POL101-2
Need a couple of paragraphs based on the following:
Read the articles by Gaumont, Panahi, and Chavalarias (2018(Links to an external site.)), Keating and Ellis (2017),(Links to an external site.) and Kiss, Rodrguez-Lara, and Rosa-Garca (2017),(Links to an external site.) which are required reading for this week. What impact does social media have on political participation? What are the pros and cons of social media as it pertains to politics? What is the role of social media in your own political education and participation?
Be sure to post an initial, substantive response. A substantive initial post answers the question presented completely and/or asks a thoughtful question pertaining to the topic.
Soc Choice Welf (2017) 49:329355
DOI 10.1007/s00355-017-1067-3
ORIGINAL PAPER
Overthrowing the dictator: a game-theoretic approach
to revolutions and media
Hubert Janos Kiss1,2 Ismael Rodrguez-Lara3
Alfonso Rosa-Garca4
Received: 13 January 2016 / Accepted: 8 June 2017 / Published online: 16 June 2017
The Author(s) 2017. This article is an open access publication
Abstract A distinctive feature of recent revolutions was the key role of social media
(e.g. Facebook, Twitter and YouTube). In this paper, we study its role in mobilization.
We assume that social media allow potential participants to observe the individual
participation decisions of others, while traditional mass media allow potential par-
Hubert Janos Kiss: MTA KRTKResearch fellow in the Momentum (LD-004/2010) Game Theory
Research Group.
We are grateful for comments and suggestions from participants at the MKE Conference in Budapest and
the SING 2014 Meeting on Game Theory in Krakow, and seminar participants at the Corvinus Game
Theory Seminar (Budapest), the Universidad de Murcia and Universidad de Malaga (Spain). Hubert Janos
Kiss gratefully acknowledges financial support from the Spanish Ministry of Economics under research
project ECO2014-52372, the Jnos Bolyai Research Scholarship of the Hungarian Academy of Sciences
and the National Research, Development and Innovation (NKFIH) under the project K 119683. Ismael
Rodriguez-Lara and Alfonso Rosa-Garcia acknowledge financial support from the Spanish Ministry of
Economics under research projects ECO2014-58297-R, ECO2013-45698-P and ECO2016-76178-P.
B Ismael Rodrguez-Lara
[emailprotected]
Hubert Janos Kiss
[emailprotected]
Alfonso Rosa-Garca
[emailprotected]
1 MTA KRTK KTI, Budarsi t 45, 1112 Budapest, Hungary
2 Department of Economics, Etvs Lornd University, Lgymnyosi Campus, Budapest 1117,
Hungary
3 Department of Economics, Middlesex University London, Hendon Campus, The Burroughs,
London NW4 4BT, UK
4 Facultad de Ciencias Jurdicas y de la Empresa, Universidad Catlica San Antonio de Murcia,
Campus de Los Jernimos, s/n Guadalupe, 30107 Murcia, Spain
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http://orcid.org/0000-0003-3666-9331
http://orcid.org/0000-0002-0739-6234
330 H. J. Kiss et al.
ticipants to see only the total number of people who participated before them. We
show that when individuals willingness to revolt is publicly known, then both sorts
of media foster a successful revolution. However, when willingness to revolt is private
information, only social media ensure that a revolt succeeds, with mass media multiple
outcomes are possible, one of which has individuals not participating in the revolt.
This suggests that social media enhance the likelihood that a revolution triumphs more
than traditional mass media.
We use Facebook to schedule protests, Twitter to coordinate, and YouTube to tell the world.
Anonymous Cairo Activist
1 Introduction
Coordination failures occur when individuals do not act in unison to achieve an
outcome that would benefit them. Examples include, among others, poverty traps,
economic cycles or inefficient conventions (Masiliunas 2017; Cooper and John 1988;
Adsera and Ray 1998; Morris 2014). In these settings, individuals may benefit from
choosing an action that changes the status quo, but it would require the coordina-
tion of a sufficient number of individuals to do so. Revolutions are also akin to these
setups. Citizens that protest might change a bad regime if the number of participants
is above a certain threshold. One issue to be considered is that part of the population
might be unwilling to participate in the revolt. In this paper, we look at the effect of
communication technology (mass or social media) to overthrow a dictator when the
majority wants to change the regime, but there is heterogeneity of types and part of
the population is unwilling to change the status quo.
