multi-issue negotiation
dialogues, we use GPT-3 to build GPT-Negochat, a synthesized dataset that we
make publicly available. We present a strong initial baseline for our task by
transfer-learning a T5 model trained on the MultiWOZ 2.4 corpus. Pre-training
T5-small and T5-base on MultiWOZ 2.4’s DST task enhances results by 21% and 9%
respectively over training solely on GPT-Negochat. We validate our method’s
sample-efficiency via smaller training subset experiments. By releasing GPT-
Negochat and our baseline models, we aim to encourage further research in
multi-issue negotiation dialogue agreement tracking.

##  1 Introduction

Negotiation dialogues are common in both adversarial and collaborative
contexts. However, a long line of foundational research in psychology and
business has established that in general, humans tend to be poor negotiators,
often failing to maximize favorable outcomes. Consequently, developing
capabilities to build automated systems that can support human negotiators has
been an active area of research Prakken (2006); Wang et al. (2019).

We focus specifically on multi-issue negotiation dialogues,111Also called
“integrative” negotiation Zhan et al. (2022). where participants negotiate
over more than one issue, e.g., salary and hours for a job, or location and
time for a meeting. These type of dialogues arise in a wide range of real-life
situations that span the adversarial-cooperative spectrum. For example, most
job negotiations fall on the adversarial end of the spectrum, since the two
parties often have opposing objectives. On the other hand, planning-based
meetings are characterized as more cooperative in that participants
collaborate on a shared plan to achieve a common goal. Regardless of the
specific real-world context for the multi-issue negotiation, the ability to
track agreements in real-time is a mission-critical capability for any system
aiming to effectively support the participants.

Previous work has examined related tasks such as dialogue summarization and
action-item generation at the end of a dialogue. Our work is the first to
investigate the task of agreement tracking for multi-issue negotiation
dialogues over a structured state space (i.e. an “ontology”). Agreement
tracking requires reasoning over multiple turns in a dialogue, in contrast to
single utterance-level natural language understanding (NLU).

Agreement tracking also differs from dialogue state tracking (DST) in that it
necessitates explicit agreement from both interlocutors in contrast to DST’s
estimation of the goals of a single interlocutor. However, it is not at all
obvious how one leverages existing task formulations (including DST), model
designs, and training objectives for agreement tracking without manually
collecting and labelling a substantial amount of in-domain data. We
demonstrate a deficiency in existing methods for three closely-related tasks:
building negotiation dialogue agents, summarization of meetings, and dialogue
state tracking for task-oriented dialogues.

  1. 1.

Negotiation Dialogue Agents: Existing research on automated negotiation
systems focuses on strategic aspects, e.g., undervaluing or appealing to the
opposing party Zhou et al. (2019); He et al. (2018); Keizer et al. (2017).
This is orthogonal to the problem of tracking agreements. End-to-end
negotiators, which directly generate responses He et al. (2017), do not
generate intermediate structured representations of the dialogue state. A
limited number of studies have investigated language understanding in this
context, but have done so only at the level of single utterances Chawla et al.
(2021); Yamaguchi et al. (2021); Frampton et al. (2009). Agreement tracking,
in contrast, necessitates reasoning across multiple turns since acceptances
and rejections can only be understood in reference to offers made in previous
turns.

  2. 2.

Meeting Summarization: The release of the AMI Meeting Corpus Mccowan et al.
(2005) has stimulated significant research on meeting and dialogue
summarization Gliwa et al. (2019); Wang and Cardie (2013); Rennard et al.
(2022); Kryscinski et al. (2020); Liu et al. (2019). However, meeting
summarization differs from agreement tracking in two crucial ways. First,
summarization is applied at the end of a dialogue, whereas tracking takes
place continuously. Second, summarization focuses on generating a human-
readable output of the key decisions made during the meetings, whereas the
tracking task generates a structured representation of the agreements based on
a fixed ontology, and this representation serves as input to downstream
modules.

  3. 3.

Dialogue State Tracking (DST): The goal of DST in task-oriented dialogue is to
extract users’ goals by inferring the values for a predefined set of keys
(commonly referred to as “slots”). As we shall see later, we re-purpose this
notion of a slot to track agreement over a single issue in our multi-issue
negotiation dialogue setup. Dialogue state tracking has been a long-standing
task in task-oriented dialogue systems literature Williams et al. (2016);
Jacqmin et al. (2022); Zhao et al. (2021); Rastogi et al. (2020). Although
there has been extensive work in recent years to improve the ability of task-
oriented DST models to generalize to unseen domains with zero-shot Lin et al.
(2021b); Campagna et al. (2020) and few-shot Wu et al. (2019) models, these
are still limited to form-filling dialogues (e.g., restaurant reservation and
hotel booking). Moreover, these models are challenged by agreement tracking,
as it requires explicit agreement from both interlocutors, unlike DST that
estimate the goals of a single interlocutor. Hence, the question of how
effectively state-of-the-art DST techniques can be used for state tracking in
vastly different dialogue paradigms (such as negotiation) remains open-ended.

To establish a strong foundation for future modeling efforts in agreement
tracking, we introduce a transfer-learning approach that involves pre-training
a T5 model Raffel et al. (2020) using the MultiWOZ 2.4 corpus. Subsequently,
we fine-tune the model on the GPT-Negochat corpus, which we introduce in
Section 2, for the agreement tracking task. Our approach outperforms a T5
model that is fine-tuned only on GPT-Negochat (without the MultiWOZ corpus).
Additionally, we investigate the sample-efficiency of our model in low-
resource settings by experimenting with various fractional splits of our
training data. Sample efficiency (ability to learn from a small number of
demonstrations) is a key concern for our task since it is expensive to collect
a lot of annotated dialogue samples for a new domain. We assess slot
prediction accuracy of all models using Joint Slot Accuracy and Joint F1
Score. Our findings illustrate that incorporating a pre-training phase, using
T5-small and T5-base on MultiWOZ 2.4’s DST task, improves performance by 21%
and 9% respectively (in absolute percentage points), compared to exclusively
training on GPT-Negochat.

