Interim Efficient Allocations under Uncertainty

This paper considers an exchange economy under uncertainty with asymmetric information. Uncertainty is represented by multiple priors and posteriors of agents who have either Bewley's incomplete preferences or Gilboa-Schmeidler's maximin expected utility preferences. The main results characterize interim efficient allocations under uncertainty; that is, they provide conditions on the sets of posteriors, thus implicitly on the way how agents update the sets of priors, for non-existence of a trade which makes all agents better off at any realization of private information. For agents with the incomplete preferences, the condition is necessary and sufficient, but for agents with the maximin expected utility preferences, the condition is sufficient only. A couple of necessary conditions for the latter case are provided.multiple priors; interim efficiency; no trade; dynamic consistency; rectangular prior set

Generalized Potentials and Robust Sets of Equilibria

This paper introduces generalized potential functions of complete information games and studies the robustness of sets of equilibria to incomplete information. A set of equilibria of a complete information game is robust if every incomplete information game where payoffs are almost always given by the complete information game has an equilibrium which generates behavior close to some equilibrium in the set. This paper provides sufficient conditions for the robustness of sets of equilibria in terms of argmax sets of generalized potential functions and shows that the sufficient conditions generalize the existing sufficient conditions for the robustness of equilibria.Incomplete information, Potential, Refinements, Robustness

Incomplete Information Games with Multiple Priors

We present a model of incomplete information games with sets of priors. Upon arrival of private information, each player "updates" by the Bayes rule each of priors in this set to construct the set of posteriors consistent with the arrived piece of information. Then the player uses a possibly proper subset of this set of posteriors to form beliefs about the opponents' strategic choices. And finally the player evaluates his actions by the most pessimistic posterior beliefs `a la Gilboa and Schmeidler (1989). So each player's preferences may exhibit non-linearity in probabilities which can be interpreted as the player's aversion to ambiguity or uncertainty. In this setup, we define a couple of equilibrium concepts, establish existence results for them, and demonstrate by examples how players' views on uncertainty about the environment affect the strategic outcomes.incomplete information games; multiple priors; ambiguity aversion; uncertainty aversion

Equivalence of the Dempster-Shafer rule and the maximum likelihood rule implies convexity

It is known that if a capacity is convex then the Dempster-Shafer rule for the capacity is equivalent to the maximum likelihood rule for the core of the capacity. This paper shows that the converse is also true that is, a capacity must be convex if these two rules are equivalent.

Agreeable Bets with Multiple Priors

This paper considers a two agent model of trade with multiple priors. First, we characterize the existence of an agreeable bet on some event in terms of the set of priors. It is then shown that the existence of an agreeable bet on some event is a strictly stronger condition than the existence of an agreeable trade, whereas the two conditions are equivalent in the standard Bayesian framework. Secondly, we show that the two conditions are equivalent when the set of priors is the core of a convex capacity.multiple priors, convex capacity, agreeing and disagreeing, Choquet integralm

Trade with Heterogeneous Multiple Priors

This paper presents a general framework to understand the possibility of a purely speculative trade under asymmetric information, where the decision making rule of each trader conforms to the multiple priors model (Gibloa and Schmeidler, 1989): the agents are interested in the minimum of the conditional expected value of trade where the minimum is taken over the set of posteriors. In this framework, we derive a necessary and sufficient condition on the sets of posteriors, thus implicitly on the updating rules adopted by the agents, for non-existence of trade such that it is always common knowledge that every agent expects a positive gain.no trade; dynamic consistency; interim efficiency; rectangularity

Best Response Equivalence

Two games are best-response equivalent if they have the same best-response correspondence. We provide a characterization of when two games are best-response equivalent. The characterizations exploit a dual relationship between payoff differences and beliefs. Some "potential game" arguments (cf. Monderer and Shapley, 1996, Games. Econ. Behav. 14, 124-143) rely only on the property that potential games are best-response equivalent to identical interest games. Our results show that a large class of games are best-response equivalent to identical interest games, but are not potential games. Thus we show how some existing potential game arguments can be extended.Best response equivalence; Duality; Farkas' Lemma; Potential games