Polytope games

R Bhattacharjee*, F Thuijsman, OJ Vrieze

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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 languageEnglish
Pages (from-to)567-588
JournalJournal of Optimization Theory and Applications
Issue number3
Publication statusPublished - Jun 2000


  • game theory
  • bimatrix games
  • Nash equilibria
  • restricted games

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