Faculty of Economics and Business Administration Publications Database

The Women of Cairo: Equilibria in Large Anonymous Games

Volume: 41
Number: 3
Pages: 253 - 264
Month: April
ISSN-Print: 0304-4068
Link External Source: Online Version
Year: 2005
Keywords: Large games; Co-ordination problem; Anonymous games; Equilibrium characterization
Abstract: In this article, I characterize Nash equilibria of large anonymous games by providing the following neccessary and sufficient condition for an equilibrium distribution: for no subset K of actions more players play actions in K than have a best response in K to the given distribution. While neccessity is trivial the proof for sufficiency relies on a theorem by [Math. Proc. Camb. Philos. Soc. 78 (1974) 323] which is an extension of Hall’s theorem or the marriage lemma well known from graph theory. The veiling problem for the women of Cairo serves as an illustrating heuristic example explaining the nature of the result.