On the (Non-)Lattice Structure of the Equilibrium Set in Games with Strategic Substitutes
Issue Date
2008Author
Roy, Sunanda
Sabarwal, Tarun
Publisher
Springer-Verlag
Type
Article
Article Version
Scholarly/refereed, author accepted manuscript
Metadata
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This paper studies models where the optimal response functions under consideration are not 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.)
Description
This is the author's accepted manuscript. The original publication is available at http://www.springerlink.com.
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Citation
Roy, Sunanda and Tarun Sabarwal (2008): “On the (Non-)Lattice Structure of the Equilibrium Set in Games with Strategic Substitutes,” Economic Theory, 37(1),161-169. http://dx.doi.org/10.1007/s00199-007-0285-9
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