A number of papers have shown that a strict Nash equilibrium action pro¯le of a game may never be played if there is a small amount of incomplete information (see, for example, Carlsson and van Damme (1993a)). We present a general approach to analyzing the robustness of equilibria to a small amount of incomplete information. A Nash equilibrium of a complete information game is said to be robust to incomplete information if every incomplete information game with payo®s almost always given by the complete information game has an equilibrium which generates behavior close to the Nash equilibrium. We show that an open set of games has no robust equilibrium and examine why we get such di®erent results from the re¯nements literature. We show that if a game has a unique correlated equilibrium, it is robust. Finally, a natural many-player many-action generalization of risk dominance is shown to be a su±cient condition for robustness. ¤ We are grateful to Eddie Dekel, Drew Fudenberg and George Mailath for valuable comments.

In this paper we re-examine generic constrained suboptimality of equilibrium allocations with incomplete numeraire asset markets. We provide a general framework which is capable of resolving some issues left open by the previous literature, and encompasses many kinds of intervention in partially controlled market economies. In particular, we establish generic constrained suboptimality, as studied by Geanakoplos and Polemarchakis, even without an upper bound on the number of households. Moreover, we consider the case where asset markets are left open, and the planner can make lump-sum transfers in a limited number of goods. We show that such a perfectly anticipated wealth redistribution policy, though consistent with the assumed incomplete financial structure, is typically effective

Suppose agents value information not only to make contingent plans but also intrinsically. How are such attitudes toward information related to attitudes toward risk? We generalize the Kreps Porteus recursive expected utility model, dropping both recursivity and expected utility. There is a geometric analogy between risk and information. We characterize intrinsic information loving, in general, by a substitution property analogous to multivariate risk loving; and, for smooth preferences, by the convexity of Gateaux derivatives. Even with recursivity, preference for information does not imply expected utility: we provide an example. We examine connections between information loving and risk aversion for early-and late-resolving risks. Journal of Economic Literature Classification Numbers: D80, D81. 1998Academic Press

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We present a model of incomplete information games, where each player is endowed with a set of priors. Upon arrival of private information, it is assumed that each player "updates" his set of priors to a set of posterior beliefs, and then evaluates his actions by the most pessimistic posterior beliefs. So each player's preferences may exhibit aversion to ambiguity or uncertainty. 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. JEL Classification Numbers: C72, D81, D82.

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.

This paper proposes a class of weak additivity concepts for an operator on the set of real valued functions on a finite state space Ω, which include additivity and comonotonic additivity as extreme cases. Let E ⊆ 2 Ω be a collection of subsets of Ω. Two functions x and y on Ω are E-cominimum if, for each E ∈ E, the set of minimizers of x restricted on E and that of y have a common element. An operator I on the set of functions on Ω is E-cominimum additive if I(x + y) = I(x) + I(y) whenever x and y are E-cominimum. The main result characterizes homogeneous E-cominimum additive operators in terms of the Choquet integrals and the corresponding non-additive signed measures. As applications, this paper gives an alternative proof for the characterization of the E-capacity expected utility model of Eichberger and Kelsey [Eichberger, J., Kelsey, D., 1999. E-capacities and the Ellsberg paradox. Theory and Decision 46, 107-140] and that of the multiperiod decision model of Gilboa [Gilboa, I., 1989. Expectation and variation in multiperiod decisions.

This paper presents a simple framework that allows us to survey and relate some different strands of the game theory literature. We describe a “canonical” way of adding incomplete information to a complete information game. This framework allows us to give a simple “complete theory” interpretation (Kreps in Game theory and economic modelling. Clarendon Press, Oxford, 1990) of standard normal form refinements such as perfection, and to relate refinements both to the “higher-order beliefs literature” (Rubinstein in Am Econ Rev 79:385–391, 1989; Monderer and Samet in Games Econ Behav 1:170–190, 1989; Morris et al. in Econ J Econ Soc 63:145–157, 1995; Kajii and Morris in Econ J Econ Soc 65:1283–1309, 1997a) and the “payoff uncertainty approach” (Fudenberg et al. in J Econ Theory 44:354–380, 1988; Dekel and Fudenberg in J Econ Theory 52:243–267, 1990).