In the last years, there have been many mass mobilizations that attracted con-
siderable public attention internationally. The mass protests that started the uprisings
against the regimes in the Arab world, the demonstrations of the Indignados movement
in Spain, the Occupy Wall Street movement or the Hong Kongs Umbrella revolution
are the most prominent examples. A distinguishing feature of these events was the
omnipresence of social media (especially, Facebook, Twitter and YouTube). Many
scholars (e.g. Castells 2011; Edmond 2013; Manacorda and Tesei 2016; Enikolopov
et al. 2016) wonder how these new information technologies affect social movements.
Do they help to overthrow autocratic regimes more easily than the former technology?
Social media affect the evolution of protests in various ways. First, social media
provide access to alternative information about the true state of the economy and
the governments performance. This information may be limited under mass media,
especially when the government controls it. Social media help to inform audiences
around the world about the unfolding of the events, attracting international attention
and provoking diplomatic pressure. Finally, social media offer an easy, quick and
inexpensive means of communication that facilitates the spread of information among
the participants. This, in turn, may help to foster coordination, a key factor to achieve
the goals of any movement. One interesting insight along these lines is one by Daron
Acemoglu. When asked about overthrowing dictators he pointed out the following: It
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Overthrowing the dictator: a game-theoretic approach. . . 331
is a question of coordinating peoples beliefs, I need to know if other people agree with
me and are willing to act. What really stops people who are oppressed by a regime
from protesting is the fear that they will be part of an unsuccessful protest. When you
are living in these regimes, you have to be extremely afraid of what happens if you
participate and the regime doesnt change.1 Descriptions of the recent revolutions
seem to highlight the importance of social media in efficient mobilization. Individuals
fear that not enough people will go to the protests, so uncertainty about the turnout is
a major obstacle. When mass media (e.g., TV or radio) report about attendance, then
the audience does not know the reasons why individuals did not go. In social media
these reasons can be revealed. For instance, Ghonim (2012) mentions the existence
of opinion polls online to find out why people decided (not) to go to the protest. The
comments on Facebook help also to get insight into the decision-making of others
and serve to raise spirits. Ghonim describes that he was surprised to see among the
supporters persons that he did not expect to see. All this together helps to break the
barrier of fear (Ghonim 2012) and allows individuals know that they are enough and
together they can bring down the dictator.
Although social media seem to have a notable effect on mobilizing the masses, we
lack a formal model that attempts to capture its effects on mobilization. In this paper,
we use game theory to show how this technology may help to change the status quo in
an autocratic regime. Our starting point is that willingness to participate in the protests
depends on the perceived costs and benefits of participation. Arguably, heading out
onto the streets implies the costs of facing tear gas, rubber bullets and potential arrest
and incarceration. Benefits involve the perceived gains in participating in an uprising
that may bring about a better future, provided it succeeds. The probability of success
is highly related to the number of participants. Yet, when a potential protester decides
whether to participate, possibly she has only a vague idea about if sufficient other
people will participate. Different types of media may affect these beliefs (and the
resulting mobilization) in diverse ways.
To investigate the effects of social media on mobilization, we study how individuals
decisions to participate in the revolution are affected by two different communication
technologies: mass and social media. We posit that when an individual obtains infor-
mation through mass media then she gets to know the actual state of the revolution
in that moment, whereas when informed via social media she is able to observe the
sequence of decisions leading up to that state. For instance, when searching in Twitter
the individual gets the last conversations about the topic, and by scrolling down the
page she is able to see all previous tweets about it, the use of hashtags indeed facil-
itates this task. In Facebook, the users may comment on the events and all previous
comments can be read. When people chat in a group with Whatsapp, the complete
talk is recorded in the smartphone of each participant. We suppose that tweets, chats
and comments are informative about the individuals decision to join the protests or
1 The New York Times, February 17, 2011, Web Solutions Applied to the Problem of Toppling Autocrats,
retrieved from http://www.nytimes.com/2011/02/18/world/americas/18iht-letter18.html?_r=0 on July 14,
2014. Manacorda and Tesei (2016) posit a similar argument and discuss the possible benefits of information:
Knowledge, albeit imperfect, of others likelihood of participating can, in particular, foster individuals
willingness to participate, and lead to the emergence of protests in equilibrium, an outcome that would not
result in a world where individuals act atomistically. (page 3).
