Overthrowing the dictator: a game-theoretic approach to revolutions and media

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1 Soc Choice Welf (2017) 49: DOI / ORIGINAL PAPER Ovethowing the dictato: a game-theoetic appoach to evolution and media Hubet Jano Ki 1,2 Imael Rodíguez-Laa 3 Alfono Roa-Gacía 4 Received: 13 Januay 2016 / Accepted: 8 June 2017 / Publihed online: 16 June 2017 The Autho() Thi aticle i an open acce publication Abtact A ditinctive featue of ecent evolution wa the key ole of ocial media (e.g. Facebook, Twitte and YouTube). In thi pape, we tudy it ole in mobilization. We aume that ocial media allow potential paticipant to obeve the individual paticipation deciion of othe, while taditional ma media allow potential pa- Hubet Jano Ki: MTA KRTK Reeach fellow in the Momentum (LD-004/2010) Game Theoy Reeach Goup. We ae gateful fo comment and uggetion fom paticipant at the MKE Confeence in Budapet and the SING 2014 Meeting on Game Theoy in Kakow, and emina paticipant at the Covinu Game Theoy Semina (Budapet), the Univeidad de Mucia and Univeidad de Malaga (Spain). Hubet Jano Ki gatefully acknowledge financial uppot fom the Spanih Minity of Economic unde eeach poject ECO , the Jáno Bolyai Reeach Scholahip of the Hungaian Academy of Science and the National Reeach, Development and Innovation (NKFIH) unde the poject K Imael Rodiguez-Laa and Alfono Roa-Gacia acknowledge financial uppot fom the Spanih Minity of Economic unde eeach poject ECO R, ECO P and ECO P. B Imael Rodíguez-Laa I.Rodiguez-Laa@mdx.ac.uk Hubet Jano Ki ki.hubet.jano@ktk.mta.hu Alfono Roa-Gacía aoa@ucam.edu 1 MTA KRTK KTI, Budaöi út 45, 1112 Budapet, Hungay 2 Depatment of Economic, Eötvö Loánd Univeity, Lágymányoi Campu, Budapet 1117, Hungay 3 Depatment of Economic, Middleex Univeity London, Hendon Campu, The Buough, London NW4 4BT, UK 4 Facultad de Ciencia Juídica y de la Empea, Univeidad Católica San Antonio de Mucia, Campu de Lo Jeónimo, /n Guadalupe, Mucia, Spain

2 330 H. J. Ki et al. ticipant to ee only the total numbe of people who paticipated befoe them. We how that when individual willingne to evolt i publicly known, then both ot of media fote a ucceful evolution. Howeve, when willingne to evolt i pivate infomation, only ocial media enue that a evolt ucceed, with ma media multiple outcome ae poible, one of which ha individual not paticipating in the evolt. Thi ugget that ocial media enhance the likelihood that a evolution tiumph moe than taditional ma media. We ue Facebook to chedule potet, Twitte to coodinate, and YouTube to tell the wold. Anonymou Caio Activit 1 Intoduction Coodination failue occu when individual do not act in union to achieve an outcome that would benefit them. Example include, among othe, povety tap, economic cycle o inefficient convention (Mailiūna 2017; Coope and John 1988; Adea and Ray 1998; Moi 2014). In thee etting, individual may benefit fom chooing an action that change the tatu quo, but it would equie the coodination of a ufficient numbe of individual to do o. Revolution ae alo akin to thee etup. Citizen that potet might change a bad egime if the numbe of paticipant i above a cetain thehold. One iue to be conideed i that pat of the population might be unwilling to paticipate in the evolt. In thi pape, we look at the effect of communication technology (ma o ocial media) to ovethow a dictato when the majoity want to change the egime, but thee i heteogeneity of type and pat of the population i unwilling to change the tatu quo. In the lat yea, thee have been many ma mobilization that attacted conideable public attention intenationally. The ma potet that tated the upiing againt the egime in the Aab wold, the demontation of the Indignado movement in Spain, the Occupy Wall Steet movement o the Hong Kong Umbella evolution ae the mot pominent example. A ditinguihing featue of thee event wa the omnipeence of ocial media (epecially, Facebook, Twitte and YouTube). Many chola (e.g. Catell 2011; Edmond 2013; Manacoda and Teei 2016; Enikolopov et al. 2016) wonde how thee new infomation technologie affect ocial movement. Do they help to ovethow autocatic egime moe eaily than the fome technology? Social media affect the evolution of potet in vaiou way. Fit, ocial media povide acce to altenative infomation about the tue tate of the economy and the govenment pefomance. Thi infomation may be limited unde ma media, epecially when the govenment contol it. Social media help to infom audience aound the wold about the unfolding of the event, attacting intenational attention and povoking diplomatic peue. Finally, ocial media offe an eay, quick and inexpenive mean of communication that facilitate the pead of infomation among the paticipant. Thi, in tun, may help to fote coodination, a key facto to achieve the goal of any movement. One inteeting inight along thee line i one by Daon Acemoglu. When aked about ovethowing dictato he pointed out the following: It

