Department of Economics

Faculty of Arts and Social Sciences


Seminar - Upcoming

2013 Asia Summer Institute in Behavioral Economics
Asian Meeting of the Econometric Society 2013
Past Events
Department Seminar


Ordinal potentials in smooth games


Christian Ewerhart
University of Zurich

Date: Nov 7, Tue

Time: 4 - 5:30 pm

Venue: Lim Tay Boh Seminar Room (AS2 03-12)
National University of Singapore
1 Arts Link, Singapore 117570

Chair: Lu Jingfeng


While smooth exact potential games are easily characterized in terms of the cross-derivatives of players' payoff functions, an analogous differentiable characterization of ordinal or generalized ordinal potential games has been elusive for a long time. In this paper, it is shown that the existence of a generalized ordinal potential in a smooth game with multi-dimensional strategy spaces is crucially linked to the semipositivity (Fiedler and Ptak, 1966) of a modified Jacobian matrix on the set of interior strategy profiles at which at least two first-order conditions hold. Our findings imply, in particular, that any generalized ordinal potential game must exhibit pairwise strategic complements or substitutes at any interior Cournot-Nash equilibrium. Moreover, provided that there are more than two players, the cross-derivatives at any interior equilibrium must satisfy a rather stringent equality constraint. The two conditions, which may be conveniently condensed into a local variant of the differentiable condition for weighted potential games, are made explicit for sum-aggregative games, symmetric games, and two-person zero-sum games. For the purpose of illustration, the results are applied to classic games, including probabilistic all-pay contests with heterogeneous valuations, models of mixed oligopoly, and Cournot games with a dominant firm.