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http://www.nytimes.com/2011/02/18/world/americas/18iht-letter18.html?_r=0
332 H. J. Kiss et al.
to stay at home. As stated by participants in the Hong Kongs Umbrella revolution, If
your friends ask you to join the protest, they just Whatsapp you: Hey, I am going, are
you? Then you quickly decide. (Parker 2014). By contrast, when TV or radio inform
about the state of a given event, the precise history remains hidden, only aggregate
information about the turnout is reported.2
We rely on these distinctive features of mass and social media and model the prob-
lem of revolution as a coordination problem. We suppose that there are two groups in
the society. One of them consists of individuals who want to overthrow the dictator
(willing individuals). The another one is composed of individuals who do not want
to change the regime but prefer the status quo (unwilling individuals). We assume
that there are enough willing individuals to bring about a change and overthrow-
ing the dictator is the socially efficient outcome. That is, if all willing individuals
revolt, then the dictator is toppled. However, if the number of protesters (those will-
ing individuals who actually head onto the streets) falls short of a critical mass, then
the dictator remains in power and may punish those who participated in the failed
revolt.
We assume that individuals choose in sequence whether or not to revolt. Before
making her decision, each individual is informed about the state of the revolution. The
information that an individual receives depends on the communication technology.
As discussed above, mass media allow individuals to learn how many people have
already chosen to participate (i.e. the actual state of the revolution), whereas individ-
uals observe each of the past decisions (e.g. the precise history) when information is
channeled through social media.
First, we show that when the type of individuals (that is, if she is willing to revolt
or not) is public information, willing individuals take part in the revolution in case of
both communication technologies and, thus, the dictator is overthrown. Interestingly
enough, it is not necessarily the case when there is no communication technology and
thus individuals receive no information about the state of the revolution. If willing
individuals believe that other willing individuals will not revolt, then it is possible to
have an equilibrium outcome where nobody revolts. This, in turn, shows that the mere
existence of communication technologies (i.e., mass or social media) can facilitate that
social movements achieve their objective by shrinking the set of beliefs, compared with
the case in which no information is disclosed.
Second, we study a more realistic setup in which the type of individuals is not
observed (i.e. it is private information). Although it is common knowledge in our
model that there are enough willing individuals in the society to change the regime,
the type of communication technology becomes relevant in this setup. We show that
mass media do not necessarily enable willing individuals to organize themselves effi-
ciently. Thus, depending on the perceived costs and benefits, willing individuals might
choose not to revolt in equilibrium. However, successful revolution is the unique
equilibrium outcome when individuals use social media, independently of the sever-
ity of punishment that protesters may suffer if they fail to overthrow the dictator.
2 There are features of social media that foster spreading information quickly and to a wide audience.
For instance in the case of Twitter retweeting allows to repost a content referencing to the source of the
content; trending topic highlights content that an in-built algorithm considers collectively relevant.
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Overthrowing the dictator: a game-theoretic approach. . . 333
This result shows that communication through social media facilitates that revolu-
tions succeed more than when communication is channeled through traditional mass
media.
Although our comparison of mass and social media suggests that they are competing
communication technologies, our results are aimed at answering the question about
how social media enhance mass medias ability to mobilize individuals. The results
gleaned from the empirical evidence support the idea that citizens perceived social
media to be very important during the Arab Spring (Howard et al. 2011; Lang and De
Sterck 2014), including the Tunisian revolution (Marzouki et al. 2012) or the protests
in Egypt (Attia et al. 2011; Azab 2012; Lim 2012; Tufekci and Wilson 2012). Hence,
microblogging activity (Qin et al. 2016) or the amount of tweets (Acemoglu et al.
2014; Steinert-Threlkeld et al. 2015) might have been related to the incidence and
the intensity of protests. There is indeed a causal relationship between social media
and mobilization according to Manacorda and Tesei (2016) and Enikolopov et al.
(2016). Manacorda and Tesei (2016) study how coverage of mobile phone signals
affected the occurrence of protest and individual participation on the whole African
continent between 1998 and 2012.3 They show that mobile phones promoted protests
and helped mass mobilization during economic downturn. Enikolopov et al. (2016)
show that the penetration of VK, the dominant Russian online social network, affected
protest participation in a series of protest during 2011. More concretely, a 10% increase
in penetration increased the probability of a protest by almost 5% and the number of
participants by roughly 20%.
Section 2 reviews briefly the relevant literature. Section 3 presents our model. We
derive our theoretical results in Sect. 4, where we also discuss the application of our
model, by presenting two examples in which we assess the differences between mass
and social media in yielding different outcomes in a revolution. We discuss some
caveats of our model and possible extensions in Sect. 5. Section 6 concludes. All the
proofs are relegated to the Appendix.