3 Ovethowing the dictato: a game-theoetic appoach i a quetion of coodinating people belief, I need to know if othe people agee with me and ae willing to act. What eally top people who ae oppeed by a egime fom poteting i the fea that they will be pat of an unucceful potet. When you ae living in thee egime, you have to be extemely afaid of what happen if you paticipate and the egime doen t change. 1 Deciption of the ecent evolution eem to highlight the impotance of ocial media in efficient mobilization. Individual fea that not enough people will go to the potet, o uncetainty about the tunout i a majo obtacle. When ma media (e.g., TV o adio) epot about attendance, then the audience doe not know the eaon why individual did not go. In ocial media thee eaon can be evealed. Fo intance, Ghonim (2012) mention the exitence of opinion poll online to find out why people decided (not) to go to the potet. The comment on Facebook help alo to get inight into the deciion-making of othe and eve to aie piit. Ghonim decibe that he wa upied to ee among the uppote peon that he did not expect to ee. All thi togethe help to beak the baie of fea (Ghonim 2012) and allow individual know that they ae enough and togethe they can bing down the dictato. Although ocial media eem to have a notable effect on mobilizing the mae, we lack a fomal model that attempt to captue it effect on mobilization. In thi pape, we ue game theoy to how how thi technology may help to change the tatu quo in an autocatic egime. Ou tating point i that willingne to paticipate in the potet depend on the peceived cot and benefit of paticipation. Aguably, heading out onto the teet implie the cot of facing tea ga, ubbe bullet and potential aet and incaceation. Benefit involve the peceived gain in paticipating in an upiing that may bing about a bette futue, povided it ucceed. The pobability of ucce i highly elated to the numbe of paticipant. Yet, when a potential potete decide whethe to paticipate, poibly he ha only a vague idea about if ufficient othe people will paticipate. Diffeent type of media may affect thee belief (and the eulting mobilization) in divee way. To invetigate the effect of ocial media on mobilization, we tudy how individual deciion to paticipate in the evolution ae affected by two diffeent communication technologie: ma and ocial media. We poit that when an individual obtain infomation though ma media then he get to know the actual tate of the evolution in that moment, wheea when infomed via ocial media he i able to obeve the equence of deciion leading up to that tate. Fo intance, when eaching in Twitte the individual get the lat conveation about the topic, and by colling down the page he i able to ee all peviou tweet about it, the ue of hahtag indeed facilitate thi tak. In Facebook, the ue may comment on the event and all peviou comment can be ead. When people chat in a goup with Whatapp, the complete talk i ecoded in the matphone of each paticipant. We uppoe that tweet, chat and comment ae infomative about the individual deciion to join the potet o 1 The New Yok Time, Febuay 17, 2011, Web Solution Applied to the Poblem of Toppling Autocat, etieved fom on July 14, 2014.Manacoda and Teei (2016) poit a imila agument and dicu the poible benefit of infomation: Knowledge, albeit impefect, of othe likelihood of paticipating can, in paticula, fote individual willingne to paticipate, and lead to the emegence of potet in equilibium, an outcome that would not eult in a wold whee individual act atomitically. (page 3).

4 332 H. J. Ki et al. to tay at home. A tated by paticipant in the Hong Kong Umbella evolution, If you fiend ak you to join the potet, they jut Whatapp you: Hey, I am going, ae you? Then you quickly decide. (Pake 2014). By contat, when TV o adio infom about the tate of a given event, the pecie hitoy emain hidden, only aggegate infomation about the tunout i epoted. 2 We ely on thee ditinctive featue of ma and ocial media and model the poblem of evolution a a coodination poblem. We uppoe that thee ae two goup in the ociety. One of them conit of individual who want to ovethow the dictato (willing individual). The anothe one i compoed of individual who do not want to change the egime but pefe the tatu quo (unwilling individual). We aume that thee ae enough willing individual to bing about a change and ovethowing the dictato i the ocially efficient outcome. That i, if all willing individual evolt, then the dictato i toppled. Howeve, if the numbe of potete (thoe willing individual who actually head onto the teet) fall hot of a citical ma, then the dictato emain in powe and may punih thoe who paticipated in the failed evolt. We aume that individual chooe in equence whethe o not to evolt. Befoe making he deciion, each individual i infomed about the tate of the evolution. The infomation that an individual eceive depend on the communication technology. A dicued above, ma media allow individual to lean how many people have aleady choen to paticipate (i.e. the actual tate of the evolution), wheea individual obeve each of the pat deciion (e.g. the pecie hitoy) when infomation i channeled though ocial media. Fit, we how that when the type of individual (that i, if he i willing to evolt o not) i public infomation, willing individual take pat in the evolution in cae of both communication technologie and, thu, the dictato i ovethown. Inteetingly enough, it i not neceaily the cae when thee i no communication technology and thu individual eceive no infomation about the tate of the evolution. If willing individual believe that othe willing individual will not evolt, then it i poible to have an equilibium outcome whee nobody evolt. Thi, in tun, how that the mee exitence of communication technologie (i.e., ma o ocial media) can facilitate that ocial movement achieve thei objective by hinking the et of belief, compaed with the cae in which no infomation i dicloed. Second, we tudy a moe ealitic etup in which the type of individual i not obeved (i.e. it i pivate infomation). Although it i common knowledge in ou model that thee ae enough willing individual in the ociety to change the egime, the type of communication technology become elevant in thi etup. We how that ma media do not neceaily enable willing individual to oganize themelve efficiently. Thu, depending on the peceived cot and benefit, willing individual might chooe not to evolt in equilibium. Howeve, ucceful evolution i the unique equilibium outcome when individual ue ocial media, independently of the eveity of punihment that potete may uffe if they fail to ovethow the dictato. 2 Thee ae featue of ocial media that fote peading infomation quickly and to a wide audience. Fo intance in the cae of Twitte etweeting allow to epot a content efeencing to the ouce of the content; tending topic highlight content that an in-built algoithm conide collectively elevant.

