# Some Results on Ethnic Conflicts Based on Evolutionary Game Simulation

Jun Qin1, Yunfei Yi4,5, Hongrun Wu5, Yuhang Liu1, Xiaonian Tong1, Bojin
Zheng*1,2,3 1 College of Computer Science, South-Central University for
Nationalities, Wuhan 430074, China  2 State Key Laboratory of Networking and
Switching Technology, Beijing University of Posts and Telecommunications,
Beijing 100876, China  3 School of Software, Tsinghua University, Beijing
100084, China  4 College of Computer and Information Science, Hechi
University, Yizhou 546300, China  5 State Key Laboratory of Software
Engineering, Wuhan University, Wuhan 430074, China<EMAIL_ADDRESS>
###### Abstract

The force of the ethnic separatism, essentially origining from negative effect
of ethnic identity, is damaging the stability and harmony of multiethnic
countries. In order to eliminate the foundation of the ethnic separatism and
set up a harmonious ethnic relationship, some scholars have proposed a
viewpoint: ethnic harmony could be promoted by popularizing civic identity.
However, this viewpoint is discussed only from a philosophical prospective and
still lack supports of scientific evidences. Because ethic group and ethnic
identity are products of evolution and ethnic identity is the parochialism
strategy under the perspective of game theory, this paper proposes an
evolutionary game simulation model to study the relationship between civic
identity and ethnic conflict based on evolutionary game theory. The simulation
results indicate that: 1) the ratio of individuals with civic identity has a
positive association with the frequency of ethnic conflicts; 2) ethnic
conflict will not die out by killing all ethnic members once for all, and it
also cannot be reduced by a forcible pressure, i.e., increasing the ratio of
individuals with civic identity; 3) the average frequencies of conflicts can
stay in a low level by promoting civic identity periodically and persistently.

###### keywords:

Civic identity, Ethnic identity, Ethnic conflict, Evolutionary game simulation

##  1 Introduction

Ethnic groups, a named social group of people based on what is perceived as
shared ancestry, cultural traditions, communicational interaction, and
history, are the primary entities to provide human’s basic needs[1]. However,
the ethnic group identity, i.e. ethnic identity(dividing the world into
categories of ‘us’ and ‘them’[2]), may result in long-term and destructive
conflicts between different groups[2, 3]. Kelman et al. pointed out that moral
exclusion of ethnic identity, in the extreme, may result in ethnic cleansing
and genocide[4, 5]. Rupesinghe and Burton concurred that most ethnic conflicts
involved inconsistence of identity[6, 7]. Further, the ethnic identity may
evolve into ethnic separatism in multi-ethnic countries, which may lead to
ethnic conflicts between ethnic groups or even divide a country into new
sovereign territories, such as the Yugoslav wars and Sudan’s Darfur conflict
etc.. China- a country with 56 ethnic groups, has been threated by the force
of ethnic separatism and ethnic conflicts for many years[8, 9]. Chinese
scholars have conducted many related works on the solution of ethnic conflicts
and the elimination of negative effect of ethnic identity[10, 11, 12]. Most of
those scholars concured a viewpoint: ethnic harmony could be promoted by
popularizing civic identity. Because civic identity leads people to tolerate
others despite of other people’s ethnicity [13, 14]. However, this viewpoint
was only discussed based on philosophy, and it required sufficient evidences
to convince people.

Current papers conducted lots of eminent and significant works on explaining
social phenomenon by evolutionary theory. For examples, P. James and D. Goetze
explained ethnic conflict and ethnic formation by evolutionary theory[15, 16];
Bester and Guth explained altruistic preferences by evolutionary game
theory[17]; Rajiv Sethi and E. Somanathan explained reciprocity as an aspect
of preference interdependence by evolutionary game theory[18]; Choi and Samuel
studied the relation of parochial altruism and war by evolutionary
simulation[19].

Inspired by these remarkable works[15, 16, 17, 18, 19], in this paper we try
to test the viewpoint ‘ethnic harmony could be promoted by popularizing civic
identity’ and explore a possible way for the solution of conflicts by a
scientific method- based on evolutionary game simulation. To meet this goal,
we firstly map the related concepts(such as ethnic group, ethnic identity,
civic identity behaviors etc.) to corresponding concepts in evolutionary game
theory. Then we establish a model to simulate the relationship between ethnic
conflicts and civic identity. We carried out this model for 30 times. The
simulation results indicate that ethnic conflicts will not die out by cleaning
all the ethnic identity members once and for all, though the number of
individuals with civic identity has a negative association with the
frequencies of conflicts. Moreover, the frequencies of conflicts cannot be
reduced just by increasing the number of individuals with civic identity,
because the frequencies will bound back quickly or even higher. However, it is
possible to control the ethnic conflicts within a low level by promoting the
ratio of civic identity individuals persistently/periodly.

##  2 Method

Based on the current studies on ethnology, evolutionary game theory, and Choi
and Samuel’s model, we illustrated the relationship of ethnic identity, civic
identity and ethnic conflicts by evolutionary game theory.

