Supplementary Appendix to. Rich Communication, Social Preferences, and Coordinated Resistance against Divide-and-

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1 Supplementary ppendx to Rch Communcaton, Socal Preferences, and Coordnated Resstance aganst Dvde-and- Conquer: Laboratory Investgaton (2013) by Tmothy N. Cason and Va-Lam Mu In the text, before proceedng to our expermental desgn, we frst dscuss how rch communcaton may affect the behavor of vctms and benefcares. s background for ths dscusson, we nformally sketch n the text a model developed n Cason and Mu (2013) that was desgned to study how ncomplete nformaton about socal preferences and non-bndng restrctve communcaton (n the form of a bnary message) affect behavor n the repeated CR game. We then nformally explan how the model can be used to demonstrate that the presence of heterogeneous socal preferences transforms the subgame followng a DC transgresson (the DC subgame) nto a game of ncomplete nformaton. We also state that t can be shown that an nformatve equlbrum exsts n the CR game wth socal preferences and non-bndng restrctve communcaton, n whch restrctve communcaton can help coordnate resstance between the vctm and the (SP-type) benefcary. Ths appendx sketches the model that we dscussed nformally n the text. Detaled dscusson of the model and proofs of results are reported n the Techncal ppendx of Cason and Mu (2013) that s avalable at Consder a model n whch all agents are of two types. Wth probablty p an agent has standard preferences, and wth probablty (1-p) the agent has socal preferences. n agent s type s her prvate nformaton. Cox et al. (2007) assume that n a (two-player) sequental move game, when a second-mover wth socal preferences makes her decson after observng the acton chosen by the frst-mover, the second-mover s margnal rate of substtuton between her ncome and the ncome of the frst-mover depends on her emotonal state toward the frst-mover. Followng ths approach, and for smplcty we assume that the only emotonal reacton that can be trggered n the CR game s the negatve reacton toward a transgressng leader by the responders. Qualtatvely, our man results hold for any socal preferences models n whch a

2 socal preference type benefcary prefers that DC be defeated. 1 If agent s a Socal Preferences type (hereafter the SP-type) and a responder, she regards a DC transgresson by the leader as undesrable, modeled wth the utlty functon 1 ( 1,0) f al T, T, T U yl, y, yj y yl), 0faL NT (1) Here, y s agent s ncome, y L s the leader s ncome, y j s the ncome of the other responder, s the (condtonal) emotonal state varable, and 1 (and 0 ) s an elastcty of substtuton parameter. T denotes transgresson aganst both responders, NT denotes No Transgresson, and T and T denote dvde-and-conquer transgresson aganst and, respectvely. If an agent s a Standard type (hereafter the S-type), then regardless of whether she s a leader or a responder, she has a utlty functon 1 U y y. (2) ecause the only emotonal reacton we focus on s the negatve reacton by a responder towards a transgressng leader, an SP-type leader wll also have a utlty functon of 1 U y y. Result 1: If 9 7 /8 and p 7 2 / 7 1, then each of the three followng strategy profles consttutes a ayesan Nash Equlbrum n the DC subgame wth socal preferences: () oth the S-type vctm and the SP-type vctm acquesce, and both the S- type benefcary and the SP-type benefcary acquesce. 1 Note that gven the chosen parameter values, ntroducng smple nequty averson, such as that captured n Fehr and Schmdt s (1999) well-known model, does not affect the benefcares domnant strategy to acquesce. benefcary challengng a transgresson reduces the dsutlty from earnng more than the transgresson vctm. ut he also reduces hs materal payoff and ncreases hs dsutlty from earnng more than the leader when the resstance succeeds. Therefore, acquescng remans a domnant strategy for the benefcary. Furthermore, one can show that ths mples that a leader wth nequty averson stll prefers DC transgresson to no transgresson. Therefore, ncorporatng nequty averson does not change the concluson that no transgresson aganst any responder cannot be supported as part of an equlbrum. Inequty averson could change the set of equlbra for other payoff parameters, however, such as the lower leader payoffs used n Wengast s (1997) orgnal verson of the game.

