Ordinal potentials in smooth games

Arbeitspapier

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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Working Paper ; No. 265

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Noncooperative Games ; Market Structure, Pricing, and Design: Oligopoly and Other Forms of Market Imperfection ; Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
• Thema: Ordinal potentials ; smooth games ; strategic complements and substitutes ; semipositive matrices

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Ewerhart, Christian
• Ereignis: Veröffentlichung
• (wer): University of Zurich, Department of Economics
• (wo): Zurich
• (wann): 2017

Weitere Informationen

• DOI: doi:10.5167/uzh-140858
• Handle: http://hdl.handle.net/10419/173423
• Letzte Aktualisierung: 10.03.2025, 11:43 MEZ