A necessary and sufficient condition for a unique maximum with an application to potential games

Finn Christensen

Economics Letters, 2017, vol. 161, issue C, 120-123

Abstract: Under regularity and boundary conditions which ensure an interior maximum, I show that there is a unique critical point which is a global maximum if and only if the Hessian determinant of the negated objective function is strictly positive at any critical point. Within the large class of Morse functions, and subject to boundary conditions, this local and ordinal condition generalizes strict concavity, and is satisfied by nearly all strictly quasiconcave functions. The result also provides a new uniqueness theorem for potential games.

Keywords: Optimization; Index theory; Potential games (search for similar items in EconPapers)
JEL-codes: C02 C72 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:161:y:2017:i:c:p:120-123

DOI: 10.1016/j.econlet.2017.10.008

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