††thanks: Corresponding author<EMAIL_ADDRESS>
# From Reddit to Wall Street: The role of committed minorities in financial
collective action

Lorenzo Lucchini  FBK - Fondazione Bruno Kessler, 38123 Trento, Italy  Luca
Maria Aiello  IT University of Copenhagen, DK  Laura Alessandretti  Technical
University of Denmark, DK-2800 Kgs. Lyngby, DK
Gianmarco De Francisci Morales  ISI Foundation, via Chisola 5, 10126 Torino,
Italy  Michele Starnini  ISI Foundation, via Chisola 5, 10126 Torino, Italy
Andrea Baronchelli  City University of London, Department of Mathematics,
London EC1V 0HB, UK  The Alan Turing Institute, British Library, 96 Euston
Road, London NW12DB, UK  UCL Centre for Blockchain Technologies, University
College London, London, UK

###### Abstract

In January 2021, retail investors coordinated on Reddit to target short
selling activity by hedge funds on GameStop shares, causing a surge in the
share price and triggering significant losses for the funds involved. Such an
effective collective action was unprecedented in finance, and its dynamics
remain unclear. Here, we analyse Reddit and financial data and rationalise the
events based on recent findings describing how a small fraction of committed
individuals may trigger behavioural cascades. First, we operationalise the
concept of individual commitment in financial discussions. Second, we show
that the increase of commitment within Reddit predated the initial surge in
price. Third, we reveal that initial committed users occupied a central
position in the network of Reddit conversations. Finally, we show that the
social identity of the broader Reddit community grew as the collective action
unfolded. These findings shed light on financial collective action, as several
observers anticipate it will grow in importance.

## Introduction

In January 2021, the GameStop shares traded on the New York Stock Exchange
experienced a classic “short squeeze” Asquith  _et al._ (2005); Barberis and
Thaler (2005). As the price sharply jumped higher, traders who had bet that
its price would fall (i.e., who “shorted” it) were forced to buy it in order
to prevent even greater losses, thus further promoting the price rally
Barberis and Thaler (2005); Gam (2021); cnb (2021). Victims of the squeeze
were professional hedge funds, and particularly Melvin Capital Management who
lost 53% of its investments for a total estimated $4.5$ billion USD Chung
(2021). The short squeeze was initially and primarily triggered by users of
the subreddit r/wallstreetbets (WSB), a popular Internet forum on the social
news website Reddit, who managed to translate online discussions into an
highly coordinated financial operation.

These events garnered huge attention from the media, professionals, and
financial authorities. Notably, the US Treasury Secretary Janet Yellen
convened a meeting of financial regulators including the heads of the
Securities and Exchange Commission, Federal Reserve, Federal Reserve Bank of
New York, and the Commodity Futures Trading Commission to examine the GameStop
squeeze Lawder and Hunnicutt (2021). Cindicator Capital, a fund specialized in
digital assets, published a hiring call for a sentiment trader with three
years of active trading experience and having been a member of WallStreetBets
for more than a year with karma—a Reddit measure of “how much good the user
has done” for the community—of more than $1000$ Kochkodin (2021). Finally, the
House Committee on Financial Services of the U.S. Congress held a hearing
titled _‘Game Stopped? Who Wins and Loses When Short Sellers, Social Media,
and Retail Investors Collide’_ to discuss the events DFV (2021). They called
as witness Reddit user Keith Gill, known as u/DeepFuckingValue on WSB, who had
a central role in triggering the collective action. At the hearing, committee
members expressed concern with respect to gamification of investment
111https://www.bloomberg.com/news/articles/2021-03-17/democrats-eye-game-like-
trading-apps-at-house-hearing-on-markets, encouraged by trading platform such
as Robinhood, largely adopted by retail investors due to low commissions.
However, how the coordination on WSB took place in the first place remains
unclear, despite the importance of clarifying this mechanism in order to
assess risks and devise regulations.

In this paper, we analyse discussions on WSB from Nov 27, 2020, to Feb 3, 2021
and investigate how they translated into collective action before and during
the squeeze. Motivated by recent theoretical Xie  _et al._ (2011); Niu  _et
al._ (2017) and experimental Centola  _et al._ (2018) evidence that minorities
of committed individuals may mobilise large fractions of a population
Granovetter (1978); Schelling (2006); Xie  _et al._ (2011) even when they are
extremely small Iacopini  _et al._ (2021), we investigate whether committed
users on WSB had a role in triggering the collective action. To this aim, we
operationalise the commitment of a user as an exhibited proof that the user
has financial stakes in the asset. We consider specific labels on $128\,033$
posts (called flairs) and apply computer vision to classify $22\,277$
screenshot posted as proofs, to identify a total of $36\,128$ events of
commitment by $30\,133$ users. We show that a sustained commitment activity
systematically predates the increase of GameStop share returns, while simple
measures of public attention towards the phenomenon cannot predict the share
increase. Additionally, we also show that the success of the squeeze operation
determines a growth of the social identity of WSB participants, despite the
continuous flow of new users into the group. Finally, we find that users who
committed early occupy a central position in the discussion network, as
reconstructed by WSB posts and comments, during the weeks preceding the stock
price surge, while more peripheral users show commitment only in the last
phases of the saga.

