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Characterization of optimal strategies in matrix games with convexity properties

Author

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  • Tadeusz Radzik

    (Institute of Mathematics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland)

Abstract

This paper gives a full characterization of matrices with rows and columns having properties closely related to the (quasi-) convexity-concavity of functions. The matrix games described by such payoff matrices well approximate continuous games on the unit square with payoff functions F (x, y) concave in x for each y, and convex in y for each x. It is shown that the optimal strategies in such matrix games have a very simple structure and a search-procedure is given. The results have a very close relationship with the known theorem of Debreu and Glicksberg about the existence of a pure Nash equilibrium in n-person games.

Suggested Citation

  • Tadeusz Radzik, 2000. "Characterization of optimal strategies in matrix games with convexity properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(2), pages 211-227.
    • Handle: RePEc:spr:jogath:v:29:y:2000:i:2:p:211-227
    Note: Received: May 1997/Final version: August 1999
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    Cited by:

    1. Wojciech Połowczuk & Piotr Więcek & Tadeusz Radzik, 2007. "On the existence of almost-pure-strategy Nash equilibrium in n-person finite games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 141-152, February.
    2. Tadeusz Radzik, 2014. "Poor convexity and Nash equilibria in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 169-192, February.

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