Polytope Games

R. Bhattacharjee, F. Thuijsman and O. J. Vrieze
Additional contact information
R. Bhattacharjee: Boston University
F. Thuijsman: Maastricht University
O. J. Vrieze: Maastricht University

Journal of Optimization Theory and Applications, 2000, vol. 105, issue 3, No 6, 567-588

Abstract: Abstract Starting from the definition of a bimatrix game, we restrict the pair of strategy sets jointly, not independently. Thus, we have a set $$P \subset S_m \times S_n$$ , which is the set of all feasible strategy pairs. We pose the question of whether a Nash equilibrium exists, in that no player can obtain a higher payoff by deviating. We answer this question affirmatively for a very general case, imposing a minimum of conditions on the restricted sets and the payoff. Next, we concentrate on a special class of restricted games, the polytope bimatrix game, where the restrictions are linear and the payoff functions are bilinear. Further, we show how the polytope bimatrix game is a generalization of the bimatrix game. We give an algorithm for solving such a polytope bimatrix game; finally, we discuss refinements to the equilibrium point concept where we generalize results from the theory of bimatrix games.

Keywords: game theory; bimatrix games; Nash equilibria; restricted games (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1004689006566

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