Table 1: Key events relevant to the GME short squeeze. | Event | Date |  Description
---|---|---|---
_a_ |  GME earnings | 2020-12-08 |  GME earning reports revealed a $257\%$ increase in e-commerce revenues
_b_ | New board | 2021-01-11 |  GME announced a renewed Board of Directors, which included experts in e-commerce.
_c_ | Citron prediction | 2021-01-19 |  Citron Research, a popular stock commentary website, published a piece predicting the value of the GME stock would decrease. Citron Research is managed by Andrew Edward Left, a financial analyst and renowned short seller.
_d_ | Elon Musk’s tweet | 2021-01-26 |  Business magnate Elon Musk tweeted “Gamestonk!!” along with a link to WSB.

### The GameStop saga

GameStop (GME) is a U.S. video game retailer which was at the center of the
short squeeze in January 2021. The timeline of the events around to the
squeeze is summarized in Table 1, and it unfolded as follows. In 2019, Reddit
user u/DeepFuckingValue entered a long position on GME and started sharing
regular updates in WSB. On October 27, 2020, Reddit user u/Stonksflyingup
shared a video explaining how a short position held by Melvin Capital, a hedge
fund, could be used to trigger a short squeeze. On January 11, 2021, GME
announced a renewed Board of Directors, which included experts in e-commerce.
This move was widely regarded as positive for the company, and sparked some
initial chatter on WSB. On January 19, Citron Research (an investment website
focused on shorting stocks) released a prediction that GME’s price would
decrease rapidly. On January 22, users of WSB initiated the short squeeze. By
January 26, the stock price increased more than 600%, and its trading was
halted several times due to its high volatility. On that same date, business
magnate Elon Musk tweeted “Gamestonk!!” along with a link to WSB. On January
28, GME reached its all-time intra-day highest price, and more than 1 million
of its shares were deemed failed-to-deliver, which sealed the success of the
squeeze. A failure to deliver is the inability of a party to deliver a
tradable asset, or meet a contractual obligation; a typical example is the
failure to deliver shares as part of a short transaction. On January 28, the
financial service company Robinhood, whose trading application was popular
among WSB users, halted all the purchases of GME stocks. On February 1 and 2,
the stock price declined substantially.

By the end of January 2021, Melvin Capital, which had heavily shorted
GameStop, declared to have covered its short position (i.e., closed it by
buying the underlying stock). As a result, it lost 30% of its value since the
start of 2021, and suffered a loss of 53% of its investments, i.e., more than
4 billion USD.

### The r/wallstreeetbets ecosystem

Reddit is a public discussion website structured in an ever-growing set of
independent _subreddits_ dedicated to a broad range of topics. Users can
submit new _posts_ to any subreddit, and other users can add _comments_ to
existing posts or comments, thus creating nested conversation threads. One
such subreddit is r/wallstreeetbets (WSB), a forum for investors and traders
on Reddit, which self-describes with the tagline “Like 4chan with a Bloomberg
terminal”. It is dedicated to high-risk trades involving derivative financial
products (e.g., options and futures, often leveraged), and is thus not
targeted to the beginner investor, but to somewhat experienced retail traders.
Created in 2012, as of June 2021, it counts more than 10M subscribers (self
proclaimed ‘degenerates’, but also known as ‘autists’, ‘retards’, and ‘apes’,
depending on the type of information shared on the subreddit). As clear from
its description so far, the WSB community is known for its profane and
juvenile humor, and has a well defined identity reinforced also by the common
use of jargon (e.g., ‘stonks’ for stocks, ‘tendies’ for profits, and ‘diamond
hands’ or ‘paper hands’ for people that hold stocks through turbulent times or
sell them at the first loss, respectively). The popularity of this forum has
increased in recent years (since 2017 especially), possibly also due to the
widespread adoption of no-commission brokers and mobile online trading
platforms such as robinhood.com.

The topics of discussion on the forum are varied, but there are some common
patterns of behaviors which are also described in the FAQ wsb (2021). When
submitting a post, a user can apply a category tag called ‘flair’, which
serves as an indication of its content. The allowed flairs, together with a
short description, are reported in Table 2. The community takes flairs
seriously and strictly enforces them (e.g., the FAQ report that misusing
important flairs can lead to getting permanently banned). It is thus very
common to find posts containing screenshots of an open position on a risky bet
tagged with a YOLO flair, all interspersed with unhinged humorous posts and
memes.

The discussion within the subreddit follows a simple post-comment dynamic,
where each post separately grows its multi-level comment tree. Each
interaction, it being a post or a comment, can additionally receive ‘upvotes’
and ‘downvotes’. While ‘upvoting’/ or ‘downvoting’ represents a typical
‘slacktivist’ practice for anonymously expressing one’s position, other users
can also choose to ‘award’ prizes to more emphatically recognize a post or
comment.

Table 2: Flairs allowed on r/wallstreeetbets and their meaning as per the subreddit guidelines. Flair |  Meaning
---|---
YOLO (You Only Live Once) |  YOLO flair is for dank trades only. The minimum value at risk must be at least $10,000 in options, or $25,000 in equity.
DD (Due Diligence) |  The research you have done on a specific company/sector/trade idea. This is a high effort text post. It should include sources and citations. It should be a long post and not just a link to a submission.
Discussion |  An idea or article that you would like to talk about. Needs to be more involved than ”up or down today?”
Gain |  Use this flair to show off a solid winning trade. Minimum gain is $2,500 for options, $10,000 for shares. You must show or explain your trade. If you have to say something like ”position in comments” then it’s a bad screenshot.
Loss |  Show off a brutal, crushing loss. Minimum loss $2,500 for options, $10,000 for shares. You must show or explain your trade. If you have to say something like ”position in comments” then it’s a bad screenshot.