2 Literature review
In this section first we show why observability of actions and social networks (that are
the basis of social media) are important in the evolution of revolts. Then we go over
the most relevant and recent theoretical papers on revolutions and the corresponding
literature on coordination games.
Our interpretation of the process why an individual joins a protests follows the
rationalist view that the citizens assess the costs and benefits of participating in a
revolt (see, for instance, Goldstone 2001 and the references therein).4 Social networks
play an important role at several stages of the process. Passy (2003) claims that social
media create social networks that are important in community creation, in connecting
3 The authors point out that in Africa there is a lack of fixed phone line and high-speed Internet cabling,
so generally mobile phones provide the access to the Internet and social media.
4 There are other views on protests that emphasize the role of identity and social-psychological factors
(see for instance, Klandermans 1984). In revolts, both rational and non-rational elements play a role, in this
paper we focus on the former ones.
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334 H. J. Kiss et al.
the prospective participants and also in the decision-making, since individuals use the
information coming from the social network to anticipate and evaluate the potential
costs and outcome of participation. Gunitsky (2015) and Battaglini (2017) highlight
also the effects of social media in allowing individuals to communicate their informa-
tion. Importantly, the decision to join the revolution depends also on the intentions and
action of other participants. If many other citizens are expected to join, then the revo-
lution is likely to succeed and this makes participation more attractive. In the opposite
case, staying at home may be the optimal decision. Both mass and social media enable
individuals to form beliefs about the turnout at the protest. Our approach aims to show
that social media promote better mobilization, because from an individuals point of
view they give more accurate information about previous decisions and they allow that
subsequent individuals observe the decision. The fact that decisions can be observed
and may affect the behavior of others relates our work to models of informational
influence; i.e., herding and informational cascades (e.g., Banerjee 1992; Bikhchan-
dani et al. 1992, 1998). However, in these models there is a clear best choice (e.g.,
which restaurant or product is better) and individuals have some private information
about it. Individuals update their signals upon observing the decision of others, thus
it may be rational to follow others to choose the payoff-maximizing alternative. In
our setting, there is heterogeneity of types in that willing and unwilling individuals
have different preferences. Relevant to our setting, willing individuals should revolt
in equilibrium only if the revolution turns out to be successful, thus a coordination
problem is embedded in our framework. These features make our paper divert from
the literature on informational influence.
Turningtotheoreticalmodelsofrevolutions,acommonpointinmostofthesepapers
is that the regime can be overthrown if enough citizens participate in an uprising. The
studies differ mainly in (i) what types of individuals they assume, (ii) if the individuals
have different willingness to revolt, (iii) the channels of coordination (e.g., what can
be observed?), and (iv) the regimes role. De Mesquita (2010) assumes the existence
of a vanguard, a continuum of citizens with varying antigovernment sentiment and
a passive regime. It is a pure coordination game with simultaneous moves after the
vanguard chose the level of costly violence. The vanguard uses violence and it is
informative about the discontent in the society and individuals sensing the increased
dissatisfaction are more likely to join the revolution.5 Individuals do not observe other
individuals decision to join the protest, therefore the role of media is disregarded
in this model, which has multiple equilibria: with and without successful regime
change. Chwe (2000) is the closest paper to ours in spirit. He assumes two types
of individuals: willing (those who want change and are ready to go to the streets)
and unwilling (those who stay at home). In his model, the social network allows
individuals to communicate their private type (e.g., Gunitsky 2015; Battaglini 2017).
Chwe characterizes the minimal sufficient networks that make coordination feasible
among willing individuals, regardless on the prior beliefs about the willingness of the
others. He shows the importance of cliques (a subset of individuals where everybody is
5 Barbera and Jackson (2016) argue that demonstrations may help in providing information to enable
revolutions. See also Ginkel and Smith (1999) for a model in which a group of willing individuals choose
whether or not to revolt before the mass public.
