A Necessary and Sufficient Condition for a Unique Maximum with an Application to Potential Games

Finn Christensen

No 2017-04, Working Papers from Towson University, Department of Economics

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)
Pages: 12 pages
Date: 2017-08, Revised 2017-10
New Economics Papers: this item is included in nep-gth and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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http://webapps.towson.edu/cbe/economics/workingpapers/2017-04.pdf First version, 2017 (application/pdf)

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Journal Article: A necessary and sufficient condition for a unique maximum with an application to potential games (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:tow:wpaper:2017-04

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