 Ordinal potentials in smooth gamesEconomic Theory, 2020, vol. 70, issue 4, No 7, 1069-1100 Abstract: 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 cross-derivatives (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. Keywords: Ordinal potentials; Smooth games; Strategic complements and substitutes; Semipositive matrices (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:joecth:v:70:y:2020:i:4:d:10.1007_s00199-020-01257-1 Ordering information: This journal article can be ordered from DOI: 10.1007/s00199-020-01257-1 Access Statistics for this article Economic Theory is currently edited by Nichoals Yanneils More articles in Economic Theory from Springer, Society for the Advancement of Economic Theory (SAET) Contact information at EDIRC. |
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