EconPapers    
Economics at your fingertips  
 

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: C61 C72 C62 C60 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth
Date: 2006-12, Revised 2007-05-23
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (3) Track citations by RSS feed

Downloads: (external link)
http://mpra.ub.uni-muenchen.de/4120/ original version (application/pdf)

Related works:
Journal Article: On the (non-)lattice structure of the equilibrium set in games with strategic substitutes (2008) Downloads
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:pra:mprapa:4120

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany
Address: Schackstr. 4, D-80539 Munich, Germany
Contact information at EDIRC.
Series data maintained by Ekkehart Schlicht ().

 
Page updated 2014-09-19
Handle: RePEc:pra:mprapa:4120