5 Ovethowing the dictato: a game-theoetic appoach Thi eult how that communication though ocial media facilitate that evolution ucceed moe than when communication i channeled though taditional ma media. Although ou compaion of ma and ocial media ugget that they ae competing communication technologie, ou eult ae aimed at anweing the quetion about how ocial media enhance ma media ability to mobilize individual. The eult gleaned fom the empiical evidence uppot the idea that citizen peceived ocial media to be vey impotant duing the Aab Sping (Howad et al. 2011; Lang and De Steck 2014), including the Tuniian evolution (Mazouki et al. 2012) o the potet in Egypt (Attia et al. 2011; Azab 2012; Lim 2012; Tufekci and Wilon 2012). Hence, micoblogging activity (Qin et al. 2016) o the amount of tweet (Acemoglu et al. 2014; Steinet-Thelkeld et al. 2015) might have been elated to the incidence and the intenity of potet. Thee i indeed a caual elationhip between ocial media and mobilization accoding to Manacoda and Teei (2016) and Enikolopov et al. (2016). Manacoda and Teei (2016) tudy how coveage of mobile phone ignal affected the occuence of potet and individual paticipation on the whole Afican continent between 1998 and They how that mobile phone pomoted potet and helped ma mobilization duing economic downtun. Enikolopov et al. (2016) how that the penetation of VK, the dominant Ruian online ocial netwok, affected potet paticipation in a eie of potet duing Moe concetely, a 10% inceae in penetation inceaed the pobability of a potet by almot 5% and the numbe of paticipant by oughly 20%. Section 2 eview biefly the elevant liteatue. Section 3 peent ou model. We deive ou theoetical eult in Sect. 4, whee we alo dicu the application of ou model, by peenting two example in which we ae the diffeence between ma and ocial media in yielding diffeent outcome in a evolution. We dicu ome caveat of ou model and poible extenion in Sect. 5. Section 6 conclude. All the poof ae elegated to the Appendix. 2 Liteatue eview In thi ection fit we how why obevability of action and ocial netwok (that ae the bai of ocial media) ae impotant in the evolution of evolt. Then we go ove the mot elevant and ecent theoetical pape on evolution and the coeponding liteatue on coodination game. Ou intepetation of the poce why an individual join a potet follow the ationalit view that the citizen ae the cot and benefit of paticipating in a evolt (ee, fo intance, Goldtone 2001 and the efeence theein). 4 Social netwok play an impotant ole at eveal tage of the poce. Pay (2003) claim that ocial media ceate ocial netwok that ae impotant in community ceation, in connecting 3 The autho point out that in Afica thee i a lack of fixed phone line and high-peed Intenet cabling, o geneally mobile phone povide the acce to the Intenet and ocial media. 4 Thee ae othe view on potet that emphaize the ole of identity and ocial-pychological facto (ee fo intance, Klandeman 1984). In evolt, both ational and non-ational element play a ole, in thi pape we focu on the fome one.

6 334 H. J. Ki et al. the popective paticipant and alo in the deciion-making, ince individual ue the infomation coming fom the ocial netwok to anticipate and evaluate the potential cot and outcome of paticipation. Gunitky (2015) and Battaglini (2017) highlight alo the effect of ocial media in allowing individual to communicate thei infomation. Impotantly, the deciion to join the evolution depend alo on the intention and action of othe paticipant. If many othe citizen ae expected to join, then the evolution i likely to ucceed and thi make paticipation moe attactive. In the oppoite cae, taying at home may be the optimal deciion. Both ma and ocial media enable individual to fom belief about the tunout at the potet. Ou appoach aim to how that ocial media pomote bette mobilization, becaue fom an individual point of view they give moe accuate infomation about peviou deciion and they allow that ubequent individual obeve the deciion. The fact that deciion can be obeved and may affect the behavio of othe elate ou wok to model of infomational influence; i.e., heding and infomational cacade (e.g., Banejee 1992; Bikhchandani et al. 1992, 1998). Howeve, in thee model thee i a clea bet choice (e.g., which etauant o poduct i bette) and individual have ome pivate infomation about it. Individual update thei ignal upon obeving the deciion of othe, thu it may be ational to follow othe to chooe the payoff-maximizing altenative. In ou etting, thee i heteogeneity of type in that willing and unwilling individual have diffeent pefeence. Relevant to ou etting, willing individual hould evolt in equilibium only if the evolution tun out to be ucceful, thu a coodination poblem i embedded in ou famewok. Thee featue make ou pape divet fom the liteatue on infomational influence. Tuning to theoetical model of evolution, a common point in mot of thee pape i that the egime can be ovethown if enough citizen paticipate in an upiing. The tudie diffe mainly in (i) what type of individual they aume, (ii) if the individual have diffeent willingne to evolt, (iii) the channel of coodination (e.g., what can be obeved?), and (iv) the egime ole. De Mequita (2010) aume the exitence of a vanguad, a continuum of citizen with vaying antigovenment entiment and a paive egime. It i a pue coodination game with imultaneou move afte the vanguad choe the level of cotly violence. The vanguad ue violence and it i infomative about the dicontent in the ociety and individual ening the inceaed diatifaction ae moe likely to join the evolution. 5 Individual do not obeve othe individual deciion to join the potet, theefoe the ole of media i diegaded in thi model, which ha multiple equilibia: with and without ucceful egime change. Chwe (2000) i the cloet pape to ou in piit. He aume two type of individual: willing (thoe who want change and ae eady to go to the teet) and unwilling (thoe who tay at home). In hi model, the ocial netwok allow individual to communicate thei pivate type (e.g., Gunitky 2015; Battaglini 2017). Chwe chaacteize the minimal ufficient netwok that make coodination feaible among willing individual, egadle on the pio belief about the willingne of the othe. He how the impotance of clique (a ubet of individual whee eveybody i 5 Babea and Jackon (2016) ague that demontation may help in poviding infomation to enable evolution. See alo Ginkel and Smith (1999) fo a model in which a goup of willing individual chooe whethe o not to evolt befoe the ma public.

