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Polytope games
Bhattacharjee R, Thuijsman F, Vrieze OJ
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 105 (3): 567-588 JUN 2000

Document type: Article

Language: English

Cited References: 10

Times Cited: 0

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 of S-m x 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 Same; finally, we discuss refinements to the equilibrium point concept where we generalize results from the theory of bimatrix games.

Author Keywords:
game theory, bimatrix games, Nash equilibria, restricted games

Addresses:
Bhattacharjee R, Boston Univ, Dept Math, Boston, MA 02215 USA
Boston Univ, Dept Math, Boston, MA 02215 USA
Maastricht Univ, Dept Math, Maastricht, Netherlands

Publisher:
KLUWER ACADEMIC/PLENUM PUBL, NEW YORK

IDS Number:
345AN

ISSN:
0022-3239

Article 8 of 40

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