## Results

### Collective attention, Commitment, and Identity on WSB

Figure 1: GME stock returns compared with: (a) number of posts submitted on
WSB; (b) number of posts on WSB that showed financial commitment; (c) level of
group identity (shaded areas corresponds to two standard errors of the daily
average).

Figure 1 compares the daily returns of GME (the percent increase of price
compared to the previous day) with three quantities calculated over time on a
daily basis: _i)_ activity within the community measured as the number of
posts submitted on WSB; _ii)_ number of posts on WSB that showed financial
commitment towards GME stocks; and _iii)_ level of group identity signaled by
language markers in WSB submissions about GME.

The posting activity in the WSB community is characterised by a weekly
periodicity that endures stably until the announcement of a renewed Board of
Directors (event _b_). After the first considerable increase in the stock
price on January 14 ($+57$%), the activity grows noticeably. Posting activity
raises exponentially after the second price spike on January 26 ($+92$%) and
it culminates on January 28, two days after the stock evaluation reached its
maximum. Public attention to the GME phenomenon spreads far beyond the
boundaries of Reddit. The number of GME-related tweets follows a similar
exponential growth starting on January 27 after Elon Musk’s endorsement (event
_d_) and peaking on January 28 (Figure SI 1(a)). The growing interest on
Twitter matches the explosive growth in the number of new subscribers to the
WSB subreddit (Figure SI 1(b-c)). Overall, these results support three
conclusions. First, collective attention towards GME follows the asset price
growth with a delay. Second, despite the collective action being designed and
coordinated on Reddit, wide interest was expressed on other social media as
well. Last, not only the discussion originated from Reddit gradually attracted
the attention of larger crowds to the topic, but it also engaged those crowds
to the point of attracting them to the original source of the discussion—the
WSB subreddit.

The evolution of commitment over time differs considerably from the growth of
collective attention. Figure 1(b) shows the number of daily commitment events
measured by counting “Gain”, “Loss”, “YOLO” posts (i.e., posts with one of
these flairs), and the screenshots that WSB users submitted as proof of stake
(see Methods for details). Before the new board of directors was announced
(event _b_), WSB users uploaded a few dozens of commitment posts per day. The
number of commitment posts increases tenfold on the day of the first price
spike and keeps growing steadily afterwards. For eleven days, between the
first price spike on January 14 until the next spike on January 25, such
increase in commitment takes place in absence of any growth in financial
returns. In summary, commitment predates price surges and is sustained also in
absence of gains.

The presence of commitment in absence of returns raises the question of
whether commitment was supported by other processes endogenous to the WSB
community. A recent ethnographic study found that active members of WSB use
shared linguistic markers and reciprocation of custom awards to express and
reinforce the community’s sense of identity Boylston  _et al._ (2021).
Identity is a shared sense of belonging to a group Brewer and Gardner (1996)
that can influence inter-group behavior Tajfel  _et al._ (1979), not least by
fostering cooperation Yamagishi and Kiyonari (2000); Simpson (2006). Identity
is often signaled explicitly through symbols Mach (1993) or language cues Ochs
(1993). To measure the group identity in GME-related submissions, we used a
validated indicator of group identity Tausczik and Pennebaker (2010): for each
submission, we calculated the fraction of the first person pronouns that are
the plural pronoun _“we”_ , and averaged those fractions across all the
submissions of a given day (more details in Methods). Figure 1(c) shows the
group identity expressed by GME-related submissions within the WSB community.
The signal oscillates heavily until mid-January, due to the relatively low
number of submissions. As the number of submissions increases, we detect two
peaks. The first peak follows the market analysis from Citron Research (event
_c_) that forecast a drop in GME stock price and antagonized the members of
the WSB community by referring to them as “suckers at this poker game”. This
finding is in agreement with the theoretical expectation of community identity
being created during processes of struggle between social groups Cook-Huffman
(2008)—in this case, between WSB and its detractors. The second peak matches
the maximum increase of the stock price, and it is likely caused by the
acknowledgment of collective success in performing the short squeeze. In
short, we find that expressions of identity emerged concurrently with the
increase of commitment and might have played a role in sustaining it, but
identity is unlikely to be the origin of the collective action.

### Commitment and reach of core vs peripheral authors

The sustained flow of commitment events during the weeks preceding stock price
surge indicates the presence of a minority of committed users. As the
interaction between the committed minority and the rest of the community is
crucial to the success of a collective action Granovetter (1978); Schelling
(2006); Xie  _et al._ (2011), we study the dynamics of social interactions
between committed individuals and other WSB users. These interactions occur
over a rapidly evolving social network. Figure 2(a) shows a few snapshots of
the network of replies over time. In these networks, users are connected if
they submitted a comment in reply to the post or comment of another during the
time-span considered. As new users join, the number of small disconnected
components in the network increases (see Figure SI 4(b-c)), while the
connected component tends to cluster around few popular discussion threads
(especially the so-called _daily megathreads_ Boylston  _et al._ (2021))
created with the purpose of summarizing the events of the day and planning
future actions. The structural transformation of the network happens abruptly
rather than gradually.