The rest of the paper is organized as follows. Section 2 describes the
creation and characteristics of GPT-Negochat, the dataset used for our
experiments. Section 3 formally defines the task of agreement tracking, the
tokenization scheme, the training objective, and the evaluation metrics used
in this study. Sections 4 and 5 describe our experimental procedure and
results, respectively. Section 6 presents the related work. Finally, Section 7
talks about the limitations of our work.

##  2 GPT-Negochat: A Multi-Issue Negotiation Dialogue Corpus

The corpus selected for our experiments must satisfy two criteria: inclusion
of multi-issue negotiation dialogues and availability of ground-truth
annotations for agreements at each dialogue turn. Two publicly-available
corpora meet these requirements: the Negochat corpus Konovalov et al. (2016)
and the Metalogue corpus for multi-issue bargaining dialogues Petukhova et al.
(2016). However, we ruled out Metalogue (due to paywall restrictions) and
conduct experiments solely on the Negochat corpus, which is freely accessible
and imposes no copyright limitations on usage.

The Negochat corpus Konovalov et al. (2016) contains 105 crowd-sourced
dialogues (1484 utterances) between an Employer and a Candidate who negotiate
over issues surrounding a job offer such as salary, role, and working hours
(the complete ontology of the Negochat corpus is outlined in Table 1). While
the Employer-side of the conversations is supplied by human participants on
Amazon M-Turk,222https://www.mturk.com/ an automated agent plays the role of
the Candidate. A second human “wizard” is responsible for acting as a live
Natural Language Understanding (NLU) module that parses the Employers’
utterances into a structured semantic representation. This parsed input is
then processed by an automated dialogue manager, which generates a response
using a template-based NLG module.

Slot Type |  Possible Values
---|---
Working Hours |  8 hours, 9 hours, 10 hours
Pension Fund |  10%, 20%
Job Description |  Programmer, Team Manager, Project Manager
Promotion Possibilities |  Slow promotion track, Fast promotion track
Salary |  90k USD, 60k USD, 120k USD
Leased Car |  With leased car, Without leased car, No agreement

Table 1: Ontology of the GPT-Negochat corpus.

Due to limited lexical diversity in the Candidate-side utterances of the
Negochat corpus (see Table 2), attributed to its basic template-based NLG
module, we employed GPT-3 to enrich and naturalize the corpus Brown et al.
(2020). We used prompt templates (Appendix A) to rephrase the utterances, with
the revised version’s efficacy evaluated by two sets of human annotations on a
random 10% dataset slice, adjudicating any discrepancies.

Out of the utterance pairs presented to the annotators, the rephrased
utterances of GPT-Negochat were reported as being more realistic in 78.4% of
the cases, and in 7% of the cases, both the original and rephrased utterances
were rated as equally realistic. The utterance pairs were deemed to carry the
same meaning in the context of the previous turn in 91.4% of the annotated
instances, attesting to the effectiveness of the updated GPT-Negochat corpus.
The full text of the instructions presented to the annotators are shown in
Appendix E.

Despite being smaller than some multi-domain DST datasets, the resulting
dataset provides a valuable benchmark for agreement tracking models in
negotiations, especially taking into consideration that constructing a high-
quality, labeled dataset is timeconsuming. Dialogue comparisons between the
original Negochat and GPT-Negochat are provided in Table 2 and Appendix D. We
name this revised version of the Negochat corpus as “GPT-Negochat” and make it
publicly available for use by the broader research community.333Hidden for
review

Speaker |  Original Utterance |  Rephrased Utterance
---|---|---
Candidate |  I would like a position of project manager |  I’m interested in a position as a project manager.
Employer |  are you sure you wouldnt rather be a programmer? |  Are you sure that’s the job you’re looking for? Wouldn’t you prefer to be a programmer?
Candidate |  I refuse programmer position. I am expecting a position of project manager |  I’m sorry, but I’m not interested in the programmer position. I’m looking for a project manager role instead.
Employer |  what about Quality assurance? |  What about a Quality Assurance role?
Candidate |  I reject qa position. I would like a position of project manager |  No, thank you. I’m only interested in a project manager position.

Table 2: An excerpt from a dialogue from the Negochat corpus alongside its
rephrased counterpart from GPT-Negochat.

##  3 Preliminaries

This section provides formal definitions for notations and describes the input
and output representations used in our model.

###  3.1 Notations

We consider a negotiation dialogue between two participants taking alternating
turns with utterances $\\{T_{1},\dots,T_{N}\\}$. To maintain a strict
alternating turn structure, consecutive utterances made by the same
participant are merged into a single utterance; thus, for each $T_{i}$ the odd
$i$’s represent one speaker, and the even $i$’s represent the other. The
negotiation focuses on a predefined set of issues, i.e., the domain’s
“ontology,” in accordance with the DST framework. Each issue is associated
with one of $M$ slots $\\{s_{1},\dots,s_{M}\\}$ from our ontology, for example
slot $s_{1}$ could refer to Salary, slot $s_{2}$ to Working Hours, and so on.

At each dialogue turn $t$, the agreement state $A_{t}$ is defined as a slot-
value mapping between each issue in the ontology and the corresponding value
that both participants have agreed upon for it. We denote this slot-value
relationship in the agreement state as $A_{t}(s_{j})=v$ (where $v=\epsilon$
indicates that no agreement has been reached thus far).

Finally, we associate each utterance $T_{t}$ with a list of (one or more)
dialogue acts, $D_{t}=[d_{t}^{1},\dots,d_{t}^{|d_{t}|}]$, where $d_{t}^{i}$ is
one of $\\{\textsc{Offer},\textsc{Accept},\textsc{Reject},\textsc{Other}\\}$.
These dialogue acts, defined as stated below, are important inputs for our
rule-based algorithm defined in Section 4.2.

  1. 1.

