Ordinal Games

Center of Economic Research Working Paper No. 07/74

50 Pages Posted: 23 Oct 2007

See all articles by Jacques Durieu

Jacques Durieu

University of Saint Etienne

Hans H. Haller

Virginia Polytechnic Institute & State University - Department of Economics

Nicolas Querou

Queen's University Belfast - School of Management and Economics

Philippe Solal

University of Saint Etienne

Date Written: October 2007

Abstract

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 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.

Keywords: Ordinal Games, Potential Games, Quasi-Supermodularity, Rationalizable Sets, Sets Closed under Behavior Correspondences

JEL Classification: C72

Suggested Citation

Durieu, Jacques and Haller, Hans H. and Querou, Nicolas and Solal, Philippe, Ordinal Games (October 2007). Center of Economic Research Working Paper No. 07/74, Available at SSRN: https://ssrn.com/abstract=1023841 or http://dx.doi.org/10.2139/ssrn.1023841

Jacques Durieu

University of Saint Etienne ( email )

6, rue basse des rives
Saint Etienne, 42023
France

Hans H. Haller (Contact Author)

Virginia Polytechnic Institute & State University - Department of Economics ( email )

3021 Pamplin Hall
Blacksburg, VA 24061
United States
540-231-7591 (Phone)
540-231-5097 (Fax)

Nicolas Querou

Queen's University Belfast - School of Management and Economics ( email )

25 University Square
Belfast, Northern Ireland BT7 1NN
Northern Ireland

Philippe Solal

University of Saint Etienne ( email )

6, rue basse des rives
Saint Etienne, 42023
France

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