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Continuity and Equilibrium Stability

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  • C. D. Aliprantis
  • I. Topolyan
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    Abstract

    This paper discusses the problem of stability of equilibrium points in normal form games in the tremling-hand framework. An equilibrium point is called perffect if it is stable against at least one seqence of trembles approaching zero. A strictly perfect equilibrium point is stable against every such sequence. We 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, we show that continuity of the best response correspondence (which can be stated in terms of the primitives of the game) implies strict perfectness; we prove a number of other useful theorems regarding the structure of best responce correspondence in normal form games.

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    Bibliographic Info

    Paper provided by Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1224.

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    Length: 13 pages
    Date of creation: Aug 2009
    Date of revision:
    Handle: RePEc:pur:prukra:1224

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    Related research

    Keywords: Strictly perfect equilibrium; best responce correspondence; unit simplex; face of a unit simplex;

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