On the (Non-)Lattice Structure of the Equilibrium Set in Games with Strategic Substitutes

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 co...

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Podrobná bibliografie
Vydáno v:	Economic theory Ročník 37; číslo 1; s. 161 - 169
Hlavní autoři:	Roy, Sunanda, Sabarwal, Tarun
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer 01.10.2008 Springer-Verlag Springer Nature B.V
Témata:	Correspondence Decreasing functions Economic models Economic theory Economic Theory/Quantitative Economics/Mathematical Methods Economics Economics and Finance Endogenous Equilibrium Equilibrium models Exposita Note Exposita Notes Family papers Game Theory Games Marginal costs Mathematical economics Mathematical functions Mathematical independent variables Mathematical lattices Mathematical monotonicity Microeconomics Nash equilibrium Partially ordered sets Public Finance Research papers Social and Behav. Sciences Studies Variables Never increasing correspondences Non-increasing functions Equilibrium set Monotone comparative statics C60 Strategic substitutes C62 C61 C72
ISSN:	0938-2259, 1432-0479
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Popis
Shrnutí:	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.)
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0938-2259 1432-0479
DOI:	10.1007/s00199-007-0285-9