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Overthrowing the dictator: a game-theoretic approach. . . 335
linked to everybody else). In our setting the main difficulty comes from what a willing
individual believes when observing that somebody stays at home (i.e., she can be an
unwilling individual who does not want to change the regime or a willing individual
that prefers not to revolt). Our approaches differ in that we do not allow individuals
communicate their willingness to participate using the network, but to observe the
action of others. Chwe (2000) also looks at the minimal sufficient network for the
revolution to succeed, while we assume that the network is complete and study how
different sorts of information (mass vs. social media) might help to overthrow the
dictator.6 Ellis and Fender (2011) is also akin to our approach in that observing other
individuals behavior is possible. This helps to make inferences about the information
that other individuals have about the state of the world. The revolution is successful
if an information cascade forms and poor agents rebel. We do not have a herding
model as Ellis and Fender (2011) and contrary to their model individuals in our setup
revolt only if they can be sure that the uprising will succeed. Edmond (2013) studies
the revolution also as a coordination game in a global games framework. Citizens are
ex ante identical and then they receive noisy signals about the regimes strength from
several media outlets, but not about the decisions of other citizens. Lang and De Sterck
(2014) show that mobilization is successful only if protesters are enthusiastic enough
and their action is visible.
In the previous papers, revolution is modeled as a coordination problem that might
be overcome in different ways. In the models without observing other citizens deci-
sions (De Mesquita 2010; Edmond 2013) observing correlated signals makes a revolt
potentially successful. In the models where observing other individuals plays a role
(Ellis and Fender 2011; Lang and De Sterck 2014) there is only one type of individuals
and if enough of them decide to revolt, then the dictator is overthrown. Our model
attempts to capture the uncertainty involved in mobilization, resorting to unwilling
individuals whose choice is always the same. Arguably, their presence makes coor-
dination difficult, since a willing individual who observes somebody staying at home
does not know if it is due to an unwilling citizen or a willing one who decided not
to participate in the revolt. This feature makes our paper divert from the literature
on global games (Carlsson and Van Damme 1993; Morris and Shin 2003; Angeletos
et al. 2007) where introducing (and not removing) some uncertainty might help in
efficiently resolving the multiple equilibria problem, yielding a unique equilibrium
prediction.
3 The model
We study in a model how different communication technologies determine the out-
come of a revolt. Suppose a finite set of individuals, N = {1, 2, . . . , n} and a dictator.
Each individual chooses an action ai {r, s} where r means revolt and s stay at
home. Each individual i is either of type i = w (willing to revolt) or i = x (unwill-
6 The network structure in Chen et al. (2016) is such that individuals receive information about about the
strength of the regime, and then communicate to each other the informativeness of the rumor. Kiss et al.
(2016) is also related to Chwe (2000) in that they look at the minimal sufficient network, but in line with
our modeling choice they assume that the network allows for the observability of actions.
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336 H. J. Kiss et al.
ing). Willing individuals are ready to participate in protests, unwilling individuals are
reluctant to do so. We denote by W the amount of individuals that are willing to revolt,
i.e., #{i : i = w} = W , where W (0, n).
Individuals decide in a sequence. Let the type vector = (1, 2, . . . , n) denote
the sequence of individuals.7 The set of sequences of length n with W willing citizens
is given by
n,W = { : #{ j : j = w} = W }.
There are
( n
W
)
possible type vectors and any of them is selected with equal proba-
bility.8
We suppose that the index of the individual (i N) corresponds to her position
in the sequence of decisions. The utility of each individual i depends on her type and
the outcome of the revolution. The revolution is successful if at least t individuals
decide to revolt (i.e., #{ j N : aj = r} t), otherwise the dictator will remain
in power. We follow De Mesquita (2010) and assume that the value of the threshold
is common knowledge.9 We consider the case in which W t and W is common
knowledge, so that individuals know that there are sufficient people willing to revolt.10
Changing the regime is assumed to be the socially efficient outcome (as it will also
be clear from the payoffs). Although it is common knowledge that there are sufficient
willing individuals in the society to change the regime, and overthrowing the dictator
is efficient, the change requires coordination. This, in turn, depends on the individuals
expected costs and benefits of participating in the revolt.
Let ai be the action chosen by individual i and let a = (a1, a2, . . . , an) be the
profile of actions. A willing individual that decides to stay at home (ai = s) will
receive utility uw,s. If the willing individual decides to participate in the revolt, the
utility will depend on whether the revolt succeeds (uw,r,R) or fails (uw,r,F), where
uw,r,R > uw,s > uw,r,F is assumed.
11 In words, willing individuals utility is highest
when they participate in a successful revolution (uw,r,R). If they stay at home, they
derive less utility (uw,s), although the smallest utility is derived when individuals take
part in a revolution that is defeated. The payoff uw,r,F can then be interpreted as the
7 Abusing somewhat the notation, denotes a sequence of individuals, but also the set of individuals in the
sequence.