Offer: When making an offer, a participant puts forth one or more slot-value
pairs for consideration by the other participant. We formally represent an
offer as a list of these key-value pairs:
$O(\\{(s_{1},v_{1}),\dots,(s_{n_{i}},v_{n_{i}}))\\}$. We constrain each issue
to a single slot value.

  2. 2.

Accept and Reject: While accepting or rejecting an offer, a participant can do
so either partially or completely. As an example of partial acceptance, if the
Candidate demands an 8-hour workday with a pension of 20%, the Employer might
choose to accept the 8-hour workday, but not the 20% pension.

  3. 3.

Other: Utterances of other types (e.g., greetings) are categorized under the
Other label as they have no direct effect on the agreement state.

Conversation | Agreement State
---|---
E: No company car included? | No agreements
C: Right, no car. Let’s move on. I was hoping for a pension of 20%. |  Company Car: No
E: If you work 10 hours, I can offer you a 20% pension - what do you think? |  Company Car: No
C: No thanks. I’m expecting an 8-hour workday and I want a 10% pension |  Company Car: No
E: How about a salary of 60K if you agree to the 10% pension? |  Company Car: No
C: I’m sorry, but I’m looking for a salary of 120,000 and a pension of 20%. |  Company Car: No
E: What about offering you a fast promotion tract with a 90k salary? |  Company Car: No
C: No, I’m afraid that won’t work for me. |  Company Car: No
E: Would you be comfortable with a salary of 60 or 90k? |  Company Car: No
C: 90,000 sounds good to me. Is there anything else we need to discuss? |  |  Company Car: No
---
Salary: 90,000
Table 3: An excerpt of a dialogue from GPT-Negochat with turn-level agreement
annotations. C and E stand for Candidate and Employer respectively.

###  3.2 Representing Dialogue Context

Transformer-based generative language models, such as those introduced by
Vaswani et al. (2017), have commonly been used for representing dialogue
context in dialogue tasks. This typically involves concatenating utterances
within a context window. Dialogue state tracking (DST) models have followed
this practice.

Full-history based DST models consider the entire dialogue up to a turn as
their context Hosseini-Asl et al. (2020); Feng et al. (2021b); Peng et al.
(2021). However, as the number of utterances increases beyond a certain point,
these models struggle to retain information. Recursive approaches to DST
combat this issue by considering a small window of utterances (typically one
to four) as their dialogue context Lin et al. (2020); Budzianowski and Vulić
(2019); Lei et al. (2018). Rather than predicting the entire dialogue state
from scratch at every turn, these approaches use the previously predicted
dialogue state as a starting point. For our experiments, we opt for a
recursive-based approach due to the relatively high average turn-length of
34.27 GPT-Negochat, which exceeds that of most task-oriented dialogue corpora.

###  3.3 Levenshtein Belief Spans

In task-oriented dialogue, a belief refers to the dialogue system’s
understanding of the user’s goal at a given dialogue turn. This belief is
continuously updated based on the user’s incoming utterances. A belief span is
a text-based representation of the system’s belief. For example, a belief span
such as “cuisine = Chinese; area = center” may indicate that a user is seeking
a downtown Chinese restaurant. Recent DST approaches adopt conditional text
generation models to generate belief spans corresponding to the updated
dialogue state. This allows for easier expansion to new slot types and values
without complete model retraining.

We employ the Levenshtein Belief Spans (Levs) tokenization method Lin et al.
(2020). This approach, which we term A-Lev, combines a domain prefix (either
[gpt-negochat] or [multiwoz]) with a sequence of edit operations. Edit
operations include insertion, deletion, and substitution. Although GPT-
Negochat focuses on a single domain (job offer negotiation), we apply a common
domain prefix across all samples. A more detailed explanation of the Lev
construction method can be found in the original paper Lin et al. (2020).
Figure 1 shows a tokenized training example used to train our agreement
tracking models.

##  4 Experiments

We present a rule-based reference model that serves as the basis for our main
results. We then introduce our experimental setup, including our choice of
backbone model, rule-based baseline model, training objectives, and evaluation
metrics.

###  4.1 Backbone Model (T5)

We choose T5 Raffel et al. (2020) as our backbone model. T5 is a text-to-text
Transformer model consisting of a multi-layer encoder and decoder pre-trained
on autoregressive language modeling, text denoising, and deshuffling
objectives. Its text-based input-output representation enables broad NLP task
applicability without architectural changes. Table 4 enumerates the
parameters, layers, embedding dimension, and attention heads for each T5
variant. However, due to computational constraints, we restrict our
experiments to the T5-small and T5-base versions. While we recognize the
benefits of exploring other LLMs, our focus presently is to set T5 as a
benchmark for this task, intending to evaluate and compare with other models
in future research.

Model Parameters # layers d_model # heads Small 60M 6 512 8 Base 220M 12 768
12

Table 4: Properties of the Small and Base variants of the T5 model.
$d\\_model$ and # heads refer to the dimensionality of the model’s hidden
state and the number of attention heads respectively. Figure 1: This figure
shows the tokenization schemes for both Gen (left) and the Clf (right) tasks.
The Gen task input includes task prefix (green), dataset prefix (blue), belief
span representation (red), and concatenated utterances within a window size
(yellow). Its output contains the dataset prefix (blue) and the updated
Levenshtein belief span (dark green). The input in the Clf scheme is mostly
identical to that of Gen, except for its unique task-prefix and an appended
candidate belief span. Its output is simply “yes” or a “no”. Alternating spans
are underlined for visual clarity.

###  4.2 Rule-Based Agreement Tracker

We develop a rule-based reference model, Oracle-Tracker, with oracle access to
turn-level ground truth annotations to contextualize our transfer-learning
model’s results and assess the multi-turn reasoning difficulty in agreement
tracking. This model focuses on tracking agreements across multiple turns,
assuming known dialogue acts (Offer, Accept, Reject, and Other) and entities.

The model addresses two subtasks: (1) natural language understanding (NLU) at
the utterance level, where it classifies dialogue acts and extracts slot-value
pairs; and (2) tracking agreements over multiple turns. In designing this
rule-based reference model, we focus on the demonstrably more difficult second
task that involves multi-turn reasoning as described below.