Figure 2: _The evolution of the GME discussion network._ Panel (a) shows three
examples of GME discussion networks, reconstructed in different time windows
with the same number of nodes, $N$ = 3000. Nodes are WSB users, colored
according to whether they posted a commitment submission (red) or not (gray).
The size of nodes is inversely proportional to their k-shell, i.e. nodes
belonging to the core are bigger than peripheral nodes. A link exists between
two nodes if one of the two replied to the other at least once. Panels (b) and
(c) show two key topological features of networks reconstructed over a rolling
time window of 7 days: (b) The heterogeneity of the degree distribution
$\kappa$, defined as $\kappa\equiv\langle k^{2}\rangle/\langle k\rangle^{2}$,
where $\langle k\rangle$ and $\langle k^{2}\rangle$ are the first and second
moments of the degree distribution, and _n_ -th moment is $\langle
k^{n}\rangle\equiv\sum_{i}^{N}k_{i}^{n}/N$ Newman (2010). (c) The average
network reciprocity. Shaded areas represent $2$ standard deviations of the
network metrics aggregated on a daily rolling window basis.

We quantify this structural change by reconstructing networks over a rolling
time window of 7 days, and looking at the evolution of two key topological
quantities of these networks in time. First, we observe that the heterogeneity
of the distribution of the nodes’ degree (i.e., the number of different users
each user replies to) Newman (2010) increases three-fold in the span of 20
days after event _c_ , thus reflecting the simultaneous emergence of super-
hubs of discussion together with users engaging only in isolated interactions.
Second, the direct reciprocity of interaction (i.e., the fraction of replies
that are reciprocated within the time window considered) gets roughly halved
in the same time span. This signal, combined with the increase in expressions
of group identity (Figure 1(c)), is compatible with the emergence of
generalized reciprocity Yamagishi and Kiyonari (2000), a norm according to
which individual messages are not expected to receive direct responses;
comments are not perceived as pieces of a conversation but rather as
contributions to a collective discussion from which everyone benefits.

The complex and dynamic nature of the social network raises the question of
what is the typical position of committed users in the network, and whether
this position changes over time. To answer this question, we operationalise
the notion of network position with the concept of $k$_-core shell_ Seidman
(1983): the set of nodes in which every node is connected with other members
of the set with at least $k$ links. This measure is a good indicator of a
node’s centrality because it directly gauges embeddedness (the density of
connections around it), and it is a good proxy for reachability (how quickly
it can be reached from any other node of the network). For each temporal slice
of the network, we perform its $k$-core decomposition (see Methods), and we
measure the level of commitment exhibited in each $k$-core shell. Borrowing
from previous work Barberá  _et al._ (2015), we estimate the potential
influence that commitment events have on the community at large by measuring
not only the volume of commitment events in a shell, but also the number of
people that these events _reach_ —namely the number of WSB members who
commented on a post that is submitted by a committed node in that shell.

Figure 3 shows how commitment activity and its reach are distributed between
users in the core of the network (high $k$-core shells) and peripheral users
(low $k$-core shells), as a function of time. First, in Figure 3(a-b) we show
the fraction of commitment activity and reach that are generated by nodes
belonging to an increasingly large number of $k$-core shells, taken from the
core to the periphery. To disentangle the effect of the network’s evolution
from the distribution of commitment and reach on the network, and meaningfully
compare commitment distribution over networks reconstructed in different
periods, we contrast the observed commitment activity and its reach to a null
model benchmark which preserves the commitment but randomizes the network’s
topology (see Methods). In Figure 3(a-b), the curve being higher (lower) than
the benchmark indicates that commitment volume or reach are generated
predominantly by nodes in the core (periphery) of the network. For example, in
the network of interactions between November 11 and December 18, central nodes
are those who pledge more commitment to the GME cause (Figure 3(a)); on the
contrary, when considering interactions between January 20 and January 27,
commitment comes mostly from peripheral actors (Figure 3(b)).

To get a comprehensive picture of the coreness of committed users over time,
we measure the difference between the area below the observed curve and the
area below the benchmark curve at a given temporal slice, for all the slices
computed on networks reconstructed by using a rolling time window of 7 days.
Results are robust to the slicing strategy chosen for constructing the
networks (see Supplementary Information (SI), Sec. A.6, Fig. SI 6 and 7).
Figure 3(c) shows the value of such difference as a function of time. Relative
to the benchmark model, both commitment and reach are concentrated in the
network’s core until event _c_ (January 19). From that moment onward, the
commitment activity obtains a larger reach within the periphery. While always
remaining more concentrated in the core, the commitment activity spreads more
and more towards the periphery following event _c_. Therefore, the committed
minority which may have triggered the first price increase in the GME stock is
formed by central users in the discussion network unfolding on WSB. Only in
the last phases of the collective action, when the price has already increased
considerably, peripheral users step in and show commitment, which reaches more
peripheral peers.

Figure 3: _The evolution of commitment and reach._ (a-b) Fraction of observed
commitment activity (red line) and reach (blue line) produced by nodes
belonging to an increasingly large fraction of $k$-core shells (from core to
periphery). Curves constructed using the observed data (filled lines) are
compared to those obtained for the benchmark model (dashed lines). Results are
shown for two network slices, the first constructed between December 11 and
December 18 (a), the second between January 20 and January 27 (b). (c) Average
difference between the area below the observed curve and the area below the
benchmark curve over time, for commitment (red dashed-dotted line) and reach
(blue dashed-dotted line). Shaded areas corresponds to the $2$ standard
deviation area computed for each slice. Dashed vertical lines indicate
relevant events (see Table 1). For values of difference larger than zero (gray
shaded area), activity is concentrated in the core of the network, relative to
the benchmark model. Networks are constructed using a sliding window of $7$
days.