7 Ovethowing the dictato: a game-theoetic appoach linked to eveybody ele). In ou etting the main difficulty come fom what a willing individual believe when obeving that omebody tay at home (i.e., he can be an unwilling individual who doe not want to change the egime o a willing individual that pefe not to evolt). Ou appoache diffe in that we do not allow individual communicate thei willingne to paticipate uing the netwok, but to obeve the action of othe. Chwe (2000) alo look at the minimal ufficient netwok fo the evolution to ucceed, while we aume that the netwok i complete and tudy how diffeent ot of infomation (ma v. ocial media) might help to ovethow the dictato. 6 Elli and Fende (2011) i alo akin to ou appoach in that obeving othe individual behavio i poible. Thi help to make infeence about the infomation that othe individual have about the tate of the wold. The evolution i ucceful if an infomation cacade fom and poo agent ebel. We do not have a heding model a Elli and Fende (2011) and contay to thei model individual in ou etup evolt only if they can be ue that the upiing will ucceed. Edmond (2013) tudie the evolution alo a a coodination game in a global game famewok. Citizen ae ex ante identical and then they eceive noiy ignal about the egime tength fom eveal media outlet, but not about the deciion of othe citizen. Lang and De Steck (2014) how that mobilization i ucceful only if potete ae enthuiatic enough and thei action i viible. In the peviou pape, evolution i modeled a a coodination poblem that might be ovecome in diffeent way. In the model without obeving othe citizen deciion (De Mequita 2010; Edmond 2013) obeving coelated ignal make a evolt potentially ucceful. In the model whee obeving othe individual play a ole (Elli and Fende 2011; Lang and De Steck 2014) thee i only one type of individual and if enough of them decide to evolt, then the dictato i ovethown. Ou model attempt to captue the uncetainty involved in mobilization, eoting to unwilling individual whoe choice i alway the ame. Aguably, thei peence make coodination difficult, ince a willing individual who obeve omebody taying at home doe not know if it i due to an unwilling citizen o a willing one who decided not to paticipate in the evolt. Thi featue make ou pape divet fom the liteatue on global game (Calon and Van Damme 1993; Moi and Shin 2003; Angeleto et al. 2007) whee intoducing (and not emoving) ome uncetainty might help in efficiently eolving the multiple equilibia poblem, yielding a unique equilibium pediction. 3 The model We tudy in a model how diffeent communication technologie detemine the outcome of a evolt. Suppoe a finite et of individual, N ={1, 2,...,n} and a dictato. Each individual chooe an action a i {, } whee mean evolt and tay at home. Each individual i i eithe of type τ i = w (willing to evolt) o τ i = x (unwill- 6 The netwok tuctue in Chen et al. (2016) i uch that individual eceive infomation about about the tength of the egime, and then communicate to each othe the infomativene of the umo. Ki et al. (2016) i alo elated to Chwe (2000) in that they look at the minimal ufficient netwok, but in line with ou modeling choice they aume that the netwok allow fo the obevability of action.

8 336 H. J. Ki et al. ing). Willing individual ae eady to paticipate in potet, unwilling individual ae eluctant to do o. We denote by W the amount of individual that ae willing to evolt, i.e., #{i : τ i = w} =W, whee W (0, n). Individual decide in a equence. Let the type vecto τ = (τ 1,τ 2,...,τ n ) denote the equence of individual. 7 The et of equence of length n with W willing citizen i given by ϒ n,w ={τ : #{τ j τ : τ j = w} =W }. Thee ae ( n W) poible type vecto and any of them i elected with equal pobability. 8 We uppoe that the index of the individual (i N) coepond to he poition in the equence of deciion. The utility of each individual i depend on he type and the outcome of the evolution. The evolution i ucceful if at leat t individual decide to evolt (i.e., #{ j N : a j = } t), othewie the dictato will emain in powe. We follow De Mequita (2010) and aume that the value of the thehold i common knowledge. 9 We conide the cae in which W t and W i common knowledge, o that individual know that thee ae ufficient people willing to evolt. 10 Changing the egime i aumed to be the ocially efficient outcome (a it will alo be clea fom the payoff). Although it i common knowledge that thee ae ufficient willing individual in the ociety to change the egime, and ovethowing the dictato i efficient, the change equie coodination. Thi, in tun, depend on the individual expected cot and benefit of paticipating in the evolt. Let a i be the action choen by individual i and let a = (a 1, a 2,...,a n ) be the pofile of action. A willing individual that decide to tay at home (a i = ) will eceive utility u w,. If the willing individual decide to paticipate in the evolt, the utility will depend on whethe the evolt ucceed (u w,,r )ofail(u w,,f ), whee u w,,r > u w, > u w,,f i aumed. 11 In wod, willing individual utility i highet when they paticipate in a ucceful evolution (u w,,r ). If they tay at home, they deive le utility (u w, ), although the mallet utility i deived when individual take pat in a evolution that i defeated. The payoff u w,,f can then be intepeted a the 7 Abuing omewhat the notation, τ denote a equence of individual, but alo the et of individual in the equence. 8 Thi, in tun, implie that we tudy any poible configuation that may occu in equilibium in a pegame, in which individual have to chooe when to decide. We ae not awae of any pape that tudie how the equence of deciion in a evolt i detemined. We dicu thi iue in Sect Schelling (1978) andganovette (1978) ue model with individual thehold to tudy poblem that involve collective action. In Edmond (2013) oangeleto et al. (2007) thee i uncetainty about the thehold. In Chwe (2000) each peon ha an individual thehold. 10 If W < t, then it i clea that individual do not evolt in equilibium. 11 Note that in the utilitie, the fit ubcipt efe to the type of the individual, the econd to the action that he undetake, wheea the thid one indicate the outcome. R epeent a ucceful evolution, while F denote that it ha failed.

