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Solution concepts in two-person multicriteria games. (English) Zbl 0662.90093
We propose new solution concepts for multicriteria games and compare them with existing ones. The general setting is that of two-person finite games in normal form (matrix games) with pure and mixed strategy sets for the players. The notions of efficiency (Pareto optimality), security levels, and response strategies have all been used in defining solutions ranging from equilibrium points to Pareto saddle points. Methods for obtaining strategies that yield Pareto security levels to the players or Pareto saddle points to the game, when they exist, are presented. Finally, we study games with more than two qualitative outcomes such as combat games. Using the notion of guaranteed outcomes, we obtain saddlepoint solutions in mixed strategies for a number of cases. Examples illustrating the concepts, methods, and solutions are included.
Reviewer: D.Ghose

MSC:
91A05 2-person games
90C31 Sensitivity, stability, parametric optimization
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