## Discussion

In this paper we showed that the collective action originated on Reddit and
culminated in the successful short squeeze of GameStop shares was driven by a
small number of committed individuals. We operationalised financial commitment
on Reddit as providing proof of stakes in a given asset, often in the form of
a screenshot. We then showed that events of commitment predated the initial
surge in price, which in turn attracted more participants to the GameStop
discussion and thus triggered new events of commitment. Finally, we described
how initial committed users were part of the core of the network of Reddit
conversations, and that the social identity of the broader group of Reddit
users grew as the collective action unfolds.

Our study focused on an single, unprecedented, event of financial collective
action. While this is certainly a limitation, as more events would allow us to
corroborate or falsify our findings, a prompt investigation of the GameStop
events was in order. The events that unfolded over the course of the few weeks
that we analysed in our study caused sustained effects on the market. Seven
months later (at the time of writing this manuscript), the value of the
GameStop stocks had risen by $1000\%$ compared to the beginning of 2021. The
price increase inflicted enormous financial losses to multiple hedge funds,
one of which was forced to shut down Fletcher (2021).

The influence of retail investors in equity markets is rapidly growing, and
now accounts for almost as much volume as hedge and mutual funds
combined.222https://www.ft.com/content/7a91e3ea-b9ec-4611-9a03-a8dd3b8bddb5
This rise has been mainly driven by the emergence of commission-free trading
platforms, that offer the possibility to trade fractions of shares, so that
users can start trading even with very small amounts. Moreover, these
platforms allow investors to use leverage, by buying and selling options and
accessing to cheap margin loans from brokerages, in a gamified user
experience. This “democratization of trading and investing” is unlikely to
disappear any time soon Aramonte and Avalos (2021), so other financial
collective actions might be coordinated in the future, possibly through
different social media channels.

In this perspective, beyond the role of committed individuals in promoting the
coordinated action, our findings have other potential implications to be
tested in future research. (i) The fact that initial committed individuals
were part of the core of the Reddit discussions implies that the system may be
resilient against adversarial attacks where freshly created “committed” bots
try to influence the community. (ii) The finding that identity was not the
driver of the collective action but, on the contrary, a byproduct of it may
imply that successive actions that leverage it might be easier to coordinate.
(iii) The change in network structure ensuing from the arrival of new users,
who joined the discussion motivated by the initial success of the squeeze, and
the corresponding shift of the bulk of commitment and reach from the core to
the periphery of the network, highlights the role of the system’s openness and
the hierarchies that catalyse a successful collective action.

Taken together, our findings highlight that financial collective action cannot
be reduced to the impact of social coordination on financial markets. The
effect –and, particularly, the success– of an action have profound
consequences on the membership, structure, and dynamics of the original group,
whose evolution may have in its turn consequences on future actions. Thus, the
initial committed individuals trigger a behavioural cascade which is self-
sustaining and transforms the group itself. More events and data are needed to
clarify this interplay between bottom-up processes of social coordination and
financial markets, and this is a direction for future work. Our results
represent a first step in this direction, and we anticipate that, as financial
collective action is expected to acquire even more importance in the future,
they will be of interest to researchers, industry professionals, and
regulators.

## Methods

### Data

We used two main sources of data: the activity on the subreddit
r/wallstreetbets and the price of GameStop shares, ticker GME.

Reddit is organized in communities, called _subreddits_ , that share a common
topic and a specific set of rules. Users subscribe to subreddits, which
contribute to the news feed of the user (their home) with new posts. Inside
each subreddit, a user can publish _posts_ (also called “submissions”), or
_comment_ on other posts and comments, thus creating trees of discussion that
grow over time. Users can attach _flairs_ to posts: a set of community-defined
tags to define the semantic scope of the post, thus facilitating content
search and filtering. Users can assign _awards_ to posts or comments to
recognize their value. Awards are sold by Reddit for money, they come in a
variety of types, and some of them reward the recipient with money or perks
such as access to exclusive subreddits.

We collected all posts and comments submitted to the r/wallstreetbets
subreddit from January $1$, $2016$ up to the beginning of February $2021$. We
did so by querying the Pushshift API Baumgartner  _et al._ (2020), which
stores all Reddit activity over time—using the PMAW wrapper Podolak (2021)
(see SI, Sec A.1 for more details). The API returns rich metadata, including
the timestamp of submission, the identity of the authors, its text content,
and the awards each submission and comment received. In total we retrieved
$1\,132\,897$ posts and $29\,566\,180$ comments submitted to the subreddit by
$1\,364\,080$ different authors. We specialize only to posts related to GME by
searching for posts containing either in the title of in the text-body the
word “GME” or “Gamestop” (lowercase occurrences included) and all the comment
trees associated with those submissions. This selected set consists of
$129\,731$ posts and $2\,575\,742$ comments. The period over which our study
focuses its attention (from November 27, 2020 to February 3, 2021) includes
$99\%$ of the posts and $98\%$ of the comments submitted since January 1, 2016
until February 3, 2021.

We retrieved GameStop daily prices from Yahoo Finance, using the Python
library yfinance Aroussi (2021), and computed the daily price return as the
daily relative change, $r(t)=\frac{p(t)}{p(t-1)}-1$ where $p(t)$ is the Open
price at day $t$.