To quantify the relative simplicity of the single-turn NLU problem, we train a
T5-base model on just 10 GPT-Negochat dialogues to classify the dialogue acts
and extract corresponding slot-value pairs from each utterance. The model
achieves a correct prediction rate of 74.33% on the test set. In contrast, our
top-performing model for agreement tracking, also trained on 10 dialogues,
manages only a 20% joint slot accuracy (refer to Section 5).

###  4.3 Transfer Learning from Dialogue State Tracking

Tracking information across dialogue turns is a shared goal of agreement
tracking and dialogue state tracking, despite differing focus areas
(agreements vs user goals). To leverage the abundance of publicly annotated
data for dialogue state tracking, we choose to pre-train our model on this
task. This pre-training equips the model with transferable representations for
this general tracking problem, enabling efficient adaptation to agreement
tracking. In our experiments, we compare joint slot accuracy results of two T5
models to assess transfer efficiency: one solely fine-tuned for agreement
tracking, the other sequentially fine-tuned for dialogue state tracking and
agreement tracking.

Figure 2: Results of Agreement Tracking models.

####  4.3.1 Multi-Task Training

To address inaccuracies in the agreement tracking task, we borrow from multi-
task training with contrastive-learning objectives in other dialogue-related
tasks, e.g., summarization and state tracking Chen et al. (2021); Cao and Wang
(2021); Tang et al. (2022). Our approach penalizes incorrect outputs by
separating them in the model’s latent space, and the model then learns to
discriminate negatively-sampled A-Levs from the correct one.

Since we use a T5 model, a text-to-text paradigm, we implement the contrastive
learning objective by incorporating an additional tokenization scheme during
training. The main tokenization scheme teaches the model to predict the
correct Lev given the previous set of agreements and the dialogue context
(referred to as Gen). We also incorporate an auxiliary tokenization scheme to
meet our contrastive learning goals, providing additional training signals
from which the model learns discriminative representations (referred to as
Clf). Here, we describe these two training tasks, along with their respective
tokenization schemes. (Also, see examples in Figure 1.)

  1. 1.

Gen: Our primary task focuses on conditional generation, where the model is
trained to generate Levenshtein belief spans for each turn while being
conditioned on: 1) the previous agreement state, and 2) the dialogue context.

$\mathcal{L}_{{\textsc{Gen}}}=-log\ P(A_{t}|C_{t},A_{t-1})$

  2. 2.

Gen + Clf In our multi-task setup, we supplement the primary task of agreement
state prediction (Gen) with an auxiliary task that explicitly trains the model
to discern between correct belief spans and negatively sampled incorrect
outputs.

Clf is designed as a binary classification task that takes three inputs: 1)
the set of agreements as of the previous turn, 2) the dialogue context, and 3)
an A-Lev, which is randomly assigned as either the correct output or a
negatively sampled variant based on the ontology. The expected output for this
task is a boolean, either “yes” to indicate that the A-Lev is indeed the
correct output or “no”, to indicate that theLev is negatively sampled.

$\mathcal{L}_{{\textsc{Gen}}+{\textsc{Clf}}}=-log\ P(A_{t}|C_{t},A_{t-1})\\\
-log\ P(Y_{t}|C_{t},A^{\prime}_{t},A_{t-1})$

where $A^{\prime}_{t}$ represents a randomly sampled Lev, which can either be
a distractor or the correct answer. $Y_{t}$ is the label of our binary
classification task (the binary label is tokenized in the form of “yes” or
“no”).

###  4.4 Evaluation Metrics

We assess our models using Joint Slot Accuracy and Joint F1 Score, standard
dialogue state tracking metrics. Joint Slot Accuracy compares predicted
agreements to ground truth, requiring an exact match. Joint F1 Score, a more
lenient metric, calculates precision and recall instead of using binary 0 or 1
for mispredictions.

###  4.5 Training Setup

We implement our models using HuggingFace Transformers Wolf et al. (2020) and
PyTorch Lightning444https://github.com/Lightning-AI/lightning. During the
fine-tuning process, we use a batch size of 32 and apply early stopping based
on the performance on a separate validation set. We employ the Adam optimizer
Kingma and Ba (2014) with the learning rate set to $6\times 10^{-4}$. To
ensure reliable estimates, we conduct a 3-fold cross-validation scheme,
averaging the results across the folds. Since sample efficiency is one of our
key concerns, we run all our main experiments using different proportions of
the training data: 10%, 20%, 30%, 40%, 50%, 75%, and 100%. We report our
hyperparameter search and best-found hyperparameter values in Appendix C.

##  5 Results

Table 2 presents the summary of results from all the models. We elaborate on
the results and make observations below.

###  5.1 Rule-Based Reference Model

Our rule-based algorithm, Oracle-Tracker, achieves a Joint Slot Accuracy of
0.5. This indicates that deducing agreements solely from utterance-level
dialogue acts and slot-value pairs is a complex task.

###  5.2 Transfer Learning from Dialogue State Tracking

Fine-tuning T5-small and T5-base on MultiWOZ2.4 before GPT-Negochat improves
Joint Slot Accuracy and Joint F1 score compared to fine-tuning on GPT-Negochat
alone. Training on MultiWOZ allows the model to specialize in dialogue-related
tasks, like tracking information across turns.

##### Multi-Task Training

The use of the auxiliary binary classification objective (Gen \+ Neg) does not
lead to a significant performance improvement as compared training with the
generation (Gen) objective alone. This result suggests that the majority of
errors made by our model are false negatives, whereas the Neg objective is
better suited to tackle the problem of false positives, or hallucinations.
Further experiments with different contrastive learning objectives and
negative sampling strategies could shed light on this hypothesis.

##### Sample Efficiency

Figure 3 illustrates the trend of Joint Slot Accuracy for models trained on
different proportions of the dataset using a three-fold split. The larger
T5-base model outperforms T5-small in low-resource settings. However, there is
no distinct advantage of T5-base over T5-small as the training split
approaches 100%.

