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Ordinal potentials in smooth games


Ewerhart, Christian (2020). Ordinal potentials in smooth games. Economic Theory, 70(4):1069-1100.

Abstract

In the class of smooth non-cooperative games, exact potential games and weighted potential games are known to admit a convenient characterization in terms of crossderivatives (Monderer and Shapley in Games Econ Behav 14:124–143, 1996a). However, no analogous characterization is known for ordinal potential games. The present paper derives necessary conditions for a smooth game to admit an ordinal potential. First, any ordinal potential game must exhibit pairwise strategic complements or substitutes at any interior equilibrium. Second, in games with more than two players, a condition is obtained on the (modified) Jacobian at any interior equilibrium. Taken together, these conditions are shown to correspond to a local analogue of the Monderer–Shapley condition for weighted potential games. We identify two classes of economic games for which our necessary conditions are also sufficient.

Abstract

In the class of smooth non-cooperative games, exact potential games and weighted potential games are known to admit a convenient characterization in terms of crossderivatives (Monderer and Shapley in Games Econ Behav 14:124–143, 1996a). However, no analogous characterization is known for ordinal potential games. The present paper derives necessary conditions for a smooth game to admit an ordinal potential. First, any ordinal potential game must exhibit pairwise strategic complements or substitutes at any interior equilibrium. Second, in games with more than two players, a condition is obtained on the (modified) Jacobian at any interior equilibrium. Taken together, these conditions are shown to correspond to a local analogue of the Monderer–Shapley condition for weighted potential games. We identify two classes of economic games for which our necessary conditions are also sufficient.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Social Sciences & Humanities > Economics and Econometrics
Uncontrolled Keywords:Economics and econometrics, ordinal potentials, smooth games, strategic complements and substitutes, semipositive matrices
Language:English
Date:1 November 2020
Deposited On:14 May 2020 10:31
Last Modified:22 Apr 2021 00:00
Publisher:Springer
ISSN:0938-2259
Additional Information:This is a post-peer-review, pre-copyedit version of an article published in Economic Theory. The final authenticated version is available online at: https://doi.org/10.1007/s00199-020-01257-1
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00199-020-01257-1
Official URL:https://rdcu.be/b4CRa

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