Arbeitspapier

Ordinal potentials in smooth games

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.

Sprache
Englisch

Erschienen in
Series: Working Paper ; No. 265

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

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

DOI
doi:10.5167/uzh-140858
Handle
Letzte Aktualisierung
10.03.2025, 11:43 MEZ

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Objekttyp

  • Arbeitspapier

Beteiligte

  • Ewerhart, Christian
  • University of Zurich, Department of Economics

Entstanden

  • 2017

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