In this section, firstly we give the foundations to research ethnic conflicts
with evolutionary game theory(see section 2.1). Secondly, we elaborate how to
map concepts in ethnology to concepts in evolutionary game theory(see section
2.2). Thirdly we show how to establish a evolutionary game model to simulate
the relation of civic identity and ethnic conflicts(see section 2.3).

###  2.1 The Foundations to study ethnic conflict by evolutionary game theory

Ethnic groups are shaped by environment, mobility and cultural transmission
etc.. Further, ethnic identity comes from cumulative changes of the
environment or the evolved mental capacities over years[16]. That’s to say,
both ethnic group and ethnic identity are products of evolution[15]. Owing to
the evolution, people with the same ethnic identity tend to cooperate
intensely with ingroups and to be hostile toward outgroups[15]. On the
contrast, members with a sense of civic identity will risk their lives to
protect national interests, and help people without considering their ethnic
group, race, or class etc[20]. As the outcome of evolution is to promote
individual and group interests(i.e. improving inclusive fitness), some
individuals may sacrifice their own well-being and reproductive potential to
fight for resources and interests of their group.

All of these behaviors are the game strategies(parochialism and tolerationism
strategy etc.) from the perspective of game theory. According to these
strategies, groups may cooperate or evoke conflicts with other groups, and
both cases are the results of game between ethnic groups. From this
perspective, we can simulate ethnic conflicts with evolutionary game theory.

###  2.2 Mapping ethnology to evolutionary game theory

To simulate ethnic conflicts by evolutionary game theory, we map the related
ethnological concepts to corresponding concepts in evolutionary game theory.
The mapping is presented as Fig.1. On the level of inter-group, we map ethnic
and civic identity to parochialism and tolerance strategy respectively. On the
level of intra-group, we map the spirit of self-sacrifice and selfish to
altruism and non-altruism strategy respectively. So each individual has four
kinds of strategies: parochial altruism, parochial nonaltruism, tolerant
altruism, tolerant nonaltruism.

Figure 1:  The mapping from concepts in ethnology to concepts in evolutionary
game theory

###  2.3 Establishing the evolutionary game simulation model

The same as the previous studies, we use the GA(Genetic Algorithm) to simulate
the evolutionary process. We represent the four types of strategies as two
alleles. Therefore, there are four genotypes: parochial altruists(abbr.PA),
tolerant altruism (abbr.TA), parochial nonaltruism(abbr.PN), and tolerant
nonaltruism (abbr.TN). Moreover, individuals with genotype P(PA or PN)-
abbreviated as P individuals, are hostile toward other groups, while T
individuals(TA or TN) are friendly to outgroups. Similarly, A individuals(PA
or TA) contribute interests to the public within one group, while N
individuals(PN or TN) do not contribute interests but grab from A individuals
in the group. When a conflict occurs between two groups, only PA individuals
engage in conflict, because the N individuals are not willing to sacrifice to
benefit their fellow group members. Yet, when two groups are in peace status,
T individuals benefit from the cooperated group according to the payoff table.

Furthermore, our evolutionary game model includes four parts: initialization,
inter-group interaction, intra-group interaction and update. The model is
shown as Fig.2.

Figure 2: The evolutionary game model

####  2.3.1 The initialization

To illustrate the association between civic identity and the frequency of
ethnic conflict, the ratio of T individuals and ethnic conflicts need to be
calculated in the simulations. Initialization with too many(or too few) T
individuals or uneven distribution of genotypes may lead to the statistical
error in the simulations. To avoid this initial statistical error, we
initialize each group individuals $m$ with four genotypes randomly.

####  2.3.2 The inter-group interaction

In the step of inter-group interaction, a conflict occurs between two
arbitrary groups $i$ and $j$ with probability $|p_{ij}|$ (where
$p_{ij}=f_{i}^{PA}-f_{j}^{PA}$ is the difference between $f_{i}^{PA}$ and
$f_{j}^{PA}$, which are parochial altruists in group $i$ and $j$
respectively). PA individuals are fighters for their group. So the more PA
individuals one group has, the greater probability this group wins a conflict,
and the smaller chance the opponent group wins. If $p_{ij}>0$(i.e. group $i$
has more PA fighters than group $j$), group $i$ has a great probability to win
a conflict. Here, we set group $i$ winning a conflict with probability
$0.5+0.5p_{ij}$. Meanwhile, group $i$ will not win the conflict with a
probability $0.5-0.5p_{ij}$, i.e., lose or tie. We set the losing probability
and the tie probability equivalently, i.e, both are $0.25-0.25p_{ij}$. These
values of probability are vice verse for $p_{ij}<0$. If $p_{ij}=0$(i.e. the
equal number of PA individuals in two groups), the conflict ends with a tie.
The probability distribution when $p_{ij}>0$ is listed in table 1.

If group $i$ wins in the conflict, a ratio $d$ of fighters(PA individuals) in
both groups $i$ and $j$ die, and a ratio $e$ of the surviving fighters and
nonfighters of the losing group $j$ are killed. Yet only fighters in both
groups are eliminated when the conflict ends in a draw. The eliminated
individuals in both groups are populated by offspring produced by randomly
selected parents in the winning group. Then the two reconstructed groups’
benefits are calculated respectively by the payoff table(table 2). However, if
the two groups are in a harmony status, each T individual in group $i$ will
receive cooperating benefit from its paired group $j$. The inter-group
interaction when $p_{ij}>0$ is shown in Fig.3.