Figure 3: This plot shows the Joint Accuracy trend of four different models
when trained with 10, 20, 30, 40, 50, 75, and 100 percentages of the training
data. We observe positive effects on the Joint Accuracy from both model size
(T5-base is larger than T5-small) as well as an additional step of fine-tuning
over DST on MultiWOZ before training it on GPT-Negochat.

Our findings demonstrate that agreement tracking, although categorized as a
“dialogue state tracking” task, cannot be adequately addressed by directly
applying existing models trained on task-oriented dialogue datasets. Instead,
it suggests the need for specialized techniques tailored specifically to this
task.

##  6 Related Work

Prior to the deep-learning era, research on agreement modeling from meeting
transcripts as discussed by Hillard et al. (2003) and Galley et al. (2004),
focuses on classifying dialogue acts using handcrafted features rather than
tracking slot values. Bui et al. (2009) introduces a labeling scheme
encompassing three dialogue acts: issue, resolution, and agreement. Frampton
et al. (2009) investigates the impact of context window size on agreement-
tracking performance. However, their model is not directly applicable to our
setting, as it relies on turn-level dialogue act annotations. In contrast, our
method requires only labels about the agreement state, making it more
efficient and practical for the task at hand.

Recent work focuses on natural language summaries of dialogues Feng et al.
(2021a); Gliwa et al. (2019) with factual correctness improvements potentially
benefiting state tracking tasks Zhao et al. (2021). Jia et al. (2022) group
these methods into: (1) pre-processed feature injection Park et al. (2022),
(2) design of self-supervised objectives Liu and Chen (2021), and (3) using
additional data Liu et al. (2021); Park et al. (2022).

Finally, while Transformer-based approaches have shown advancements in
dialogue state tracking (DST) for task-oriented dialogues Lee et al. (2021);
Peng et al. (2021); Lin et al. (2021b, a), their efficacy beyond task-oriented
dialogues, such as collaborative and negotiation dialogues, remains unproven.

##  7 Limitations and Future Work

Although GPT-Negochat features a smaller ontology compared to some multi-
domain DST datasets, its focus on a limited scope allows us to tackle the
unique challenges posed by dynamic negotiation dialogues. Future work will
seek to extend this approach to larger, multi-domain datasets. Due to
computational constraints, we did not experiment with larger T5 models or
instruction-tuned variants such as FLAN-T5 Chung et al. (2022). Lastly, while
GPT-Negochat enhances the linguistic diversity of the original Negochat
corpus, acquiring a fully organic multi-issue negotiation dialogue dataset
with turn-level agreement annotations would provide a more realistic
environment for evaluating different agreement tracking methods.

##  8 Conclusion

This study introduces a novel task, namely agreement tracking for multi-issue
negotiation dialogues, and formulates it as a variant of dialogue state
tracking. We observe that fine-tuning a language model on the dialogue state
tracking task for task-oriented dialogues yields improved performance over our
naive baseline. The significance of state tracking extends beyond form-filling
dialogues, emphasizing the ongoing need for research to improve the
transferability and sample efficiency of dialogue state tracking models to
other dialogue paradigms.

## Broader Impact and Ethical Considerations

This research introduces the task for tracking agreements in multi-issue
negotiation dialogues, offering potential advancements in promote automated
systems that support negotiation dialogues between human participants. A
robust negotiation support system can address power imbalances and prevent
exploitation or disadvantage for participants who may be in a weaker position.
Even though the agreement tracker focuses on a specific task, it may still
involve handling sensitive data related to the negotiation process.
Researchers must prioritize proper data anonymization and take measures to
protect the privacy and confidentiality of participants’ information.

