Coherent Dempster-Shafer equilibrium and ambiguous signals

This paper reappraises the Dempster-Shafer equilibrium, a novel solution concept for signaling games introduced by Eichberger and Kelsey (2004), and suggests a new refinement approach. It is demonstrated that if the types of the Sender-but not messages-are assumed to be ex-ante unambiguous, then the Receiver's conditional Choquet preference derived by the Dempster-Shafer updating rule coincides with subjective expected utility. This property of the pessimistic updating rule narrows the pooling, but not separating, Dempster-Shafer equilibrium to be behaviorally equivalent to the perfect Bayesian equilibrium. Moreover, if one refines the separating Dempster-Shafer equilibrium à la Ryan (2002a) by imposing the belief persistence axiom, then no deviations from the perfect Bayesian equilibrium are feasible. To eliminate Ryan's type of behavior, a less stringent refinement based on the notion of coherent beliefs is elaborated.