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Continuity and Equilibrium Stability

Author

Listed:
  • C. D. Aliprantis
  • I. Topolyan

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.

Suggested Citation

  • C. D. Aliprantis & I. Topolyan, 2009. "Continuity and Equilibrium Stability," Purdue University Economics Working Papers 1224, Purdue University, Department of Economics.
    • Handle: RePEc:pur:prukra:1224
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    File URL: https://business.purdue.edu/research/Working-papers-series/2009/1224.pdf
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    More about this item

    Keywords

    Strictly perfect equilibrium; best responce correspondence; unit simplex; face of a unit simplex;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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