## References

  * Brown et al. (2020) Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel Ziegler, Jeffrey Wu, Clemens Winter, Chris Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei. 2020.  Language models are few-shot learners.
  * Budzianowski and Vulić (2019) Paweł Budzianowski and Ivan Vulić. 2019.  Hello, it’s GPT-2 - how can I help you? towards the use of pretrained language models for task-oriented dialogue systems.  In _Proceedings of the 3rd Workshop on Neural Generation and Translation_ , pages 15–22, Hong Kong. Association for Computational Linguistics.
  * Bui et al. (2009) Trung Bui, Matthew Frampton, John Dowding, and Stanley Peters. 2009.  Extracting decisions from multi-party dialogue using directed graphical models and semantic similarity.  In _Proceedings of the SIGDIAL 2009 Conference_ , pages 235–243, London, UK. Association for Computational Linguistics.
  * Campagna et al. (2020) Giovanni Campagna, Agata Foryciarz, M. Moradshahi, and Monica S. Lam. 2020.  Zero-shot transfer learning with synthesized data for multi-domain dialogue state tracking.  In _Annual Meeting of the Association for Computational Linguistics_.
  * Cao and Wang (2021) Shuyang Cao and Lu Wang. 2021.  CLIFF: contrastive learning for improving faithfulness and factuality in abstractive summarization.  _CoRR_ , abs/2109.09209.
  * Chawla et al. (2021) Kushal Chawla, Jaysa Ramirez, Rene Clever, Gale Lucas, Jonathan May, and Jonathan Gratch. 2021.  CaSiNo: A corpus of campsite negotiation dialogues for automatic negotiation systems.  In _Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 3167–3185, Online. Association for Computational Linguistics.
  * Chen et al. (2021) Sihao Chen, Fan Zhang, Kazoo Sone, and Dan Roth. 2021.  Improving faithfulness in abstractive summarization with contrast candidate generation and selection.  In _Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 5935–5941, Online. Association for Computational Linguistics.
  * Chung et al. (2022) Hyung Won Chung, Le Hou, Shayne Longpre, Barret Zoph, Yi Tay, William Fedus, Yunxuan Li, Xuezhi Wang, Mostafa Dehghani, Siddhartha Brahma, Albert Webson, Shixiang Shane Gu, Zhuyun Dai, Mirac Suzgun, Xinyun Chen, Aakanksha Chowdhery, Alex Castro-Ros, Marie Pellat, Kevin Robinson, Dasha Valter, Sharan Narang, Gaurav Mishra, Adams Yu, Vincent Zhao, Yanping Huang, Andrew Dai, Hongkun Yu, Slav Petrov, Ed H. Chi, Jeff Dean, Jacob Devlin, Adam Roberts, Denny Zhou, Quoc V. Le, and Jason Wei. 2022.  Scaling instruction-finetuned language models.
  * Feng et al. (2021a) Xiachong Feng, Xiaocheng Feng, and Bing Qin. 2021a.  A survey on dialogue summarization: Recent advances and new frontiers.
  * Feng et al. (2021b) Yue Feng, Yang Wang, and Hang Li. 2021b.  A sequence-to-sequence approach to dialogue state tracking.  In _Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)_ , pages 1714–1725, Online. Association for Computational Linguistics.
  * Frampton et al. (2009) Matthew Frampton, Jia Huang, Trung Bui, and Stanley Peters. 2009.  Real-time decision detection in multi-party dialogue.  In _Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing_ , pages 1133–1141, Singapore. Association for Computational Linguistics.
  * Galley et al. (2004) Michel Galley, Kathleen McKeown, Julia Hirschberg, and Elizabeth Shriberg. 2004\.  Identifying agreement and disagreement in conversational speech: Use of Bayesian networks to model pragmatic dependencies.  In _Proceedings of the 42nd Annual Meeting of the Association for Computational Linguistics (ACL-04)_ , pages 669–676, Barcelona, Spain.
  * Gliwa et al. (2019) Bogdan Gliwa, Iwona Mochol, Maciej Biesek, and Aleksander Wawer. 2019.  SAMSum corpus: A human-annotated dialogue dataset for abstractive summarization.  In _Proceedings of the 2nd Workshop on New Frontiers in Summarization_ , pages 70–79, Hong Kong, China. Association for Computational Linguistics.
  * He et al. (2017) He He, Anusha Balakrishnan, Mihail Eric, and Percy Liang. 2017.  Learning symmetric collaborative dialogue agents with dynamic knowledge graph embeddings.  In _Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 1766–1776, Vancouver, Canada. Association for Computational Linguistics.
  * He et al. (2018) He He, Derek Chen, Anusha Balakrishnan, and Percy Liang. 2018.  Decoupling strategy and generation in negotiation dialogues.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 2333–2343, Brussels, Belgium. Association for Computational Linguistics.
  * Hillard et al. (2003) Dustin Hillard, Mari Ostendorf, and Elizabeth Shriberg. 2003.  Detection of agreement vs. disagreement in meetings: Training with unlabeled data.  In _Companion Volume of the Proceedings of HLT-NAACL 2003 - Short Papers_ , pages 34–36.
  * Hosseini-Asl et al. (2020) Ehsan Hosseini-Asl, Bryan McCann, Chien-Sheng Wu, Semih Yavuz, and Richard Socher. 2020.  A simple language model for task-oriented dialogue.  _Advances in Neural Information Processing Systems_ , 33:20179–20191.
  * Jacqmin et al. (2022) Léo Jacqmin, Lina M. Rojas Barahona, and Benoit Favre. 2022.  “do you follow me?”: A survey of recent approaches in dialogue state tracking.  In _Proceedings of the 23rd Annual Meeting of the Special Interest Group on Discourse and Dialogue_ , pages 336–350, Edinburgh, UK. Association for Computational Linguistics.
  * Jia et al. (2022) Qi Jia, Siyu Ren, Yizhu Liu, and Kenny Q. Zhu. 2022.  Taxonomy of abstractive dialogue summarization: Scenarios, approaches and future directions.
  * Keizer et al. (2017) Simon Keizer, Markus Guhe, Heriberto Cuayáhuitl, Ioannis Efstathiou, Klaus-Peter Engelbrecht, Mihai Dobre, Alex Lascarides, and Oliver Lemon. 2017\.  Evaluating persuasion strategies and deep reinforcement learning methods for negotiation dialogue agents.
  * Kingma and Ba (2014) Diederik P Kingma and Jimmy Ba. 2014.  Adam: A method for stochastic optimization.  _arXiv preprint arXiv:1412.6980_.
  * Konovalov et al. (2016) Vasily Konovalov, Ron Artstein, Oren Melamud, and Ido Dagan. 2016.  The Negochat Corpus of Human-agent Negotiation Dialogues.  In _Proceedings of the Tenth International Conference on Language Resources and Evaluation (LREC’16)_ , pages 3141–3145, Portorož, Slovenia. European Language Resources Association (ELRA).
  * Kryscinski et al. (2020) Wojciech Kryscinski, Bryan McCann, Caiming Xiong, and Richard Socher. 2020.  Evaluating the factual consistency of abstractive text summarization.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 9332–9346, Online. Association for Computational Linguistics.
  * Lee et al. (2021) Chia-Hsuan Lee, Hao Cheng, and Mari Ostendorf. 2021.  Dialogue state tracking with a language model using schema-driven prompting.  In _Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing_ , pages 4937–4949, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.
  * Lei et al. (2018) Wenqiang Lei, Xisen Jin, Min-Yen Kan, Zhaochun Ren, Xiangnan He, and Dawei Yin. 2018\.  Sequicity: Simplifying task-oriented dialogue systems with single sequence-to-sequence architectures.  In _Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 1437–1447, Melbourne, Australia. Association for Computational Linguistics.