In Table 2, individuals’ payoff of group $i$ are described as follows.
Individuals with A genotype(contributors) promote group’s benefit by
sacrificing their own interest. Here, A individuals contribute interest $b$ to
their group $i$ with cost $c$($b>c$). Each individual receives payoff
$bf_{i}^{A}$ from the A individuals. Thus, PA individuals’ payoff is
$bf_{i}^{A}-c$, and PN with $bf_{i}^{A}$. TA and TN individuals’ payoff is
same as PA and PN respectively when a conflict occurs. However, if two groups
are in a harmony status, TA and TN individuals receive another cooperating
benefit $tmbf_{j}^{T}$ respectively from the T individuals of the paired group
$j$. And $t$ is the benefit from one T individual of group $j$, $m$ for group
capacity.

Table 1: Probability distribution table when group $p_{ij}>0$. column ‘win’ means group $i$ or $j$ winning a conflict with a probability, ‘lose’ for losing a conflict, ‘tie’ for the conflict ending in a draw. $p_{ij}=f_{i}^{PA}-f_{j}^{PA}$ is the difference between $f_{i}^{PA}$ and $f_{j}^{PA}$.When $p_{ij}=0$, the conflict ends with a tie directly. group | win | lose | tie
---|---|---|---
$i$ | $0.5+0.5p_{ij}$ | $0.25-0.25p_{ij}$ | $0.25-0.25p_{ij}$
$j$ | $0.25-0.25p_{ij}$ | $0.5+0.5p_{ij}$ | $0.25-0.25p_{ij}$
Figure 3: Inter-group interaction between group $i$ and $j$ when $p_{ij}>0$

####  2.3.3 The intra-group interaction

In the step of intra-group interaction, individuals will reproduce $m$ new
offsprings. One individual can be selected as a parent according to this
individual’ share of the group’s payoff, or say, individuals with greater
payoff will have a greater chance to have more offsprings. The new offsprings
mutate in a probability $u$.

Table 2: Payoff table of group $i$. $n$ is the number of groups, $m$ for the individuals’ number in each group, $d$ for the ratio of eliminated fighters(PA individuals) when a conflict occurs, $b$ for altruists contribute to public good at a cost $c$, $t$ for the benefit of harmonious relation, $u$ for the mutation probability. | P | T
---|---|---
A | $bf_{i}^{A}-c$ | $bf_{i}^{A}-c+tmf_{j}^{T}$
N | $bf_{i}^{A}$ | $bf_{i}^{A}+tmf_{j}^{T}$

####  2.3.4 The update

In the update part, the new offsprings replace their parental generation, then
migrate to other groups randomly. For the change of identity, it is not
necessary to kill individuals if group members change their identities. Here,
the new members who have changed their ethnic identity with probability $q$
migrates to a randomly chosen group.

##  3 Simulation experiments and results

In this section, we try to validate the proposed viewpoint: ethnic harmony
could be promoted by popularizing civic identity. To validate this viewpoint,
we should firstly test the proposition: that ethnic harmony(ethnic conflicts)
has a positive(negative) association with civic identity. Therefore, we will
test whether the frequencies of ethnic conflicts has a negative correlation
with the number of people with civic identity. If the first proposition is
wrong, the viewpoint could be wrong. However, if the proposition is right,
secondly we will consider whether it is possible to keep a consistent peace by
cleaning all P individuals or increasing a ratio of T individuals. If the
second proposition is right, the solution for avoiding conflicts are given.
However, if the second proposition is wrong, we will search a possible way to
control the frequencies of conflicts in a low level.

Thus, the simulation experiments include three parts: 1)whether the number of
people with civic identity has a positive relation with the level of ethnic
harmony(i.e. has negative relation with the frequencies of conflicts);
2)whether it is possible to eliminate conflicts by cleaning P individuals
completely, and whether it is possible to deduce ethnic conflicts by
increasing T individuals; 3)how to promote between-groups’ harmonious
relationship, i.e., how to control the conflict frequency in a low level. The
related parameters in the simulations are listed in table 3.

Table 3: Parameters of simulation experiments. $n$ is the number of groups, $m$ for the capacity of each group, $d$ for the ratio of eliminated fighters(PA individuals) when a conflict occurs, $e$ for the ratio of eliminated individuals in the losing group, $b$ for A individuals contributing benefit to their group and sacrificing their own benefit $c$, $t$ for the benefit from one T individual of the paired group when two paired groups are in harmonious status, $u$ for the new offsprings’ mutation probability, $q$ for new offsprings’ migrating probability. $n$ | $m$ | $d$ | $e$ | $b$ | $c$ | $t$ | $u$ | $q$
---|---|---|---|---|---|---|---|---
18 | 30 | 0.2 | 2.5 | 0.05 | 0.03 | 0.001 | 0.005 | 0.2

###  3.1 The association between the ratio of T individuals and conflicts

In this section, the experiments focus on the association between T and the
ratio of conflicts. The variation trend between the ratio of T individuals and
conflicts in 1000 generations are shown in Fig.4. $f_{t}$ is the ratio of T
individuals in one generation, $f_{c}$ for the ratio of occured conflicts.
Moreover, the quantitative association between $f_{c}$ and $f_{t}$ of Fig.4 is
listed in table 4.

