Bargaining and War: On the Communication Equilibrium in Conflict Games

We present a version of Baliga and Sjöström’s (2012a) conflict games with two asymmetric players. The players contemplate whether to take an active engagement action to compel the leader of a neighboring state (an extremist) to give up his risky weapons. We show that a player with greater damage from the extremist is more likely to choose an active engagement action than a player with lesser damage. Furthermore, we examine cheap-talk communication equilibria with the extremist. The likelihood of both players choosing the active engagement action decreases by a hawkish extremist who can send a provocative message, if both players are coordination types. If both players are opportunistic types, a dovish extremist can send an appeasement message that causes one player to be more active while another to be more inactive. Lastly, we show that there does not exist any other communication equilibrium for either kind of extremist, for any other combination of player types.