Characterization of optimal strategies in matrix games with convexity properties |
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Authors: | Tadeusz Radzik |
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Institution: | (1) Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland, PL |
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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.
Received: May 1997/Final version: August 1999 |
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Keywords: | : Matrix game saddle point optimal strategy strategy structure convexity |
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