3 () oth the S-type vctm and the SP-type vctm challenge. The S-type benefcary always acquesces, and the SP-type benefcary challenges. () The S-type vctm challenges wth a probablty 1 p (9 8 7 ) p(9 8 ) 0,1 p(7 8 8 ), and the SP-type vctm always challenges. The S-type benefcary always acquesces, and the SP-type benefcary challenges wth a probablty p7 1 Result 1 shows that when socal preferences are suffcently strong and that there s a suffcently hgh probablty that a benefcary s an SP-type, then socal preferences transform the DC subgame nto a stag-hunt game for the responders, wth multple (and Pareto-ranked) equlbra. The model also mples that vctms wll challenge more than benefcares, whch s consstent wth the emprcal fndngs n Cason and Mu (2007). lthough jont resstance can be supported as an equlbrum, ncomplete nformaton about the types of other responders and multple equlbra can prevent jont resstance from occurrng. We refer the nterested reader to pp of the Techncal ppendx of Cason and Mu (2013) that s avalable at for detaled analyss of the one-shot CR game wth ncomplete nformaton about socal preferences that contans the proof of Result 1 and the dscusson of other results. Now consder the effect of non-bndng restrctve communcaton between the responders n the one-shot CR game. In the one-shot CR game wth socal preferences and wth communcaton, the tmng of events s as follows: 1. Nature chooses the type of each player. 2. The leader, L, chooses hs acton a T, T, T, NT L L 0, t the responder communcaton stage, responders and observe the leader s acton, and then smultaneously choose a message m M C, CH,,. 4. Observng the message sent by the other responder, a responder updates her belef about the type of the other responder.

4 5. t the responder acton stage, each responder chooses her acton a C, CH,,, as a functon of the observed message profle m, m M M sent by the responders. 6. Payoffs are realzed for the leader and the two responders. In ths game, the players strateges consttute a Perfect ayesan equlbrum f: (E1) Gven the responders strateges, L s chosen acton maxmzes hs expected utlty. (E2) t the responder communcaton stage, for any responder, gven the leader s chosen acton and the other responder s strategy, each type of ths responder s chosen message maxmzes her expected utlty. (E3) Havng observed the message sent by the other responder, a responder updates her belef about the type of the other responder based on the other responder s strategy accordng to ayes rule. (E4) t the responder acton stage, for any responder and for any observed message profle, each type of ths responder s acton maxmzes her expected utlty gven the leader s chosen acton and the other responder s strategy. Note that (E1) reflects the assumpton that an S-type leader and an SP-type leader wll behave the same n ths model Result 2: If and p 8 4, then the followng strategy profles consttute a Perfect ayesan equlbrum n the CR game wth socal preferences: () The leader chooses NT. () If the leader chooses T, then both the SP-type and the S- type of responder (who s the vctm) wll choose the message CH, whle the SP-type of responder (who s the benefcary) wll choose the message CH, and the S-type of responder wll choose the message C. oth types of wll choose the acton CH ff the observed message profle s m, m CH, CH profle s m, m CH, CH. The SP-type of wll choose the acton CH ff the message, and the S-type of wll choose the acton C for any message profle m, m. () f the leader chooses T, then (who s now the benefcary) and (who

5 s now the vctm) wll adopt strateges that are mrror mages of the strateges just descrbed when the leader chooses T. (v) f the leader chooses T, then regardless of ther type, both responders wll choose the message CH, and wll choose the acton CH ff the observed message profle s m, m CH, CH. (v) f the leader chooses NT, then regardless of ther type, both responders wll choose the message C, and wll choose the acton C for any observed message profle m, m. s common n cheap talk games, a babblng equlbrum always exsts, but Result 2 shows that an nformatve equlbrum also exsts. In ths equlbrum, both types of vctm wll ndcate Challenge and wll challenge f and only f both the vctm and the benefcary have ndcated Challenge n the communcaton stage. n SP-type benefcary wll ndcate Challenge, and wll challenge f and only f both the vctm and the benefcary have ndcated Challenge n ther messages. n S-type benefcary wll ndcate cquesce, and wll acquesce regardless of the messages sent by the vctm and benefcary. These strateges consttute an equlbrum because an SP-type benefcary prefers that a DC transgresson be defeated and has the ncentve to send a message of CH to ndcate that she s an SP-type so as to nduce coordnated resstance wth the vctm. On the other hand, an S-type benefcary prefers that a DC transgresson succeeds, and has no ncentve to devate to send a message of Challenge. Communcaton can help coordnate resstance aganst DC n ths envronment. We refer the nterested reader to pp of the Techncal ppendx of Cason and Mu (2013) that s avalable at for detaled analyss of the one-shot CR game wth ncomplete nformaton about socal preferences and restrctve communcaton that contans the proof of Result 2 and the dscusson of other results. References Cason, Tmothy and Va-Lam Mu, Coordnatng Resstance through Communcaton and Repeated Interacton, workng paper, Purdue and Monash Unverstes, Cox, James, Danel Fredman and Steven Gjerstad, Tractable Model of Recprocty and Farness, Games and Economc ehavor, 59: 17-45, Fehr, Ernst and Klaus M. Schmdt, Theory of Farness, Competton, and Cooperaton, Quarterly Journal of Economcs, 114: , 1999.