(a) The relation between $f_{c}$ and $f_{t}$ when $f_{t}$ changes in
generation 1-1000

(b) The relation between $f_{c}$ and $f_{t}$ when $f_{t}$ changes in
generation 1001-2000

Figure 4: Association between $f_{t}$ and $f_{c}$. The horizontal axis
$generation$ indicates the evolved $ith$ generation. The upper vertical axis
$f_{t}$ is the ratio of T individuals of one generation, and the bottom
vertical axis $f_{c}$ for the ratio of occured conflict frequencies account
for maximum conflict frequencies in one generation. The red dot-dash line in
the upper panel represents $f_{t}$, and The blue curve for $f_{c}$.

Fig.4 shows that $f_{t}$ has a negative correlation with $f_{c}$. Because the
level of $f_{c}$ is low when $f_{t}$ is great in Fig.4(a), and vice verse for
Fig.4(b). Correspondingly, the average value of $f_{t}$ and $f_{c}$ in 200
generations are denoted as $\overline{f_{t}}$ and $\overline{f_{c}}$ in Table
4. The groups in Fig.4(a) are in a harmony status, because $\overline{f_{c}}$
is very small- around 0.008. Conversely, the groups in Fig.4(b) are in
frequent conflicts because of $\overline{f_{c}}$ going up to 0.383 maximally.

Table 4: The quantitative association between $\overline{f_{c}}$ and $\overline{f_{t}}$ of Fig.4. Here, $Experimentgroups$ are the simulated results in Fig.4, $generations$ for continued 200 generations in Fig.4, $\overline{f_{t}}$ and $\overline{f_{c}}$ for the average $f_{t}$ and $f_{c}$ in 200 generations respectively. $Experimentgroups$ | $generations$ | $\overline{f_{t}}$ | $\overline{f_{c}}$
---|---|---|---
Fig.4(a) | 1001-1200 | 0.937 | 0.008
Fig.4(a) | 1201-1400 | 0.923 | 0.002
Fig.4(a) | 1401-1600 | 0.856 | 0.012
Fig.4(a) | 1601-1800 | 0.782 | 0.016
Fig.4(a) | 1801-2000 | 0.909 | 0.002
Fig.4(b) | 1001-1200 | 0.084 | 0.383
Fig.4(b) | 1201-1400 | 0.065 | 0.252
Fig.4(b) | 1401-1600 | 0.081 | 0.297
Fig.4(b) | 1601-1800 | 0.059 | 0.364
Fig.4(b) | 1801-2000 | 0.056 | 0.229

###  3.2 Effect on the ratio of conflicts by cleaning all P or increasing T

From the results in section 3.1, we know that the ratio of T individuals has
negative correlation with the ratio of occured conflicts. So whether is it
possible to improve harmonious groups’ relationship by eliminating all P
individuals or increasing T individuals? The following simulation experiments
on cleaning all P individuals and increasing T individuals are shown in Fig.5.

Fig.5 and Table 5 show an interesting phenomenon: the $f_{c}$ will decrease in
a short term, but it will bounce back quickly in a few generations. Thus, in
the long generations, it cannot keep the conflicts in a low level by
eliminating all P individuals or increasing T individuals.

Specifically, by eliminating all P individuals in Fig.5(a) in generation 3550,
conflicts decrease apparently in the following a few generations, yet it
bounces back in generation 3650. The similar results happened in Fig.5(b) and
Fig.5(c). The decrease of $f_{c}$ in Fig.5(b) is not as apparent as that of in
Fig.5(c), because Fig.5(c) increases more T individuals than Fig.5(b). The
average ratio of conflicts before and after the operation(cleaning P or
increasing T) in 100 and 200 generations are listed in table 5. In Table 5,
$\overline{f_{c1}}$ is the average $f_{c}$ in 100 generations before the
operation, $\overline{f_{c2}}$ for the average $f_{c}$ in 100 generations
after the operation, $\overline{f_{c3}}$ for the average $f_{c}$ in 200
generations after the operation. In table 5, we can know that $f_{c}$ has a
decrease in the following 100 generations and bounce back again in the next
200 generations. After cleaning all P individuals in generation 3550 in
Fig.5(a), $\overline{f_{c2}}$ decreases to 0.2 obviously compared with the
original average level $\overline{f_{c1}}=0.360$. Then $\overline{f_{c3}}$
increases to 0.35, which is almost close to the original level. Similarly,
$\overline{f_{c2}}$ of Fig.5(b) and Fig.5(c) has a slight decrease, and the
$\overline{f_{c3}}$ of Fig.5(b) bounces back to the original level nearly.
Moreover, $\overline{f_{c3}}$ of Fig.5(c) bounces higher compared with the
original level.

