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Ordinal Games



    (CREUSET, University of Saint-Etienne, 42023 Saint-Etienne, France)



    (Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0316, USA)



    (Queen's University Management School, Queen's University, Belfast, Northern Ireland, UK)



    (CREUSET, University of Saint-Etienne, 42023 Saint-Etienne, France)

We study strategic games where players' preferences are weak orders which need not admit utility representations. First of all, we extend Voorneveld's concept of best-response potential from cardinal to ordinal games and derive the analogue of his characterization result: An ordinal 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 topological 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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Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 10 (2008)
Issue (Month): 02 ()
Pages: 177-194

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Handle: RePEc:wsi:igtrxx:v:10:y:2008:i:02:p:177-194
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