9 Ovethowing the dictato: a game-theoetic appoach punihment that the dictato impoe on potete who paticipate in a evolution that fail, uffeing thi punihment being the potential cot of paticipation. 12 We aume that unwilling individual will not paticipate in the evolt (whateve eaon they might have). The utility of an unwilling individual that evolt (u x, )i theefoe aumed to be malle that the utility of an unwilling individual that tay at home (u x, ). Thi, in tun, implie that it i alway optimal fo an unwilling individual to tay at home. Inteetingly, the peence of thee individual complicate the coodination among willing individual. A willing individual who obeve omebody taying at home doe not know if it i due to an unwilling citizen o a willing one who decided not to paticipate in the evolt. Given ou payoff, the fit bet i achieved when willing individual coodinate and ovethow the dictato. The eaon i that unwilling individual utility i not affected by the outcome of the evolt, wheea willing individual ae bette off if the upiing i ucceful. Ou pape i an attempt to how how diffeent communication technologie may affect the outcome of the evolution. Individual decide in equence whethe o not to evolt and they have infomation about pat deciion that i available to individual depending on the communication technology a follow: No technology Individual do not have any infomation on peviou choice when deciding. Ma media technology Individual have aggegate infomation about the action that have been aleady taken (e.g., numbe of pedeceo that decided to evolt and tay at home). Thi epeent a ituation in which individual obtain infomation though adio o televiion about the tate of the evolution befoe making thei own deciion. Social media technology Individual obeve the individual action of each pedeceo. Thi mean that individual i know exactly which action wa choen by each of he i 1 pedeceo. Thi epeent a ituation in which individual obtain infomation though Facebook o Twitte (o any othe ocial media), in which individual may obeve the exact hitoy of peviou deciion. To fomalize the diffeent communication technologie, let ϕ i denote the infomation that individual i ha. When no communication technology i available, then ϕ i ={τ i }; i.e., individual only know thei own type, but nothing about othe individual deciion. Ma media technology implie ϕ i ={τ i,ρ i, i ρ i 1} whee ρ i epeent the numbe of individual who have decided to evolt up to individual i (ρ i = #{a j =, j < i}); i.e., individual know the amount of pedeceo who decided to paticipate in the evolt, and then the numbe of individual who decided to tay at home. In the piit of Lohmann (1993, 1994a, b) we aume that each pevi- 12 The utility of taying at home may depend on whethe the evolution tiumph o not. A ucceful evolt may bing bette life to a willing individual who by taying at home avoid the cot of the evolution. Thu, thee may be fee-iding iue at take a well (ee fo intance Lohmann 1993). Although thee ae inteeting quetion (and pomiing venue of futue eeach), we delibeately diegad thi iue to focu on the coodination poblem embedded in the above payoff. In thi egad, ou payoff geneate a game that eemble the claic tag-hunt ituation, although the peence of unwilling individual complicate the analyi.

10 338 H. J. Ki et al. ou deciion (odeed accoding to the poition) i obeved unde ocial media. The available infomation then i ϕ i ={τ i, {a j, j < i}}. In Fig. 1, we depict a educed extenive-fom epeentation of the game geneated by each communication technology in a imple ociety of n = 4 individual in which W = 3 of them ae willing to evolt. We name it educed fom becaue we have implified the epeentation by dawing only one of the fou banche that would follow each of the type vecto. At the beginning of the game, natue elect at andom one of them. In the fou poible type vecto willing citizen ae epeented by black cicle and the unwilling one by a white cicle. We aume that individual only obeve action but not type, o individual ae epeented by gey cicle in the et of the tee. 13 We deive in Sect. 4 the theoetical pediction of ou model both when type ae obeved and when they ae pivate infomation. At the top of Fig. 1, we epeent the cae without communication technology in which the individual decide without knowing the deciion of thei pedeceo (i.e., they only know the poition, but nothing ele). A a eult, all node at a given poition belong to the ame infomation et. Then, we depict the cae of ma media, in which individual only know the numbe of pedeceo that aleady evolt. Fo intance, imagine that the fouth individual i infomed that two individual have choen to evolt (and, conequently, one tayed at home). She i not able to ditinguih if the equence wa (,, ), (,, ) o (,, ), hence the infomation that the individual ha i compatible with thee poible equence of deciion. Finally, we daw at the bottom of Fig. 1 the cae of ocial media, in which individual ae able to identify pefectly the equence of deciion; i.e., the infomation et ae ingleton. 14 Note that the game become moe equential a we move fom the cae without communication towad ocial media. In pinciple, the effect of moe infomation i ambiguou. Moe infomation may be good fo evolution ince it allow individual to make thei action moe viible to the ubequent citizen; but at the ame time, it could alo fote coodination failue, e.g. if individual find out that too many of thei pedeceo have choen not to paticipate in the evolution. Note that they may obeve many individual taying at home becaue thoe obeved citizen wee the unwilling one. 4 Revolution unde diffeent infomation tuctue Thi ection deive thee diffeent pediction of ou model. The fit one how that thee ae multiple equilibia when no communication technology i available, theefoe it i poible to have the inefficient outcome in which individual decide not to evolt. We highlight the impotance of ma and ocial media in Sect. 4.1 and 4.2, whee we how that willing individual will evolt in the peence of any of 13 In Appendix C we epeent the complete deciion tee fo the ocial media cae. Note that in ou model the ocial netwok i aumed to be complete. Siegel how in eveal pape how in geneal the tuctue of the ocial netwok affect paticipation in collective action (Siegel 2009), the effect of epeion on collective action (Siegel 2011) and how it inteact with ma media (Siegel 2013). Impotantly, none of thee pape tudie the effect of diffeent ot of media on paticipation in evolt. 14 Recall, howeve, that type ae not obevable in the peent etting.