(a) Clear all P individuals in generation 3550

(b) Increase 40% T individuals in generation 3550

(c) Increase 60% T individuals in generation 3550

Figure 5: The effect on $f_{c}$ by cleaning all P individuals, increasing 40% T, 60% T individuals respectively. Table 5:  The quantified effect on $f_{c}$ with the increasement of T or eliminating P individuals. $Experimentgroups$ | $\overline{f_{c1}}$ | $\overline{f_{c2}}$ | $\overline{f_{c3}}$
---|---|---|---
Fig.5(a) | 0.360 | 0.200 | 0.350
Fig.5(b) | 0.372 | 0.348 | 0.350
Fig.5(c) | 0.385 | 0.336 | 0.398

###  3.3 Increasing T periodically to reduce between-groups’ conflicts

Because of the rebound, the conflict ratio cannot be controlled by the force
of increasing T individuals once for all. What the result will be if we
increase more T individuals before the rebounding point? Experiments with
increasing T individuals periodically are shown in Fig.6. Also, the
corresponding $\overline{f_{t}}$(average $f_{t}$ in 200 generations) are
listed in table 6.

(a) Increase 40% T individuals periodically each 200 generations

(b) Increase 40% T individuals periodically each 50 generations

(c) Increase 60% T individuals periodically each 50 generations

Figure 6: The effect on $f_{c}$ by increasing 40% T, 60% T individuals periodically. Table 6: The quantified effect on $f_{c}$ with the increase or decrease of $f_{t}$ $Experimentgroups$ | $generations$ | $\overline{f_{t}}$ | $\overline{f_{c}}$
---|---|---|---
Fig.6(a) | 5001-5200 | 0.280 | 0.344
Fig.6(a) | 5201-5400 | 0.269 | 0.317
Fig.6(a) | 5401-5600 | 0.336 | 0.346
Fig.6(a) | 5601-5800 | 0.257 | 0.368
Fig.6(a) | 5801-6000 | 0.377 | 0.315
Fig.6(b) | 5001-5200 | 0.477 | 0.281
Fig.6(b) | 5201-5400 | 0.367 | 0.314
Fig.6(b) | 5401-5600 | 0.359 | 0.294
Fig.6(b) | 5601-5800 | 0.552 | 0.243
Fig.6(b) | 5801-6000 | 0.560 | 0.249
Fig.6(c) | 5001-5200 | 0.97 | 0.001
Fig.6(c) | 5201-5400 | 0.964 | 0.005
Fig.6(c) | 5401-5600 | 0.945 | 0.004
Fig.6(c) | 5601-5800 | 0.966 | 0.001
Fig.6(c) | 5801-6000 | 0.957 | 0.004

In Fig.6, we increase 40% and 60% T individuals every 200 and 50 generations
respectively. From Fig.6(a) and Fig.6(b), we can see that $f_{c}$ bounce back
with the period, because the period is too long or the increased T individuals
are not enough, or both. But we can control $f_{c}$ in a low level by
increasing T individuals before the bounce. In Fig.6(c), the $f_{c}$ keeps in
a very low level by increasing 60% T individuals each 50 generations. By this
way, the $\overline{f_{c}}$ of Fig.6(c) is no more than 0.05, and it is the
smallest in the three figures.

So, under the same increasement of T individuals, the smaller the period the
lower level of $f_{c}$ is. Moreover, under the same period, the lager the
$f_{t}$ then the lower level of $f_{c}$ is.

###  3.4 Sensitivity analysis

In this section, we will analyze the effect on $f_{c}^{\prime}$ and
$f_{t}^{\prime}$ under different parameters. $f_{c}^{\prime}$ and
$f_{t}^{\prime}$ are the average value of $f_{c}$ and $f_{t}$ in 10000
generations. In the simulations, we change one parameter and fix other
parameters, and the simulations are listed in Fig.7. From Fig.7, we can see
that the value of $f_{c}^{\prime}$(or $f_{t}^{\prime}$) could be fluctuant
when the value of one parameter changes. However, the responding
$f_{c}^{\prime}$ is small when $f_{t}^{\prime}$ become great. So the negative
association between the frequencies of conflicts and the number of T
individuals still holds. Therefore, the other two conclusions in section 3.2
and 3.3 that base on the negative association also hold.

Specifically, parameters $m$(group’s capacity), $c$(altruists’ sacrificed
benefit), $q$(migrating probability) and $t$(the benefit from the paired
group’s T individuals under harmonious status) affect $f_{c}^{\prime}$ and
$f_{t}^{\prime}$ a lot. In Fig.7(a),(e),(f),(h), when $m$, $c$, $q$ and $t$
become large, the corresponding $f_{c}^{\prime}$ tend to be small. The reasons
are stated as follows: when $m$ is large, the probability of leading to a
conflict becomes small because of the large population base; when $c$ becomes
large, the $f_{c}^{\prime}$ become small because the number of T individuals
will increase(the PA individuals’ fitness become small); when $q$ is large,
the $f_{c}^{\prime}$ become small because the conflicts occur with a low
probability; when $t$ is large, individuals tend to be friendly with other
groups, then the $f_{c}^{\prime}$ will become small. On the contrast, when $b$
becomes large, the $f_{c}^{\prime}$ tend to become large. Because the large
population of altruists could increase the number of fighters(PA individuals).
The change of other parameters $d$,$e$ and $u$ have no direct association with
the increase or decrease of $f_{c}^{\prime}$.

