The equivalence between two-person symmetric games and decision problems

M.S. Ismail

Research output: Working paperProfessional

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Abstract

We illustrate an equivalence between the class of two-person symmetric games and the class of decision problems with a complete preference relation. Moreover, we show that a strategy is an optimal threat strategy (Nash, 1953) in a two-person symmetric game if and only if it is a maximal element in its equivalent decision problem. In particular, a Nash equilibrium in a two-person symmetric zero-sum game and a pair of maximal elements in its equivalent decision problem coincide. In addition, we show that a two-person symmetric zero-sum game can be extended to its von Neumann-Morgenstern (vN-M) mixed extension if and only if the extended decision problem satisfies the SSB utility (Fishburn, 1982) axioms. Furthermore, we demonstrate that a decision problem satisfies vN-M utility if and only if its equivalent symmetric game is a potential game. Accordingly, we provide a formula for the number of linearly independent equations in order for the independence axiom to be satisfied which grows quadratically as the number of alternatives increase.
Original languageEnglish
Place of PublicationMaastricht
PublisherMaastricht University, Graduate School of Business and Economics
Publication statusPublished - 1 Jan 2014

Publication series

SeriesGSBE Research Memoranda
Number023

Cite this

Ismail, M. S. (2014). The equivalence between two-person symmetric games and decision problems. Maastricht University, Graduate School of Business and Economics. GSBE Research Memoranda, No. 023