11 Ovethowing the dictato: a game-theoetic appoach Natue No communica on technology Natue Ma media Natue Social media Fig. 1 Reduced extenive-fom epeentation of a ociety with n = 4andW = 3

12 340 H. J. Ki et al. the two communication technologie when type ae public infomation. If type ae unobevable, howeve, thee ae equilibia in which willing individual decide not to evolt unde ma media, wheea evolution will alway ucceed unde ocial media. The cae without technology i ou benchmak cenaio. Ou fit eult how that when infomation about othe individual i not available (i.e., when deciion ae taken without knowing what othe individual have done) the efficient outcome in which individual evolt may fail to mateialize, even if it i known that ufficient willing individual exit. Popoition 1 If no communication technology i available in the ociety, thee ae multiple equilibia. Thi i in line with the uual eult of multiplicity of equilibia in coodination poblem. Since u w,,r > u w, > u w,,f, fo the willing individual it i optimal to evolt if the othe willing individual ae evolting, while it i optimal to tay at home if nobody ele i evolting. If a willing individual believe that the othe willing individual will paticipate in the evolution, then he bet epond to thi belief by paticipating a well. Howeve, if they hold the oppoite belief, then taying at home i the bet epone. In fact, thee ae two ymmetic equilibia: one in which all willing individual paticipate in the evolution; and anothe one in which no willing individual goe to the teet. The peviou eult doe not depend on whethe type i a public infomation o not. Howeve, when a communication technology i available thi ditinction become elevant a hown next. 4.1 Type i public infomation It i intuctive to ee how the exitence of infomation affect the outcome of evolt in a pefect infomation etup in which the willingne to evolt (that i, the type of individual) i tanmitted by the communication technology. In thi etting, an individual who obeve an action will know whethe a willing o an unwilling individual took it. Thi can be the cae, fo intance, when the people willing to ovethow the dictato belong to the ame ocial goup (e.g. eligiou aociation, ethnic goup o ocial clae), o that individual know the type of the people who have decided peviouly. Fo example, in Egypt the youth in geneal wa unatified with the egime, and o wee alo the Copt. We model thi ituation by intoducing the type of the pedeceo in the infomation available to each individual. Moe pecifically, the available infomation i ϕ i ={τ i,ρ i, i ρ i 1, W i } in the cae of ma media, whee W i denote the amount of willing individual up to (but excluding) individual i, that have aleady decided. 15 A fo ocial media, the aumption about publicly obeved type implie that the 15 Thi i a valuable infomation ince it alo eveal how many willing individual ae left to decide. Fo intance, if thee wee many willing individual who abtained fom paticipating in the potet, then it i moe pobable that the total numbe of potete will fall hot of the thehold, o taying at home may be the bet epone.

13 Ovethowing the dictato: a game-theoetic appoach infomation of individual i become ϕ i ={τ i, {a j, j < i}, {τ j, j < i}}. Inthi etting, both the type and deciion of each peceding individual ae obeved. Individual i tategy i conditioned on the available infomation. It i defined a σ i : ϕ i {, }. Let ={, } n be the game tategy pace, and let σ be a tategy pofile, that i, σ = (σ 1,...,σ n ). Let h i be the hitoy of deciion befoe individual i, h i ={a 1,...,a i 1 }. We find that given a type vecto the unique ubgame pefect equilibium with the two communication technologie i the one in which the evolution ucceed, and evey willing individual chooe to evolt. In thi cae, both technologie geneate the ame behavio in equilibium. Popoition 2 If type i public infomation, evey willing individual evolt in any ubgame pefect equilibium unde both communication technologie. Poof See Appendix A. The ationale fo thi eult i that a willing individual chooe to join the evolution if he obeve that aleady t 1 individual have evolted. Given thi fact, a willing individual who obeve t 2 people paticipating in the evolution decide to evolt if he know that afte he thee i at leat one moe willing individual. Since pedeceo type ae publicly obevable, he can infe if thee i a willing individual behind he. Iteating thi eaoning, a willing individual decide to evolt when up to he ufficient willing individual have choen to do o and he anticipate that enough willing citizen behind he will follow uit. The condition enuing that thi equiement i met at any poition imply that all willing citizen chooe to paticipate in the evolution. A commented above, ou aumption on pedeceo type being public infomation i plauible in envionment whee the people willing to ovethow the dictato can be aociated to paticula goup. Unde thee cicumtance, it i likely that when individual acquie infomation they know both the action and the type of thoe who have aleady decided. In thi cae, the exitence of any of the communication technologie guaantee that the evolution tiumph in ou implified envionment. Aguably, the uncetainty about how many individual would paticipate in a evolution i the main baie and it make mot of the individual who ae dicontented to tay at home. Thi uncetainty come at leat patly fom the uncetainty about type that we conide next. 4.2 Type i pivate infomation We tudy now the cae whee type i pivate infomation. Given the untut and fea geneated by dictato in epeive egime, howeve, type cannot be obeved, what make the etup moe plauible. A agued by eveal autho (e.g. Ginkel and Smith 1999; Kuan 1991, 1995), deciion making in any evolution i clouded by a conideable amount of uncetainty. Thi uncetainty blu the infomation about the public dicontent due to eveal eaon, e.g. the lack of fee pe, falified pefeence evelation to official public opinion poll o the peence of infomant penetating all laye of the ociety, among othe.

