Refinements and incentive efficiency in Walrasian models of insurance economies

The literature on Walrasian markets in large economies with adverse selection has used various equilibrium refinements, but has obtained no general incentive efficiency of equilibrium, namely when cross-subsidies are needed for efficiency. We show that the same refined equilibria may also be incentive inefficient even when general mechanisms that allow for such cross-subsidies are priced and can be traded. In the process, we also prove existence of some type of forward induction equilibria in this context.     

The equivalence of the Dekel–Fudenberg iterative procedure and weakly perfect rationalizability

Summary. Two approaches have been proposed in the literature to refine the rationalizability solution concept: either assuming that a player believes that with small probability her opponents choose strategies that are irrational, or assuming that their is a small amount of payoff uncertainty. We show that both approaches lead to the same refinement if strategy perturbations are made according to the concept of weakly perfect rationalizability, and if there is payoff uncertainty as in Dekel and Fudenberg [J. of Econ. Theory 52 (1990), 243–267]. For both cases, the strategies that survive are obtained by starting with one round of elimination of weakly dominated strategies followed by many rounds of elimination of strictly dominated strategies. Received: 10 December 1998; revised version: 26 April 1999     

Decision-analytic refinements of the precautionary principle

In public decision making about uncertain technological hazards, the precautionary principle calls for prompt protective action rather than delay of protections until scientific uncertainty is resolved. The precautionary principle has a sound basis in decision theory, particularly in situations where the potential hazards are serious and the costs of protective actions are tolerable. This article suggests that the precautionary principle should be refined to address three complications: (1) situations where the exposures to be reduced or prevented may have beneficial as well as hazardous consequences; (2) situations where the protective action itself will create potential hazards; and (3) situations where targeted research investments, coupled with delay of protective action, are likely to support wiser public decisions than prompt protective action. Each of these complications is shown to be relevant to contemporary policy debates about application of the precautionary principle. The usefulness of the precautionary principle in public decision making will be enhanced if these decision-analytic refinements are adopted in formal definitions of the principle.     

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.     

p-Best response set and the robustness of equilibria to incomplete information

In this paper, we use p-best response sets—a set-valued extension of p-dominance—in order to provide a new sufficient condition for the robustness of equilibria to incomplete information: if there exists a set S which is a p-best response set with , and there exists a unique correlated equilibrium μ^* whose support is in S then μ^* is a robust Nash equilibrium.