Nondegeneracy Problems in Cooperative Game Theory

J. Rosenmüller
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J. Rosenmüller: Universität Bielefeld, Institut für Mathematische Wirtschaftsforschung

A chapter in Mathematical Programming The State of the Art, 1983, pp 391-416 from Springer

Abstract: Abstract Game Theory originally is rooting to a certain extent in the various fields of optimization and programming. Most students of elementary courses in linear programming techniques are familiar with the fact that there is a close relation between the optimal solutions of an L.P. and the optimal strategies of an associated matrix game. Hence, if we introduce the mixed extension of a finite two-person zero-sum game then, according to von Neumann’s minimax theorem, there exist always optimal mixed strategies for both players and, in addition, it is easy to define a certain associated linear program such if we obtain the optimal solutions of this L.P., say, via the simplex algorithm, then this optimal solutions simultaneously yield the optimal strategies of the two-person game under consideration.

Date: 1983
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DOI: 10.1007/978-3-642-68874-4_16

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