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Continuity And Equilibrium Stability

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Executive Summary

This paper discusses the problem of stability of equilibrium points in normal form games in the tremling-hand framework. An equilibrium point is called perfect if it is stable against at least one seqence of trembles approaching zero. A strictly perfect equilibrium point is stable against every such sequence. The authors give a sufficient condition for a Nash equilibrium point to be strictly perfect in terms of the primitive characteristics of the game (payoffs and strategies), which is new and not known in the literature. In particular, they show that continuity of the best response correspondence (which can be stated in terms of the primitives of the game) implies strict perfectness; they prove a number of other useful theorems regarding the structure of best responce correspondence in normal form games.

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