### Quantifying commitment

Table 3: Commitment events per type. Count column shows the number of posts classified as commitment events because of a “YOLO”, “Gain”, “Loss’ flair, or a screenshot of commitment identified with our machine vision classifier. Unique count shows the number of posts uniquely classified by the commitment type. Event type |  Count |  Unique count |  Authors |  Unique authors
---|---|---|---|---
YOLO |  $23\,230$ |  $21\,455$ |  $20\,107$ |  $18\,484$
Gain |  $7\,293$ |  $6\,339$ |  $6\,160$ |  $5\,293$
Loss |  $2\,986$ |  $2\,387$ |  $2\,768$ |  $2\,198$
Pictures |  $5\,947$ |  $2\,619$ |  $5\,326$ |  $2\,478$

One of the widely-shared norms in the WSB community is to provide proof of one
own’s financial position when initiating a new discussion about investments
Boylston  _et al._ (2021). This is commonly achieved by supplementing
submissions with screenshots of open positions—typically gains, losses, or
orders—taken from online trading applications. We used these screenshots to
quantify commitment, as they provide a direct way to identify users who had
stakes in financial assets. To gather them, we employ two methods: _flairs_
and screenshots.

We use three flairs to mark posts containing a proof of position: the _gain_
and _loss_ flairs mark gains or losses for a minimum of $2500$ USD, and the
_YOLO_ flair indicates investment positions with a minimum value at risk of
$10\,000$ USD. Flair-tagged submissions are moderated and are approved only if
a relevant screenshot is attached. While it is mandatory for users to attach
investment screenshots to have flairs approved, they can also attach
screenshots to their submissions without using any flair.

As we are interested in capturing any signal of commitment, regardless of
their magnitude, we resort to machine vision to identify commitment
screenshots based on their visual content only. We retrieve all the
screenshots attached to any of the submissions in our dataset by querying all
URLs terminating with common image extensions (e.g., .png, .jpg). Out of this
set, we randomly sample $3745$ images and manually inspect them. We mark as
_positive_ all the screenshots which display gains, losses, or orders, and as
_negative_ all the remaining images, which include a broad variety of content
ranging from screenshots of stock prices to memes.

We label $1042$ positive examples and $2703$ negative examples. We use this
set of labeled images to train a supervised model. Among several classifiers
available off-the-shelf that we test, the most accurate is a PyTorch Paszke
_et al._ (2019) implementation of DenseNet Huang  _et al._ (2017), a deep
neural network architecture designed for image classification. We initialize
DenseNet with weights pre-trained on ImageNet Deng  _et al._ (2009), a widely-
used reference dataset of 1.2M labeled images. We then fine-tune the neural
network (i.e., update its weights) by training it further by feeding it 70% of
our labeled images. During fine-tuning, we use the Adam optimizer Kingma and
Ba (2014) to minimize cross-entropy loss. We then measure the classifier’s
performance on the remaining 30% of the examples by using _precision_ (the
fraction of pictures that the classifier labeled as positive that are actually
positive), _recall_ (the fraction of positive pictures that the classifier
labeled correctly), and F1 score (the harmonic mean between precision and
recall). On our validation set, the classifier achieves a precision of $0.85$,
a recall of $0.73$, and an F1 score of $0.77$.

We run the classifier on all images from r/wallstreeetbets and we merge the
posts which contain the images that the classifier marks as positive with the
set of flaired posts. In total, following this procedure we identify $3\,6128$
commitment events. Table 3 shows the number of commitment events divided by
event type. Posts can be classified as commitment events by flair type or
pictures of a holding position or both at the same time. The “unique count”
column shows the contribution to the identification of commitment events
uniquely coming from the single commitment type. In Figure SI 2 we show the
contributions of each commitment, revealing that commitments from “YOLO”
flairs are the dominant ones except for a three-days period in which the first
price surge was followed by a surge in the number of commitment events from
“Gain” flairs.

### Quantifying identity

To capture linguistic expression of identity, we use two methods. First, we
resort to a simple word count approach using Linguistic Inquiry Word Count
(LIWC). LIWC is a lexicon of words grouped into categories that reflect social
processes, emotions, and basic functions. It is based on the premise that the
words people use provide clues to their psychological states. In particular,
the abundant use of words in the LIWC category _we_ (i.e., first-person plural
subject pronoun) related to the use of words from the LIWC category _I_ (i.e.,
first-person singular subject pronoun) is a validated indicator of group
identity Tausczik and Pennebaker (2010). Therefore, we measure identity as the
fraction of pronoun _we_ against the number of both _we_ and _I_ pronouns
occurring in each submission text body. The results obtained with this
particular estimator of identity are robust when compared to two alternative
methods, which we discuss in SI.

### Discussion network on WSB

We reconstructed the network of social interactions on r/wallstreeetbets; each
node represents a user who submits a post or a comment on the subreddit, and
each directed link $(u,v)$ represents user $u$ commenting on a submission by
user $v$. The direction of the link represents an interaction, and it is
opposite to the information flow (user $u$ should have read what $v$ wrote to
answer, but it is not guaranteed that $v$ will read $u$’s reply). Considering
all nodes and interactions on WSB between authors discussing about GME, the
resulting networked components consist of $N=$450\,710$$ nodes and
$E=$2\,649\,108$$ directed links, activated over the entire period starting on
November 27, 2020 and concluding on February 3, 2021.

The time at which posts and comments are published can be used to obtain a
description of social interaction dynamics. We modeled such dynamic through
temporal _slicing_. In particular, we considered a rolling time window of
seven days and shift it by two hours throughout the whole timespan of our
dataset, for a total of $1092$ windows. For each time window, we constructed a
network using posts and comments published during that time window. We tested
alternative temporal slicing strategies, and discussed them in SI Sec. A.6.

