Ordinal Games

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 ¯nd 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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Submitted on : Friday, December 7, 2007 - 2:29:21 PM
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Jacques Durieu, Hans Haller, Nicolas Quérou, Philippe Solal. Ordinal Games. 2007. ⟨ujm-00194794⟩

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