The simulations enlighten us that it also exists other possible ways to
decrease the frequencies of conflicts. For examples, conflicts could be
decreased by increasing the chances of communication between groups(increasing
$q$), or by promoting the groups’ cooperating benefit(increasing $t$) etc..

Figure 7: Sensitive analysis of Parameters.

##  4 Conclusion

In this paper, we established an evolutionary game model, and simulated the
relationship between civic identity and ethnic conflicts by the evolutionary
game theory. The simulation results indicated that ethnic conflicts cannot be
avoided by just killing the ultranationalist. Though the ratio of individuals
with civic identity had a negative association with the ratio of ethnic
conflicts, ethnic conflicts cannot be kept in a low level in a long term just
by promoting civic identity, because the ration of conflicts may bounce back.
However, the frequency of conflicts could stay in a low level by propelling
civic identity persistently and periodically.

Indicated by the simulation results, we have known that it is possible to
control ethnic conflicts in a low level by promoting civic identity. However,
to predict ethnic conflicts is still a challenge, because it is hard to
collect the historical datasets about ethnic identity and ethnic conflicts.
The effects of popularizing civic identity on ethnic groups’ culture, language
are still needed to explore. Moreover, this work spawns some interesting
problems. Can the evolution of national languages be studied by the
methodology of natural science- evolutionary theory and stimulation
technology? What the interesting findings can be found by studying the
evolutionary of language with evolutionary theory and stimulation technology?
What’s more, the study in this paper could supply an example for studying
ethnic problems by the methodology of natural science.

##  5 Acknowledgments

The authors are grateful for support from the Fundamental Research Funds for
the Central Universities(No.CZY12032), Natural Science Foundation of
Guangxi(No.2011GXNSFB018074), Scientific research project of the Guangxi
Education Department(No.200911lx406,200103YB136) and the State Key Laboratory
of Networking and Switching Technology(No.SKLNST-2010-1-04). BZ is grateful
for support from the State Key Laboratory of Software Engineering
(No.2012-09-15).

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Author’s note number

Exploration of hadronization through heavy flavor production at the future
Electron-Ion Collider

Xuan Li

Physics Division, Los Alamos National Laboratory

> The future Electron-Ion Collider (EIC), which is expected to start
> construction at Brookhaven National Laboratory in 2025, will utilize high-
> luminosity high-energy electron+proton and electron+nucleus collisions to
> explore several fundamental questions in the high energy and nuclear physics
> fields. Exploring how matter is formed from quarks and gluons, which is
> referred to as the hadronization process, is one of the EIC science
> objectives. The EIC project detector design led by the ePIC collaboration
> can realize a series of high precision heavy flavor hadron and jet
> measurements. Heavy flavor jet substructure and heavy flavor hadrons inside
> jets, which can provide direct information about the heavy quark
> hadronization process, have been studied in simulation for electron+proton
> and electron+nucleus collisions at EIC. The associated physics projections
> and comparison with latest theoretical calculations will be presented.

> PRESENTED AT
>
>
>
>
> DIS2023: XXX International Workshop on Deep-Inelastic Scattering and Related
> Subjects,
> Michigan State University, USA, 27-31 March 2023
>

##  1 Introduction

The next generation Quantum Chromodynamics (QCD) facility: the Electron-Ion
Collider (EIC) is expected to start construction in 2025 at Brookhaven
National Laboratory. The future EIC will operate electron+proton ($e+p$) and
electron+nucleus ($e+A$) collisions with the instantaneous luminosity at
$10^{33-34}$ cm-2s-1 and the bunch crossing rate at around 10 ns. The electron
beam energy varies from 5 GeV to 18 GeV and the proton/nucleus beam energies
are at 41 GeV, 100-275 GeV [1]. The EIC is expected to host two detector
experiments at the 6 o’clock and 8 o’clock positions and the detector at the 6
o’clock position is referred to as the project detector (see Figure 1). The
EIC project detector design optimization is led by the ePIC collaboration. As
shown in the right panel of Figure 1, the current ePIC detector design
consists of high granularity vertex and tracking, particle identification and
calorimeter subsystems with the pseudorapidity coverage of $|\eta|\leq 3.5$.

Figure 1: Schematics of the EIC accelerator (left) and the current ePIC
detector design for the EIC project detector, which is at the 6 o’clock
location of the EIC (right). From the inner to the outer region, the ePIC
detector consists of high granularity vertex and tracking, particle
identification and calorimeter subsystems. A new 1.7 T solenoid magnet will be
built for the EIC project detector.

