A set optimization approach to zero-sum matrix games with multi-dimensional payoffs View Full Text


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Article Info

DATE

2018-12

AUTHORS

Andreas H. Hamel, Andreas Löhne

ABSTRACT

A new solution concept for two-player zero-sum matrix games with multi-dimensional payoffs is introduced. It is based on extensions of the vector order in Rd to order relations in the power set of Rd, so-called set relations, and strictly motivated by the interpretation of the payoff as multi-dimensional loss for one and gain for the other player. The new concept provides coherent worst case estimates for games with multi-dimensional payoffs. It is shown that–in contrast to games with one-dimensional payoffs–the corresponding strategies are different from equilibrium strategies for games with multi-dimensional payoffs. The two concepts are combined into new equilibrium notions for which existence theorems are given. Relationships of the new concepts to existing ones such as Shapley and vector equilibria, vector minimax and maximin solutions as well as Pareto optimal security strategies are clarified. More... »

PAGES

1-29

References to SciGraph publications

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  • 1996-04. Vector linear programming in zero-sum multicriteria matrix games in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1975-12. Games with multiple payoffs in INTERNATIONAL JOURNAL OF GAME THEORY
  • 1991-06. The equilibria of a multiple objective game in INTERNATIONAL JOURNAL OF GAME THEORY
  • 1991-03. A necessary and sufficient condition for Pareto-optimal security strategies in multicriteria matrix games in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1988-12. Some minimax problems of vector-valued functions in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2005-08. Nash equilibrium in games with incomplete preferences in ECONOMIC THEORY
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    http://scigraph.springernature.com/pub.10.1007/s00186-018-0639-z

    DOI

    http://dx.doi.org/10.1007/s00186-018-0639-z

    DIMENSIONS

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