14 342 H. J. Ki et al. When type i pivate infomation, communication technologie only tanmit to individual the action of pedeceo. Fo the ma media technology, the infomation of individual i become ϕ i ={τ i,ρ i, i ρ i 1}, o the amount of citizen of each type who have aleady decided i not known. In the cae of ocial media, citizen i infomation i given by ϕ i ={τ i, {a j, j < i}}. Hence, citizen i cannot ditinguih pefectly the type of he pedeceo although he know the exact equence of deciion. Remembe that obeving that omebody evolt indicate unambiguouly that he i of the willing type, ince unwilling citizen alway tay at home. Howeve, ince willing individual may chooe to tay at home, obeving that omeone ha choen not to paticipate in the evolt doe not imply that he i unwilling. Since type cannot be obeved, we look fo Bayeian Nah equilibium. The following popoition highlight the impotance of the communication technology. We find that unde ocial media being tuthful i the unique equilibium pofile; theefoe, taying at home when an individual i unwilling and evolting when he i willing i the unique Bayeian Nah equilibium. With ma media the evolution ucceed only when cetain condition ae met. Popoition 3 Conide the cae whee type i pivate infomation. Unde the ocial media technology, the evolution alway ucceed becaue each willing individual evolt in any Bayeian Nah equilibium. Unde the ma media technology, if t < [ n n W +1] + 1, each willing individual evolt and the evolution ucceed; if t [ n n W +1] + 1, thee ae equilibia whee the evolution i unucceful and nobody evolt fo cetain value of u w,,r ; u w, and u w,,f. Poof See Appendix B. The logic behind ou eult i that identification of type i poible unde ocial media, but not unde ma media. Moe pecifically, any individual that obeve a hitoy of deciion unde ocial media know that all willing (unwilling) pedeceo decided to potet (evolt) in equilibium. With ma media, thee may be ituation in which willing individual find it optimal to tay at home, thu a citizen that obeve a hitoy of deciion will only evolt if he i ue that thee ae enough willing to evolt behind he. Hence, a willing individual that obeve t 2 evolt will alway evolt in the cae of ocial media (even if only one individual i left to decide). Thi i becaue the individual that obeve t 2 potet can infe the type of the pedeceo and know that thee i (at leat) one willing individual to decide. In the cae of ma media, an individual that obeve t 2 evolt doe not know how many willing individual decided to evolt, thu he can only be ue that the evolution will tiumph if he evolt and thee ae at leat n W + 1 individual left to decide. While thee conideation ae embedded in the econd pat of Popoition 3, the following example i aimed to claify the mechanim why ocial media pomote evolution moe than ma media. We conide the imple ociety of Fig. 1 in which thee ae n = 4 individual, and thee of them ae willing to ovethow the dictato (W = 3). We aume that the evolution will be ucceful in thi ociety if and only if at leat thee individual decide to evolt (t = 3). We then focu on the wot poible cenaio and contuct an equilibium in which eveyone tay at home unde ma media. We how that thee i a unique equilibium whee all willing individual evolt in the cae of ocial media.

15 Ovethowing the dictato: a game-theoetic appoach Example 1 Conide the cae of n = 4, W = 3, t = When a communication technology exit, the optimal deciion of a willing individual in the lat poition i obviou. If he obeve two people evolting (ρ 4 = 2), then he evolt and the evolution tiumph. Othewie he tay at home. The ame i tue fo a willing individual in poition 3 if ρ 3 = 2 (he bet epond by evolting). A a conequence, a willing citizen in poition 2 obeving one evolting individual (ρ 2 = 1) evolt a well, becaue he anticipate that if he decide to evolt, then the lat willing individual (eithe in poition 3 o 4) will follow uit. Thu, in any equilibium a willing citizen evolt when ρ 4 = 2; ρ 3 = 2oρ 2 = 1, and tay at home when ρ 4 {0, 1} o ρ 3 = 0. In thee lat cae, a willing individual know that the evolution i doomed to fail, o he doe not join. Thu, we ae left with the following infomation et fo which a willing citizen optimal action i not clea: ρ 1 ; ρ 2 = 0 and ρ 3 = 1. In wod, we do not know yet what a willing citizen doe when he i the fit to decide; when he i in the econd poition and obeve no potete and when thid in the equence of deciion and obeve one potete. We how an equilibium fo the cae of ma media whee nobody evolt on the equilibium path fo ome payoff. Then, we how that it cannot be the cae fo ocial media. Aume the exitence of ma media and the following payoff: u w,,r = 1, u w, = 0 and u w,,f = 10, that atify u w,,r > u w, > u w,,f. If nobody chooe to evolt in the peviou infomation et (ρ 1 ; ρ 2 = 0 and ρ 3 = 1) and act optimally at the othe infomation et (i.e., evolt when ρ 4 = 2; ρ 3 = 2oρ 2 = 1, and tay at home when ρ 4 {0, 1} o ρ 3 = 0) then, we end up in an equilibium without evolution. To how that nobody ha a pofitable unilateal deviation, take the fit individual. He deviation conit in evolting intead of taying at home. Thi i pofitable if the econd individual i willing, becaue the fit individual induce the econd one to evolt a well by the agument we have een befoe. In thi cae, the evolution tiumph and the highet utility i obtained. When the econd individual i unwilling (which ha conditional pobability 1 3 ), then the popoed tategie imply that ubequent willing individual will tay at home and the evolution fail. Theefoe, the unilateal deviation i not pofitable if and only if u w, > 2 3 u w,,r u w,,f, which hold fo the popoed payoff. In the ame vein, it i eay to check that if a willing individual in poition 2 obeve that nobody ha evolted yet (ρ 2 = 0), then he doe not have a pofitable unilateal deviation given the pecibed tategy. Conide now a willing individual in poition 3 who obeve that jut one citizen ha evolted (ρ 3 = 1). Accoding to the pecibed tategy, it i an off-equilibium deciion. Thu, conitent belief may include that a willing individual followed the tategy and one willing individual deviated and evolted. Thoe belief imply that he will be followed by the unwilling citizen. Along thee line, it i the inability of a 16 It follow fom Popoition 1 that without any communication technology, thee ae two ymmetic equilibia (in pue tategie). In one of them, the thee willing individual chooe to evolt. In the othe one, they chooe to tay at home. Thi i the cae becaue fo a willing individual to evolt (tay at home) i the bet epone when he believe that the othe willing individual chooe to evolt (tay at home).