  * Lin et al. (2021a) Zhaojiang Lin, Bing Liu, Andrea Madotto, Seungwhan Moon, Paul Crook, Zhenpeng Zhou, Zhiguang Wang, Zhou Yu, Eunjoon Cho, Rajen Subba, and Pascale Fung. 2021a.  Zero-shot dialogue state tracking via cross-task transfer.
  * Lin et al. (2021b) Zhaojiang Lin, Bing Liu, Andrea Madotto, Seungwhan Moon, Zhenpeng Zhou, Paul Crook, Zhiguang Wang, Zhou Yu, Eunjoon Cho, Rajen Subba, and Pascale Fung. 2021b.  Zero-shot dialogue state tracking via cross-task transfer.  In _Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing_ , pages 7890–7900, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.
  * Lin et al. (2020) Zhaojiang Lin, Andrea Madotto, Genta Indra Winata, and Pascale Fung. 2020.  MinTL: Minimalist transfer learning for task-oriented dialogue systems.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 3391–3405, Online. Association for Computational Linguistics.
  * Liu et al. (2019) Chunyi Liu, Peng Wang, Jiang Xu, Zang Li, and Jieping Ye. 2019.  Automatic dialogue summary generation for customer service.  In _Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery Data Mining_ , KDD ’19, page 1957–1965, New York, NY, USA. Association for Computing Machinery.
  * Liu et al. (2021) Junpeng Liu, Yanyan Zou, Hainan Zhang, Hongshen Chen, Zhuoye Ding, Caixia Yuan, and Xiaojie Wang. 2021.  Topic-aware contrastive learning for abstractive dialogue summarization.  In _Findings of the Association for Computational Linguistics: EMNLP 2021_ , pages 1229–1243, Punta Cana, Dominican Republic. Association for Computational Linguistics.
  * Liu and Chen (2021) Zhengyuan Liu and Nancy Chen. 2021.  Controllable neural dialogue summarization with personal named entity planning.  In _Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing_ , pages 92–106, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.
  * Mccowan et al. (2005) Iain Mccowan, J Carletta, Wessel Kraaij, Simone Ashby, S Bourban, M Flynn, M Guillemot, Thomas Hain, J Kadlec, V Karaiskos, M Kronenthal, Guillaume Lathoud, Mike Lincoln, Agnes Lisowska Masson, Wilfried Post, Dennis Reidsma, and P Wellner. 2005.  The ami meeting corpus.  _Int’l. Conf. on Methods and Techniques in Behavioral Research_.
  * Park et al. (2022) Seongmin Park, Dongchan Shin, and Jihwa Lee. 2022.  Leveraging non-dialogue summaries for dialogue summarization.  In _Proceedings of the First Workshop On Transcript Understanding_ , pages 1–7, Gyeongju, South Korea. International Conference on Computational Linguistics.
  * Peng et al. (2021) Baolin Peng, Chunyuan Li, Jinchao Li, Shahin Shayandeh, Lars Lidén, and Jianfeng Gao. 2021.  Soloist: Building task bots at scale with transfer learning and machine teaching.  _Transactions of the Association for Computational Linguistics_ , 9:807–824.
  * Petukhova et al. (2016) Volha Petukhova, Christopher A. Stevens, Harmen de Weerd, Niels Anne Taatgen, Fokie Cnossen, and Andrei Malchanau. 2016.  Modelling multi-issue bargaining dialogues: Data collection, annotation design and corpus.  In _International Conference on Language Resources and Evaluation_.
  * Prakken (2006) Henry Prakken. 2006.  Formal systems for persuasion dialogue.  _The knowledge engineering review_ , 21(2):163–188.
  * Raffel et al. (2020) Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu. 2020.  Exploring the limits of transfer learning with a unified text-to-text transformer.  _Journal of Machine Learning Research_ , 21(140):1–67.
  * Rastogi et al. (2020) Abhinav Rastogi, Xiaoxue Zang, Srinivas Sunkara, Raghav Gupta, and Pranav Khaitan. 2020.  Towards scalable multi-domain conversational agents: The schema-guided dialogue dataset.  _Proceedings of the AAAI Conference on Artificial Intelligence_ , 34:8689–8696.
  * Rennard et al. (2022) Virgile Rennard, Guokan Shang, Julie Hunter, and Michalis Vazirgiannis. 2022.  Abstractive meeting summarization: A survey.
  * Tang et al. (2022) Xiangru Tang, Arjun Nair, Borui Wang, Bingyao Wang, Jai Desai, Aaron Wade, Haoran Li, Asli Celikyilmaz, Yashar Mehdad, and Dragomir Radev. 2022.  CONFIT: Toward faithful dialogue summarization with linguistically-informed contrastive fine-tuning.  In _Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 5657–5668, Seattle, United States. Association for Computational Linguistics.
  * Vaswani et al. (2017) Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Ł ukasz Kaiser, and Illia Polosukhin. 2017.  Attention is all you need.  In _Advances in Neural Information Processing Systems_ , volume 30. Curran Associates, Inc.
  * Wang and Cardie (2013) Lu Wang and Claire Cardie. 2013.  Domain-independent abstract generation for focused meeting summarization.  In _Proceedings of the 51st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 1395–1405, Sofia, Bulgaria. Association for Computational Linguistics.
  * Wang et al. (2019) Xuewei Wang, Weiyan Shi, Richard Kim, Yoojung Oh, Sijia Yang, Jingwen Zhang, and Zhou Yu. 2019.  Persuasion for good: Towards a personalized persuasive dialogue system for social good.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 5635–5649, Florence, Italy. Association for Computational Linguistics.
  * Williams et al. (2016) J. Williams, Antoine Raux, and Matthew Henderson. 2016.  The dialog state tracking challenge series: A review.  _Dialogue Discourse_ , 7:4–33.
  * Wolf et al. (2020) Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin Lhoest, and Alexander M. Rush. 2020.  Transformers: State-of-the-art natural language processing.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing: System Demonstrations_ , pages 38–45, Online. Association for Computational Linguistics.
  * Wu et al. (2019) Chien-Sheng Wu, Andrea Madotto, Ehsan Hosseini-Asl, Caiming Xiong, Richard Socher, and Pascale Fung. 2019.  Transferable multi-domain state generator for task-oriented dialogue systems.  In _Annual Meeting of the Association for Computational Linguistics_.
  * Yamaguchi et al. (2021) Atsuki Yamaguchi, Kosui Iwasa, and Katsuhide Fujita. 2021.  Dialogue act-based breakdown detection in negotiation dialogues.  In _Proceedings of the 16th Conference of the European Chapter of the Association for Computational Linguistics: Main Volume_ , pages 745–757, Online. Association for Computational Linguistics.
  * Zhan et al. (2022) Haolan Zhan, Yufei Wang, Tao Feng, Yuncheng Hua, Suraj Sharma, Zhuang Li, Lizhen Qu, and Gholamreza Haffari. 2022.  Let’s negotiate! a survey of negotiation dialogue systems.
  * Zhao et al. (2021) Jeffrey Zhao, Mahdis Mahdieh, Ye Zhang, Yuan Cao, and Yonghui Wu. 2021.  Effective sequence-to-sequence dialogue state tracking.  In _Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing_ , pages 7486–7493, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.
  * Zhou et al. (2019) Yiheng Zhou, He He, Alan W Black, and Yulia Tsvetkov. 2019.  A dynamic strategy coach for effective negotiation.  In _Proceedings of the 20th Annual SIGdial Meeting on Discourse and Dialogue_ , pages 367–378, Stockholm, Sweden. Association for Computational Linguistics.

