Third-Party Intervention in Conflicts and the Indirect Samaritan's Dilemma

I study a two-period model of conflict with two combatants and a third party who is an ally of one of the combatants. The third party is fully informed about the type of her ally but not about the type of her ally’s enemy. There is a signaling game between the third party and her ally’s enemy where preferences do not satisfy the single-crossing condition. There exist perfect Bayesian equilibria in which the third party’s intervention worsens the conflict by energizing her ally’s enemy wherein he (i.e., the enemy) pretends to be stronger than he actually is in order to discourage the third-party from assisting her ally. This creates a dilemma for the third party which may be referred to as the indirect Samaritan’s dilemma. I find that the expectation of a third-party’s military assistance to an ally coupled with the third-party’s limited information about the strength of her ally’s enemy can be strategically exploited by the enemy through pronouncements that would not have been credible if the third party was fully informed about her ally’s enemy. Remarkably, the third-party’s ally, who is fully informed about the enemy, is unable to counteract this behavior by using credible signals to reveal his information to the third party. In some cases, the third party and her ally are strictly better off if the third-party’s decision to withdraw from or stay in the conflict is based on her prior beliefs and not on the current conditions of the conflict even if observing the current conditions improves the third-party’s information. Unlike the standard Samaritan’s dilemma, a commitment by the third party to a given level of assistance may be welfare-improving.