On the (non-)lattice structure of the equilibrium set in games with strategic substitutes

Sunanda Roy and Tarun Sabarwal

MPRA Paper from University Library of Munich, Germany

Abstract: This paper studies models where the optimal response functions under consideration are non-increasing in endogenous variables, and weakly increasing in exogenous parameters. Such models include games with strategic substitutes, and include cases where additionally, some variables may be strategic complements. The main result here is that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. Indeed, for a given parameter value, a pair of distinct equilibria are never comparable. Therefore, with multiple equilibria, some of the established techniques for exhibiting increasing equilibria or computing equilibria that use the largest or smallest equilibrium, or that use the lattice structure of the equilibrium set do not apply to such models. Moreover, there are no ranked equilibria in such models. Additionally, the analysis here implies a new proof and a slight generalization of some existing results. It is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. (In particular, in n-player games of strategic substitutes with real-valued action spaces, symmetric equilibria increase with the parameter.)

Keywords: Monotone comparative statics; Non-increasing functions; Never increasing correspondences; Strategic substitutes; Equilibrium set (search for similar items in EconPapers)
JEL-codes: C60 C61 C62 C72 (search for similar items in EconPapers)
Date: 2006-12, Revised 2007-05-23
New Economics Papers: this item is included in nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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Related works:
Journal Article: On the (non-)lattice structure of the equilibrium set in games with strategic substitutes (2008)
Working Paper: On the (Non)-Lattice Structure of Equilibrium Sets in Games with Strategic Substitutes (2008)
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