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Ordinal Games

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Author Info
Jacques Durieu () (University of Saint Etienne, France)
Hans Haller (Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg VA, USA)
Nicolas Querou (Department of Economics, Queen's University, Belfast, Northern Ireland, UK.)
Philippe Solal () (University of Saint Etienne, France)
Abstract

We study strategic games where players' preferences are weak orders which need not admit utility representations. First of all, we ex- tend Voorneveld's concept of best-response potential from cardinal to ordi- nal games and derive the analogue of his characterization result: An ordi- nal game is a best-response potential game if and only if it does not have a best-response cycle. Further, Milgrom and Shannon's concept of quasi- supermodularity is extended from cardinal games to ordinal games. We find that under certain compactness and semicontinuity assumptions, the ordinal Nash equilibria of a quasi-supermodular game form a nonempty complete lattice. Finally, we extend several set-valued solution concepts from cardinal to ordinal games in our sense.

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Paper provided by CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich in its series CER-ETH Economics working paper series with number 07/74.

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Length: 50 pages
Date of creation: Oct 2007
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Handle: RePEc:eth:wpswif:07-74

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Related research
Keywords: Ordinal Games; Potential Games; Quasi-Supermodularity; Rationalizable Sets; Sets Closed under Behavior Correspondences;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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