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Contribution Details

Type Journal Article
Scope Discipline-based scholarship
Title Ordinal potentials in smooth games
Organization Unit
  • Christian Ewerhart
Item Subtype Original Work
Refereed Yes
Status Published in final form
  • English
Journal Title Economic Theory
Publisher Springer
Geographical Reach international
ISSN 0938-2259
Volume 70
Number 4
Page Range 1069 - 1100
Date 2020
Abstract Text 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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Digital Object Identifier 10.1007/s00199-020-01257-1
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Keywords Economics and econometrics, ordinal potentials, smooth games, strategic complements and substitutes, semipositive matrices
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: