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.
Original language | English |
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Pages (from-to) | 567-588 |
Journal | Journal of Optimization Theory and Applications |
Volume | 105 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jun 2000 |
Keywords
- game theory
- bimatrix games
- Nash equilibria
- restricted games