A number of papers have shown that a strict Nash equilibrium action profile of a game may never be played if there is a small amount of incomplete information. The authors 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 payoffs almost always given by the complete information game has an equilibrium which generates behavior close to the Nash equilibrium. The authors show that many games with strict equilibria have no robust equilibrium and examine why they get such different results from existing refinements. If a game has a unique correlated equilibrium, it is robust. A natural many-player many-action generalization of risk dominance is a sufficient condition for robustness.

This paper examines the structure of sunspot equilibria in a standard two period exchange economy with real assets. We show that for a generic choice of utility functions and endowments, there exists an open set of real asset structures whose payoffs are independent of sunspots such that the economy with this asset structure has a regular sunspot equilibrium. An important implication of our result is that the multiplicity of non-sunspot equilibria is not necessary for the existence of sunspot equilibria. Our technique is general and can be applied to show the existence of sunspot equilibria in other frameworks.

In a recent paper Rubinstein, Safra, and Thomson (RST) have provided an interesting re-examination of the widely applied Nash solution for a two-person bargaining problem. They recast the usual Nash bargaining problem into a more natural setting of feasible alternatives with a disagreement outcome. The two players are then described by their risk preferences defined on the set of lotteries over the alternatives and the disagreement outcome. This enables them to define an ordinal Nash solution in terms of the agents' risk preferences. Essentially, their ordinal solution is an outcome that is immune against possible objections. Freeing the definition of the Nash solution from utility naturally led RST to extending its scope to Non-Expected Utility (NEU) preferences. We contend, however, that the family of NEU preferences considered by RST is unduly restrictive. The assumptions imposed on the risk preferences by RST essentially exclude any members of the Rank Dependent Expected Utility (RDEU) and betweenness families that can accommodate the very choice paradoxes that stimulated the development of NEU theory. As these are two of the most extensively analyzed and widely applied NEU models in the literature, this seems to cast doubt on how broad an extension to NEU preferences the RST approach affords. We demonstrate, however, that RST's analysis can be modified so that their conclusion is valid in a wider class of preferences that can include examples of RDEU preferences. This class consists of preferences that admit what we term a disagreement linear representation.

Harsanyi's impartial observer must consider two types of lotteries: imaginary identity lotteries (“accidents of birth”) that she faces as herself and the real outcome lotteries (“life chances”) to be faced by the individuals she imagines becoming. If we maintain a distinction between identity and outcome lotteries, then Harsanyi-like axioms yield generalized utilitarianism, and allow us to accommodate concerns about different individuals' risk attitudes and concerns about fairness. Requiring an impartial observer to be indifferent as to which individual should face similar risks restricts her social welfare function, but still allows her to accommodate fairness. Requiring an impartial observer to be indifferent between identity and outcome lotteries, however, forces her to ignore both fairness and different risk attitudes, and yields a new axiomatization of Harsanyi's utilitarianism.