One of the EIC science objectives is to explore how quarks and gluons form
visible matter inside vacuum or a nuclear medium, which is referred to as the
hadronization process. Unlike light quarks, charm and bottom quarks are
produced early in collisions and don’t change into other quarks or gluons
after they are created. How heavy quarks transport inside the nuclear medium
and transform into final states hadrons is expected to be different from light
quarks. Due to these features, heavy flavor production is a unique probe to
explore the hadronization process especially in the little constrained
kinematic region [2]. The analysis framework in simulation, which includes the
event generation in PYTHIA8 [3], detector performance evaluation in GEANT4
[4], beam remnant and Quantum Chromadynamic (QCD) backgrounds, and heavy
flavor hadron and jet reconstruction algorithms, has been developed for the
EIC heavy flavor physics studies. The physics projection of the heavy flavor
jet substructure and heavy flavor hadron inside jet nuclear modification
factor with the EIC project detector performance in $e+p$ and $e+Au$
collisions will be presented.

##  2 EIC heavy flavor hadron and jet reconstruction in simulation

Figure 2: The mass spectrum of reconstructed D-mesons ($D^{\pm}$, $D^{0}$
($\bar{D^{0}}$), $D_{s}^{\pm}$) and B-mesons ($B^{\pm}$, $B^{0}$
($\bar{B^{0}}$), $B_{s}^{0}$ ($\bar{B_{s}^{0}}$)) and the transverse momentum
spectrum of reconstructed jets with different flavors in 63.2 GeV e+p
simulation. The reconstructed yields are evaluated with the EIC project
detector performance and integrated luminosity of 10 fb-1, which is equivalent
to around one year EIC operation.

A series of heavy flavor hadron and jet products have been studied with the
EIC project detector performance in simulation. As demonstrated in Figure 2,
good signal over background ratios have been obtained for reconstructed
$D^{\pm}$ ($D^{\pm}\rightarrow K^{\mp}\pi^{\pm}\pi^{\pm}$), $D^{0}$
($\bar{D^{0}}$) ($D^{0}(\bar{D^{0}})\rightarrow K^{\mp}\pi^{\pm}$),
$D_{s}^{\pm}$ ($D_{s}^{\pm}\rightarrow\phi+\pi^{\pm}$), $B^{\pm}$
($B^{\pm}\rightarrow J/\psi+K^{\pm}$), $B^{0}$ ($\bar{B^{0}}$)
($B^{0}(\bar{B^{0}})\rightarrow J/\psi+K^{\pm}+\pi^{\mp}$), and $B_{s}^{0}$
($\bar{B_{s}^{0}}$) ($B_{s}^{0}(\bar{B_{s}^{0}})\rightarrow J/\psi+\phi$) mass
spectrums in simulation for 10 GeV electron and 100 GeV proton collisions. As
shown in the bottom right panel of Figure 2, reconstructed charm and bottom
jets in 63.2 GeV $e+p$ collisions can probe the kinematics of produced charm
and bottom quarks in the low transverse momentum region ($p_{T}<15$ GeV/c)
with great precision even with around one year EIC operation. The $e+A$ event
generator is under development, therefore the reconstructed heavy flavor
hadron and jet yields in $e+A$ collisions are evaluated with the yields of the
same product in $e+p$ collisions scaled by the corresponding mass number A.

##  3 EIC heavy flavor hadron inside jet physics projection

Heavy flavor hadron inside jet production can directly access the heavy quark
hadronization process to systematically explore its flavor and kinematic
dependence. Better precision of this approach can be achieved in the Deeply
Inelastic Scattering (DIS) process as the kinematics of the produced heavy
quarks are better constrained in $e+p/A$ collisions than $p+p$/$A+A$
collisions. The hadronization process in $e+p/A$ collisions is expected to be
dominated by fragmentation [1]. One key kinematic variable to access the
fragmentation function is the hadron momentum fraction, $z_{proj}$
($z_{proj}\equiv\vec{p_{h}}\cdot\vec{p_{jet}}/|\vec{p_{jet}}|^{2}$). Figure 3
shows the hadron momentum fraction $z_{proj}$ dependent projected accuracy of
the nuclear modification factor $R_{eAu}$ ($\equiv
1/A\times\sigma_{e+Au}/\sigma_{e+p}$) of reconstructed $D^{0}$ ($\bar{D^{0}}$)
inside charm jets in the pseudorapidity regions of $-2<\eta<0$ (left),
$0<\eta<2$ (middle) and $2<\eta<3.5$ (right) in 63.2 GeV e+Au collisions.

Figure 3: The projected accuracy of hadron momentum fraction $z_{proj}$
dependent nuclear modification factor $R_{eAu}$ in 63.2 GeV $e+Au$ collisions
with the current conceptual design of the EIC project detector. These
projections in the pseudorapidity regions of $-2<\eta<0$ (left), $0<\eta<2$
(middle) and $2<\eta<3.5$ (right) are compared with the Next-to-Leading Order
(NLO) perturbative theoretical predictions based on the parton energy loss
mechanism.