##  Appendix A Prompt to Generate GPT-Negochat

The following prompt template is fed to the text-davinci-003 variant of GPT-3
to generate rephrased utterances for GPT-Negochat:

> Rephrase this while still maintaining the same meaning. Feel free to add
> some minimal niceties and make it sound less robotic. While rejecting an
> offer, try to come up with a reason. Make the tone sound like a real job
> interview: $[\texttt{original utterance}]$

##  Appendix B Sizes of Dataset Splits

For all our experiments, we follow the following steps:

  1. 1.

We first perform a three-fold split on our entire dataset, which results in
66.67% of the samples being assigned to the training split and the remaining
to the test split.

  2. 2.

For each split, we further subdivide the training split into the actual
training and the validation split using a 85%-15% split.

  3. 3.

Effectively, this strategy results in the training, validation, and test
splits containing 56.67%, 10%, and 33.33% of the dataset respectively.

##  Appendix C Hyperparameter Tuning

We restrict our hyperparameter sweep to a few values over training-related
hyperparameters such as learning rate, batch size, early stopping criterion,
and precision. We also sweep over varying sizes of the context window for
representing our dialogue context. To ensure that we do not over-optimize our
hyperparameters and stumble upon “lucky” values, we perform an initial sweep
once with a fixed configuration and apply the best-found hyperparameter values
to all our other experiments.

We report the search spaces and best-found values for our hyperparameters in
Table 5.

Hyperparameter | Sweep Range | Best Value
---|---|---
Learning Rate | 1 $\times 10^{-4},1\times 10^{-5},1\times 10^{-3},6\times 10^{-4}$ | $6\times 10^{-4}$
Batch Size | 32, 64, 128 | 32
Early Stopping (Min Delta) | 0, 0.001, 0.005, 0.1, 0.5 | 0
Early Stopping (Patience) | 0, 1, 2, 3, 4 | 4
Gradient Clip Norm | 1.0 | 1.0
Precision | 16, 32 | 32
Context Window Size | 1, 2, 3, 4 | 3
Table 5: Hyperparameter values for all experiments.

##  Appendix D A (Longer) Side-by-Side Comparison of Utterances

Table 6 shows an additional list of side-by-side examples of original and
rephrased utterances in the Negochat and GPT-Negochat datasets respectively.

Speaker |  Original Utterance |  Rephrased Utterance
---|---|---
Candidate |  I would like a workday of 8 hours |  I’m looking for something that would require 8 hours a day.
Employer |  cand you do 10? |  Can you do 10 hours a day?
Candidate |  I disagree about a workday of 10 hours. I would like a workday of 8 hours |  I’m not comfortable with that. I’d prefer 8 hours a day.
Employer |  what else pension, car? |  What else do you need, like a pension or a car?
Candidate |  I accept programmer position. Now let’s talk about how we can agree on other issues. I want a salary of 120,000? |  I’d like to accept the programmer position. How about we discuss the other details, such as salary? I was hoping for something around 120,000.
Employer |  I would like to offer you 90,000 for salary. |  That’s a bit higher than what we had in mind. We were thinking of offering 90,000.
Candidate |  I would like a pension of 20% |  Could I get a pension of 20%?
Candidate |  I accept 60,000. I would like to continue and discuss another issue. I want a position of project manager |  Yes, that’s fine. I’d also like to discuss another topic - I’m hoping for a project manager position.
Employer |  I accept project manager. |  Absolutely, we can make that happen.
Candidate |  It’s good to reach an agreement on project manager |  It’s great that we can come to an agreement on the project manager.
Candidate |  I want a company car |  I want a company car
Employer |  I do not accept leased car, can you manage without one? |  I do not accept leased car, can you manage without one?
Candidate |  I reject no company car. I would like a company car |  I definitely want a company car.

Table 6: More excerpts from the Negochat corpus alongside its rephrased
counterparts from GPT-Negochat.

##  Appendix E Instructions for Human Annotators

##### Meaning.

The key thing we are interested in is to see whether the paraphrased utterance
alters the FUNDAMENTAL meaning of the original utterance in the negotiation
dialogue. Therefore, some examples of MEANING ALTERING utterances would be:

A: No, I’d like a product manager position
B: Yes, I’d like a product manager position
A: I can only work 8 hours
B: I can only work 9 hours

Similarly, some examples of utterances that DO NOT ALTER MEANING would be:
Context: We can certainly make that happen with a 10% pension fund.
A: No, I don’t think that’s the right fit for me.
B: I disagree
Context: 9 hours sounds good to me. Now, I’m asking for a 20% pension.
A: I can agree to that pension.
B: Alright, I can work with that.

##### Naturalness.

In addition to judging the same underlying meaning/effect of the utterance,
you will also be asked to pick which of the two utterances (if any) sound more
realistic in a real-world job negotiation. For example, it’s unlikely that a
professional interview candidate would say something super casual like "Nah
man, you can do better than 80K".