16 344 H. J. Ki et al. willing individual in poition 3 to ditinguih whethe the fit o the econd individual tayed at home (and he peimim) that make it optimal fo the willing individual in poition 1 to tay at home. Note alo that the equilibium in which each willing individual paticipate exit if we imply conide a tategy pofile that etablihe that willing individual hould evolt when ρ 1 ; ρ 2 = 0 and ρ 3 = 1. Retiction on off-the-equilibium belief could eliminate the equilibium in which citizen do not evolt. Fo intance, aume that the fit individual to decide wee willing one with cetainty, o that the type vecto i (w,w,w,x). In thi cae it i pofitable to deviate unilateally fom taying at home when a willing individual i the fit to decide a given the bet epone indicated above the evolution will tiumph. In fact, ou eult ugget that epeive egime may attempt actively to inceae uncetainty about the public dicontent (even in the fom to hinde citizen to have detailed infomation about paticipation in potet) o that multiple equilibia, and hence potentially no potet emain an equilibium. Next, we how that unde ocial media thee i a unique equilibium in which all willing individual evolt and ucceed in ovethowing the dictato. Fo a willing individual in the lat poition the peviou agument apply. Thu, upon obeving that two othe citizen have evolted (the ode doe not matte) he evolt a well, othewie he tay at home. When in poition 3, a willing individual join the potet when obeving two potete. A a conequence, a willing individual in the econd poition, who obeve that the fit citizen decided to potet, will evolt a well, anticipating that the lat willing individual (eithe in poition 3 o 4) will join the potet a well. A a next tep, let u conide what happen if a willing citizen obeve that the fit citizen evolted, wheea the econd one tayed at home. We denote thi by (, ). By peviou eaoning thi individual can be ue that the econd individual wa the unwilling one (a willing individual in the econd poition would have joined the upiing upon obeving that the fit citizen evolted), o he know that the lat citizen i willing and anticipating he eaction to obeving a hitoy with two individual evolting he decide to potet a well. Given the peviou agument, a willing individual in the fit poition chooe optimally to potet, ince any hitoy tating with a evolting citizen lead to a ucceful evolution (eithe if he i followed by a willing individual who potet heelf o when followed by an unwilling one who tay at home, but then the next individual will join the potet and in any cae the lat willing individual will evolt a well). A a conequence, when obeving that the fit individual ha tayed at home, willing citizen know that he mut have been the unwilling one (i.e., individual get to know that the type vecto i (x,w,w,w)and by backwad induction they play the unique equilibium in which all of them evolt). That i, ince the willing individual in poition 4 (3) evolt when obeving two (one) peviou evolt, the willing citizen in poition 2 will evolt and thu the evolution tiumph, and the dictato i ovethown. Impotantly, thee agument apply fo any payoff uch that u w,,r > u w, > u w,,f. It i alo woth noting that with ocial media the outcome i unique becaue individual ae able to ditinguih the hitoie (, ) and (, ), while with ma media individual may believe that (with ome poitive pobability) the one who tayed at home i a willing individual.

17 Ovethowing the dictato: a game-theoetic appoach Popoition 3 etablihe alo a elationhip between the thehold t and the numbe of willing individual in the ociety W uch that it i poible to contuct an equilibium whee the evolution doe not tiumph in the peence of ma media. In the following example, we how the quantitative diffeence in the effectivene of ocial media veu ma media in foteing evolution. In paticula, Example 2 how that all willing citizen evolting can be achieved a an equilibium with ma media only if a elatively low popotion of the ociety i equied to ovethow the dictato. Example 2 Conide the cae of n = 10, W = 7, t = 5. Ou eaoning above implie that the evolution tiumph unde ocial media. Ma media can alo foment evolution fo any poible payoff, but only if jut a elatively low popotion of the ociety i equied to paticipate in the evolution in ode to ovethow the dictato. In paticula, Popoition 3 tate that the evolution ucceed fo ue only if intege [ n n W +1] + 1 = 3 o le individual ae equied to paticipate in the evolt. Since it i equied that t = 5 individual evolt, it i poible that nobody evolt unde ma media, even though moe than two-thid of the individual ae willing to ovethow the dictato in thi ociety (W = 7). 17 The intuition behind thi eult i the following. If an individual can be ue that the evolution ucceed, then he join the potet. Wheneve he may believe that with poitive pobability the evolution fail, it i poible to find a punihment that i ufficiently lage to dete individual fom paticipating in the potet. A willing individual at poition 7, 8, 9 o 10 cannot be ue that among the ubequent citizen thee i a willing one, ince poibly all of them ae unwilling. Hence, if he evolt, in the wot cae the numbe of paticipant inceae only by 1. Thu, a willing individual at thee poition only evolt if he obeve at leat t 1 peviou evolt. That i, he evolt if only one moe evolting individual i needed to bing the upiing to tiumph. At poition 6, a willing individual know that thee i fo ue one moe willing individual behind he and he can convince he to evolt with cetainty if he will obeve t 1 evolt. Thu, the willing citizen at poition 6 evolt if he obeve t 2 evolt. A willing individual at poition 5 know that thee ae at leat two willing citizen behind he, but he cannot make ue that both of them will evolt if he decide to evolt. Thi i the cae becaue poibly the fit of the willing individual i at poition 9 and then by peviou agument thi citizen cannot be ue that thee i anothe willing individual behind he. Hence, a willing citizen at poition 5 know that by evolting he can pompt fo ue one moe willing individual to paticipate, o he evolt if heobeve t 2 evolt. The ame eaoning applie to willing individual at poition 4 and 3. A willing individual at poition 2 know that thee ae at leat 5 willing individual behind he. In the wot cae, the next one i at poition 6 and by peviou eaoning even he know that thee i one moe willing citizen behind he. So, at poition 2 a willing individual know that he can induce two moe willing citizen. Hence, if he obeve that t 3 individual have aleady evolted, then he join the potet. The ame i tue fo a willing individual at poition 1. Note that a 17 The diffeence become lage if we cale up the numbe. If n = 100 and W = 70 then the evolution ucceed alway with ocial media (fo any t W ), while the potet tiumph with ma media only if t 4 individual ae equied to join.