A player who seeks to be aggressive against an opponent prefers to catch him by surprise and passive and not well-prepared.  The chance that an opponent may attack by surprise makes a player cautious and well prepared and not passive.  Hence, uncertainty about each player’s intentions can create a vicious cycle where everyone turns aggressive.  This was the topic of last week’s class.

Next we study if communication can provide a route out of conflict.  But the same incentives that generate conflict generate incentives for deception: whether a player intends to be aggressive or passive, he wants his opponent to be passive.  Hence, he might always send the message that maximizes the probability that his opponent is passive but then cheap-talk is not effective and does not affect the equilibrium. An argument along these lines was made by Aumann in a Stag Hunt game.

We show that while deception occurs in equilibrium, it is still possible to transmit enough information to create less conflict.  While players may always seek to minimize the probability their opponent is aggressive, they may also value information about his action so they can coordinate against it.   If the trade-off between these two benefits is type-dependent in a conflict game with incomplete information, separating equilibria are possible and so is coordination on peace.

The ideas above relate to conflict and escalation, where it is known that aggression begets aggression.  What if aggression may beget deterrence not escalation?  For example, revealing weapons may create deterrence but trigger escalation.  Revealing you have no weapons may reduce escalation but eliminate deterrence.  In this situation it can be optimal to employ strategic ambiguity: neither reveal weapons if you have them, nor reveal you do not have them if you do not.  Strategic ambiguity allows a player to employ “deterrence by ambiguity” as he may be armed behind the veil of ambiguity.  He has less incentive to acquire arms as he can pretend to have arms even when he does not behind the veil of ambiguity.  This reduction in arms proliferation can help all players not just the player employing ambiguity strategically.

Here are the slides.