Characterization of optimal strategies in matrix games with convexity properties

Tadeusz Radzik

International Journal of Game Theory, 2000, vol. 29, issue 2, 227 pages

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.

Keywords: Matrix; game; ·; saddle; point; ·; optimal; strategy; ·; strategy; structure; ·; convexity (search for similar items in EconPapers)
Date: 2000-07-12
Note: Received: May 1997/Final version: August 1999
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Citations: View citations in EconPapers (2)

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