For each slice, we characterized nodes with a number of features, including
their age (the time elapsed since their first interaction within the
community), in- or out-degree (number of incoming or outgoing edges), their
commitment (number of commitment events), or the reach of their commitment
(number of users who comment on their commitment events). We also ran $k$-core
decomposition Wasserman  _et al._ (1994) on the network of each temporal
slice. The algorithm partitions nodes by their _core shell_ (or core number),
i.e., the shell $k$, defined as the maximal subgraph in which every vertex has
at least degree $k$. The $k$-core decomposition algorithm does not take edge
directionality into account, and it considers the degree of a node as the sum
of its outgoing and incoming edges.

Null model for random commitment activity. When computing the commitment of
nodes as a function of their core number, to assess if committed users are
more central or peripheral in the network, it is important to compare with a
null model which takes into account the network’s topology. For this reason,
we consider a null model of random commitment in which committed events are
reshuffled randomly over the whole network, while the network’s structure is
preserved. The empirical commitment of nodes with core number $k$ is then
compared with a uniform distribution of commitment across nodes, which is
equivalent to averaging the results over an infinite number of random
shuffles.

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## Author contributions

All authors conceived and designed the experiments. L.L., L.M.A., L.A., and
G.D.F.M. performed the experiments. All authors contributed in analyzing the
data and writing the manuscript.

## Competing interests

All authors declare no competing interests.

## Supplementary Information

###  A.1 Data retrieval

We downloaded Reddit data mostly from Pushshift, an API which regularly copies
Reddit activity data directly from the Reddit API [32]. However, on January 25
and until January 27 the Pushshift servers interrupted from retrieving Reddit
comments. In our analysis we filled this gap in the data by calling the Reddit
API using the python wrapper PRAW [40]. Specifically, we requested the comment
trees for $234\,881$ posts and successfully retrieved the information for
$234\,866$ of them. The missing $15$ comment trees required an ad-hoc
procedure because of their size. We directly requested comments for such
submission by scraping the json version of their Reddit page and iterating
until the tree was completely reconstructed. The additional comments retrieved
following this two steps procedure are $322\,773$.

###  A.2 Measures of collective attention

Contrary to the sustained trend of commitment to the GME stock, which was
present days before the asset price grew, the involvement of large number of
people in the community occurred only weeks after the first signals of
commitment. To test the robustness of this observation, we complemented the
activity measure presented in Figure 1A with the number of WSB subreddit
subscribers, and its daily relative increment (see Figure 1 (a) and (b)).
Additionally, to measure exogenous interest towards GME, we gathered data from
Twitter. We queried the Twitter API for academic research (which allows to
retrieve tweets at any point in the past) to download tweets with the #GME or
#Gamestop hashtags posted between December 1st, 2020 and February 5th, 2021.
We collected a total of $5\,640\,149$ tweets, whose volume over time is shown
in Figure 1C. All indicators support the observation that commitment predates
not only the surge in prices but also the the mass attention that GME received
as a result of the short squeeze success.

Figure SI 1: _Measures of collective attention._ We compare the daily returns
(blue) with (a) total number of WSB subscribers in time, (b) daily relative
increment in subscriber number, and (c) Twitter activity, measured as the
volume of GME-related tweets.

###  A.3 Measures of commitment events

As discussed in the manuscript, we identified GME commitment events with a
two-step procedure. First we selected GME-related event by looking for
submissions whose title or text (the selftext field returned from the
Pushshift API) contains the token “GameStop” or the ticker name “GME” (both
either in uppercase or in lowercase letters). Then, we used the
r/wallstreeetbets subreddit flair classification system identifying as
commitment events those GME-related submissions with either “YOLO”, “Gain”, or
“Loss” flair. Additionally, we also include submissions sharing a screenshot
of a proof of ownership estimated using computer vision. In Figure 2, we show
the composition of commitment events for the four different categories.

Figure SI 2: _Composition of commitment events by flair and proof of
ownership._ The figure shows how the commitment events are distributed in time
over the period of interest. The number of commitment events are counted on a
daily basis. Commitment events are dominated for most of the time by “YOLO”
posts.

###  A.4 Measures of group identity

Figure SI 3: _Evolution of group identity in time_. Group identity over time
calculated as the fraction of messages that contain language expressions of
identity according to a deep-learning classifier (a), and average number of
Reddit awards that posts received at a given time (b). Raw signal is displayed
together with a smoothed signal on a 7-days rolling median.

Group identity is a broad concept that can be operationalized in multiple
ways. To check the robustness of the results obtained with LIWC, we
implemented two alternative measures of identity.

The first is based on language and uses a readily-available classifier of
identity expressions [41], implemented with a Long Short-Term Memory neural
network (LSTM) [42], a type of Recurrent Neural Network (RNN) that is commonly
used in a variety of NLP tasks [43]. Given in input a sentence, the classifier
outputs a score in the range $[0,1]$ that expresses the likelihood that the
message contains a verbal expression of identity. It is pre-trained on $9000$
manually-labeled sentences from Reddit and it achieves an Area Under the ROC
Curve (AUC) of $0.75$. AUC is a standard performance metric that assesses the
ability of a classifier to rank positive and negative instances by their
likelihood score, and gets the value of 1 for perfect probabilistic
classification. To each message, we assign an identity score equal to the
maximum score of its sentences. This approach reflects the theoretical
interpretation of the use of social dimensions in language [44]: a dimension
is conveyed effectively through language even when expressed only briefly.
Following the original approach [41], we binarize the identity scores using a
threshold equal to the value of the $90\textsuperscript{th}$ percentile of the
empirical distribution of all the scores; such a high threshold favors
precision over recall, thus focusing on a small set of messages that are very
likely to contain expressions of identity. To measure group identity over
time, we calculated the fraction of messages that the classifier marked as
positive.