8 This, in turn, implies that we study any possible configuration that may occur in equilibrium in a pre-
game, in which individuals have to choose when to decide. We are not aware of any paper that studies how
the sequence of decision in a revolt is determined. We discuss this issue in Sect. 5.
9 Schelling (1978) and Granovetter (1978) use models with individual thresholds to study problems that
involve collective action. In Edmond (2013) or Angeletos et al. (2007) there is uncertainty about the
threshold. In Chwe (2000) each person has an individual threshold.
10 If W < t, then it is clear that individuals do not revolt in equilibrium.
11 Note that in the utilities, the first subscript refers to the type of the individual, the second to the action
that she undertakes, whereas the third one indicates the outcome. R represents a successful revolution, while
F denotes that it has failed.
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Overthrowing the dictator: a game-theoretic approach. . . 337
punishment that the dictator imposes on protesters who participate in a revolution that
fails, suffering this punishment being the potential cost of participation.12
We assume that unwilling individuals will not participate in the revolt (whatever
reasons they might have). The utility of an unwilling individual that revolts (ux,r) is
therefore assumed to be smaller that the utility of an unwilling individual that stays at
home (ux,s). This, in turn, implies that it is always optimal for an unwilling individ-
ual to stay at home. Interestingly, the presence of these individuals complicates the
coordination among willing individuals. A willing individual who observes somebody
staying at home does not know if it is due to an unwilling citizen or a willing one who
decided not to participate in the revolt.
Given our payoffs, the first best is achieved when willing individuals coordinate and
overthrow the dictator. The reason is that unwilling individuals utility is not affected
by the outcome of the revolt, whereas willing individuals are better off if the uprising
is successful.
Our paper is an attempt to show how different communication technologies may
affect the outcome of the revolution. Individuals decide in sequence whether or not to
revolt and they have information about past decisions that is available to individuals
depending on the communication technology as follows:
No technology Individuals do not have any information on previous choices when
deciding.
Mass media technology Individuals have aggregate information about the actions
thathavebeenalreadytaken(e.g.,numberofpredecessorsthatdecidedtorevoltand
stay at home). This represents a situation in which individuals obtain information
through radio or television about the state of the revolution before making their
own decision.
Social media technology Individuals observe the individual action of each prede-
cessor. This means that individual i knows exactly which action was chosen by
each of her i 1 predecessors. This represents a situation in which individuals
obtain information through Facebook or Twitter (or any other social media), in
which individuals may observe the exact history of previous decisions.
To formalize the different communication technologies, let i denote the infor-
mation that individual i has. When no communication technology is available, then
i = {i }; i.e., individuals only know their own types, but nothing about other indi-
viduals decisions. Mass media technology implies i = {i , i , i i 1} where
i represents the number of individuals who have decided to revolt up to individual
i (i = #{aj = r, j < i}); i.e., individuals know the amount of predecessors who
decided to participate in the revolt, and then the number of individuals who decided
to stay at home. In the spirit of Lohmann (1993, 1994a,b) we assume that each previ-
12 The utility of staying at home may depend on whether the revolution triumphs or not. A successful
revolt may bring better life to a willing individual who by staying at home avoids the costs of the revolution.
Thus, there may be free-riding issues at stake as well (see for instance Lohmann 1993). Although these are
interesting questions (and promising venues of future research), we deliberately disregard this issue to focus
on the coordination problem embedded in the above payoffs. In this regard, our payoffs generate a game
that resembles the classic stag-hunt situation, although the presence of unwilling individuals complicates
the analysis.
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338 H. J. Kiss et al.
ous decision (ordered according to the position) is observed under social media. The
available information then is i = {i , {aj , j < i}}.
In Fig. 1, we depict a reduced extensive-form representation of the game generated
by each communication technology in a simple society of n = 4 individuals in which
W = 3 of them are willing to revolt. We name it reduced form because we have
simplified the representation by drawing only one of the four branches that would
follow each of the type vectors. At the beginning of the game, nature selects at random
one of them. In the four possible type vectors willing citizens are represented by
black circles and the unwilling one by a white circle. We assume that individuals only
observe actions but not types, so individuals are represented by grey circles in the rest
of the tree.13 We derive in Sect. 4 the theoretical predictions of our model both when
types are observed and when they are private information.
At the top of Fig. 1, we repr
