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.