As a second alternative measure of group identity, we used Reddit awards. The
practice of awarding is rather frequent in WSB, and it requires a fee from the
awarder (paid in virtual Reddit coins), thus representing a stronger
endorsement than upvoting a post or commenting on it. The abundant use of
awards has become a distinctive norm of WSB as a way to remark community
identity [17]. As a proxy of non-verbal identity, we calculated the average
number of awards received by submission within the time window considered.

Figure 3 shows that the frequency of linguistic expressions of identity
increases slowly over time, concurrent with the activity of commits, and it
soars considerably after the maximum peak of financial returns. The number of
assigned awards per post increased dramatically after the peak of returns,
likely as a signal of celebration of the community’s success, but spiked also
earlier in mid January, when the commitment activity started to increase
considerably. Overall, these results strengthen the evidence that a process of
identity construction has accompanied the dynamic of commitment.

###  A.5 Evolution of the discussion network in time

The discussion network about GME evolves in time, as new posts and comments
are continuously added. Not only the network is dynamics, but the topological
properties of static snapshots, i.e. the static networks reconstructed by data
collected within fixed time intervals, change in time, reflecting the non-
stationary evolution of the discussion structure. This behavior is showed in
Fig. 2 of the main text and more in detail in Figure 4, which displays five
different snapshot constructed by slicing the data in such a way that each
network has a total of $3\,000$ unique authors interacting in the specific
time window. With this technique, the size of the windows changes depending on
the frequency of posting. In particular, while in mid-December and at the
beginning of January to build a network with $300$ different authors requires
to aggregate within the same slice data from multiple days, after mid-January
2021 such a number of unique authors is interacting in few hours or less.

Figure SI 4: _The evolution of the discussion networks._ Networks are built in
such a way that each snapshot contains $3\,000$ different nodes. While before
December 2020 involving thousands of authors in the discussion required
several days of WSB activity, in late January 2021 thousands of users were
interacting and discussing the topic simultaneously, reaching the $3\,000$
limit in less than one hour.

In the main text, we showed that the network’s topology strongly changes in
time, indicating that the structure of the discussion evolves towards a
collective conversation. Fig. 5 shows a few more features supporting this
picture. In particular, in Fig. 5(a), we show how, as the process evolves, the
age of users discussing on the subreddit decreases significantly. At the same
time, Fig. 5(b) shows how the number of isolated components of the network
constructed with windows of the duration rapidly increases after event “b”.
Figure 5(c) complements this finding, revealing that, as the number of
components grow, the average number of nodes within the component decreases.
Here we use as components the strongly connected components of each directed
network constructed from a $7$ day window. The low average also reveal that
the vast majority of components consists of only few nodes commenting a
submission without “out-of-comment-tree” and no-reciprocal interactions.
Figure 5(d) shows the evolution of the average node degree in time. Its
increase starts right after the new directors announcement (event “b”).

Figure SI 5: _Topological properties of the discussion networks as a function
of time._ (a) Average number of days since first submission for authors
interacting within a $7$ day window. (b) Number of network components. (c)
Number of nodes per component, excluding the giant component and its nodes.
(d) Average degree of the networks.

###  A.6 Robustness of commitment activity and reach with respect to the
network’s reconstruction

The way in which the discussion network is reconstructed is determinant to
measure the distribution of commitment activity and its reach on the network.
While in the main text we showed results for a temporal slicing (networks are
constructed slicing data within a 7-days window), here we present the results
for two additional slicing strategies: windows of data with a constant number
of unique authors or submissions.

Figure SI 6: _Evolution of commitment and reach on networks with $3\,000$
nodes per network slice. Equivalent to Figure 3 of the main text._

Figure SI 6 shows the evolution of commitment and reach on networks with
$3\,000$ nodes per slice. Imposing each slice to have a fixed number of
authors is equivalent to requiring that each network slice has a fixed number
of nodes. Importantly, we stress that the slicing is pruning links between
authors which are activated at times $t<t_{start}$ or $t\geq t_{end}$, where
$t_{start}$ is the lower time-bound of the slice, while $t_{end}$ is the upper
time-bound of the slice, i.e. the time at which the $3\,001th$ author is
activating a new link. Panel (a) and (b) shows the cumulative distribution of
commitment and reach (red and blue respectively) as a function of node
coreness (from more central nodes to the peripheral ones). Two slices are
selected from two different time windows, one at mid-December 2020 and the
second during January 28,2021. Panel (c) shows a significant reduction in the
commitment and reach from core nodes also with this slicing strategy.

Figure SI 7: _Evolution of commitment and reach on networks with $500$
submissions per network slice. Slicing is performed rolling the window
including each time the next $25$ posts submitted and removing the oldest
$25$. Equivalent to Figure 3 of the main text._

Figure SI 7 shows the evolution of commitment and reach on networks
constructed including all posts and comments within the temporal boundaries
delimited by the oldest and latest time of a consecutive set of $500$ posts.
In this framework while $t_{start}$ is the time at which the oldest post was
submitted, $t_{end}$ is the time at which the $501th$ post is submitted. Also
in this case, all links activated outside these temporal boundaries are
neglected from the analysis. Also this slicing technique shows a significant
reduction in the commitment and reach from core nodes, confirming the results
discussed in the main text.