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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 (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 payoffs 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 different results from the refinements 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 sufficient condition for robustness. Download Paper
This paper established the generic existence 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. This results also clarifies the relationship between equilibrium multiplicity and existence of sunspot equilibria. Our technique is very general and can be applied to other frameworks as the overlapping generations model with sunspots. Download Paper
This paper studies the robustness of a competitive equilibrium against sunspots, or endogenous uncertainty. It is shown that an equilibrium is robust if and only if it is sequentially regular. Download Paper
This paper re-examines the conditions for the existence of local stationary sunspot equilibria (SSE) in the standard OLG model from a broader perspective than before. We say that local SSE exist around a steady state of a given OLG economy if, in any arbitrarily small neighborhood of the steady state, we can find a SSE of a “nearby” economy. We show that when the domain where “nearby” economies may lie is defined by agents’ endowments and probabilities, the indeterminacy of the steady state remains both necessary and sufficient for the existence of local SSE. On the other hand, when the domain of economies is defined by by agents’ preferences and probabilities, local SSE may exist even around determinate steady states. We also show that if a slightly weaker notion of distance is used to identify “nearby” economies, SSE in the vicinity of a steady state equilibrium generically exist. Download Paper