Comparison with the latest theoretical predications based on the Next-to-
Leading Order (NLO) perturbative parton energy loss calculations [5] indicates
that the future EIC charm hadron inside jet measurements will provide
significantly better precision in extrapolating the charm quark fragmentation
function in medium especially in the high $z_{proj}$ region ($z_{proj}>0.6$)
than existing results. Moreover, the forward D meson inside charm jet
measurements at the EIC will help determine the less-known forward charm quark
fragmentation function, which is expected to experience a large modification
in nuclear medium, with great precision. As more charm and bottom hadrons can
be fully reconstructed with the expected performance of the EIC project
detector (see Figure 2), this study will be expanded to include more heavy
flavor hadron inside jet products to extract the fragmentation functions for
different heavy flavor hadron species.

##  4 EIC heavy flavor jet substructure study

Figure 4: Normalized hadron momentum fraction $z_{proj}$ distributions of
inclusive hadrons and $D^{0}$ ($\bar{D^{0}}$) mesons inside charm jets in 63.2
GeV $e+p$ simulation. These distributions are evaluated with the EIC project
detector performance and divided into three charm jet $p_{T}$ bins: 3 GeV/c
$<p_{T,jet}<$ 5 GeV/c (left), 5 GeV/c $<p_{T,jet}<$ 8 GeV/c (middle), and
$p_{T,jet}>$ 8 GeV/c (right).

Heavy quarks usually undergo parton shower and energy loss before they
transfer into final-state hadrons especially in medium. Separating these
final-state effects in heavy flavor cross section measurements will help
improve the understanding of the hadronization process. Heavy flavor jet
substructure, which is related with the inclusive hadron inside jet
production, is one of the ideal probes to extract the heavy quark energy loss
and parton shower effects. Figure 4 shows the normalized distributions of the
hadron momentum fraction $z_{proj}$ carried by inclusive hadrons or $D^{0}$
($\bar{D^{0}}$) mesons inside charm jets within three jet $p_{T}$ bins: 3
GeV/c $<p_{T,jet}<$ 5 GeV/c (left), 5 GeV/c $<p_{T,jet}<$ 8 GeV/c (middle),
and $p_{T,jet}>$ 8 GeV/c (right) in 63.2 GeV $e+p$ collisions. These yields
are obtained with the EIC project detector performance in simulation. Enhanced
sensitivity to the parton energy loss mechanism will be provided by these low
$p_{T}$ heavy flavor jet substructure measurements at the EIC. The shape
differences between the $z_{proj}$ distributions of inclusive hadrons inside
charm jets and those of $D^{0}$ ($\bar{D^{0}}$) mesons inside charm jets are
consistent with the flavor dependent parton showering picture. Further studies
of the heavy flavor jet substructure will be expanded to other observables
such as the heavy flavor jet angularity [6], and will be performed in
different $e+A$ collisions to extract the medium induced parton showering and
energy loss effects.

##  5 Summary and Outlook

The rapidly evolving EIC project will provide an ideal environment to explore
the heavy quark hadronization dynamic process in vacuum and different nuclear
medium. The current design of the EIC project detector can realize a series of
high precision heavy flavor hadron, jet and hadron inside jet measurements.
Initial simulation studies have demonstrated that the proposed EIC heavy
flavor hadron inside jet and heavy flavor jet substructure measurements can
help extracting the heavy quark energy loss and fragmentation processes in the
less constrained kinematic regions with significantly better precisions than
existing measurements. As the optimization of the EIC project detector
technical design is ongoing, further studies will be carried out with the
updated detector performance and include more physics observables.

## References

  * [1] R. Abdul Khalek et al., _Science Requirements and Detector Concepts for the Electron-Ion Collider: EIC Yellow Report_ , Nucl. Phys. A 1026 (2022) 122447.
  * [2] X. Li et al., _A New Heavy Flavor Program for the Future Electron-Ion Collider_ EPJ Web Conf. 235 (2020) 04002
  * [3] T. Torbjorn et al., _An introduction to PYTHIA 8.2_ , Comput. Phys. Commun. 191 (2015) 159-177.
  * [4] S. Agostinelli, et al., _Geant4—a simulation toolkit_ , Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 506 (3) (2003) 250–303.
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Types and Semantics for Extensible Data Types (Extended Version)

Cas van der Rest1  Casper Bach Poulsen1

C. van der Rest and C. Bach Poulsen

$^{1}$Delft University of Technology, Delft, The Netherlands

Developing and maintaining software commonly requires (1) adding new data type
constructors to existing applications, but also (2) adding new functions that
work on existing data.  Most programming languages have native support for
defining data types and functions in a way that supports either (1) or (2),
but not both.  This lack of native support makes it difficult to use and
extend libraries.

A theoretically well-studied solution is to define data types and functions
using initial algebra semantics.  While it is possible to encode this
solution in existing programming languages, such encodings add syntactic and
interpretive overhead, and commonly fail to take advantage of the map and fold
fusion laws of initial algebras which compilers could exploit to generate more
efficient code.  A solution to these is to provide native support for initial
algebra semantics.  In this paper, we develop such a solution and present a
type discipline and core calculus for a language with native support for
initial algebra

§.§.§ Acknowledgements.

This research was partially funded by the NWO VENI Composable and
Safe-by-Construction Programming Language Definitions project (VI.Veni.192.259).

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