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
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Englisch
- Erschienen in
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Series: Working Paper ; No. 265
- Klassifikation
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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
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Ordinal potentials
smooth games
strategic complements and substitutes
semipositive matrices
- Ereignis
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Geistige Schöpfung
- (wer)
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Ewerhart, Christian
- Ereignis
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Veröffentlichung
- (wer)
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University of Zurich, Department of Economics
- (wo)
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Zurich
- (wann)
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2017
- DOI
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doi:10.5167/uzh-140858
- Handle
- Letzte Aktualisierung
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10.03.2025, 11:43 MEZ
Datenpartner
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Objekttyp
- Arbeitspapier
Beteiligte
- Ewerhart, Christian
- University of Zurich, Department of Economics
Entstanden
- 2017