Randomization and the limit points of monopolistic competition

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For a general equilibrium model of monopolistic competition, the set of competitive equilibria and the set of limits of Nash-Cournot equilibria for a sequence of replica economies coincide generically. The key feature which makes every limit of monopolistic competition perfectly competitive is that random rather than deterministic selections from the equilibrium price correspondence are considered in the definition of firms' reaction functions when there are multiple Walrasian equilibria. An existence result for mixed strategy Nash-Cournot equilibria in finite economies is also given.

Original languageEnglish (US)
Pages (from-to)205-218
Number of pages14
JournalJournal of Mathematical Economics
Issue number3
StatePublished - May 1994

Bibliographical note

Funding Information:
Correspondence to: Professor Beth Allen, Department of Economics, University of Minnesota, Minneapolis, MN 55455, USA. *Research support from the National Science Foundation (grants IST79-18464, IST83-14096, and SES88-21442), the Deutsche Forschungsgemeinschaft (through Sonderforschungsbereich 21 at the University of Bonn), a NATO research fellowship and CORE is gratefully acknowledged. Preliminary versions of this paper were presented at the 1981 Midwestern Mathematical Economics Meeting (University of Michigan, Ann Arbor) and at the 1982 North American Winter Meeting of the Econometric Society (New York City). In developing these ideas, I have benetitted from interaction with a number of colleagues at Bonn, especially Egbert Dierker, Hildegard Dierker, Birgit Grodal, and Martin Hellwig. Andreu Mas-Cole11 provided encouragement at a time when it was needed, and John Hamilton furnished useful expository comments. The standard freedom from blame is, of course, appropriate.


  • Cournot-Nash
  • General equilibrium
  • Limit for sequence of replicas
  • Monopolistic competition
  • Multiple equilibria
  • Selections
  • Upper hemicontinuous correspondence


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