Essays on signaling games under ambiguity

This dissertation studies two-person signaling games where the players are assumed to be Choquet expected utility maximizers a la Schmeidler (1989). The sender sends an ambiguous message to the receiver who updates his non-additive belief according to a f-Bayesian updating rule of Gilboa and Schmeidler (1993). When the types are unambiguous in the sense of Nehring (1999), the receiver's conditional preferences after updating on an ambiguous message are always of the subjective expected utility form. This property may serious limit the descriptive power of solution concepts under non-additive beliefs, and it is scrutinized with two extreme f-Bayesian updating rules, the Dempster-Shafer and the Bayes' rule.

In chapter 3, the Dempster-Shafer equilibrium proposed by Eichberger and Kelsey (2004) is reappraised. Under the assumption of unambiguous types, it is shown that the Dempster-Shafer equilibrium may give rise to a separating behavior that is never supported by perfect Bayesian equilibrium. However, it does not support any additional pooling equilibrium outcome. Since the Dempster-Shafer equilibrium may support implausible behaviors as exemplified in Ryan (2002), a refinement based on coherent beliefs is suggested.

In chapter 4, a variant of perfect Bayesian equilibrium, the quasi perfect Bayesian equilibrium, is proposed, and its descriptive power is investigated. It is shown that the quasi perfect Bayesian equilibrium does not support any additional separating behavior compared to perfect Bayesian equilibrium. It may support additional pooling behavior only if the receiver perceives a correlation between the types and messages.