Title: On the genericity of the finite number of equilibria in multicriteria games: a counterexample

Authors: Giuseppe De Marco

Addresses: Department of Statistics and Mathematics for Economic Research, University of Naples Parthenope, Via Medina 40, Napoli 80133, Italy

Abstract: The famous Harsanyi's (1973) Theorem states that a generic finite game has an odd number of Nash equilibria in mixed strategies. In this paper, counterexamples are given showing that for finite multicriteria games (games with vector-valued payoffs) this kind of result does not hold. In particular, it is shown that it is possible to find balls in the space of games such that every game in this set has uncountably many equilibria. This result then formalises the intuitive idea that games with uncountable sets of equilibria are not non-generic in the multicriteria case.

Keywords: finite multicriteria games; Pareto-Nash equilibrium; genericity; vector-valued payoffs; generic.

DOI: 10.1504/IJMOR.2013.057494

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.6, pp.764 - 777

Received: 22 Aug 2012
Accepted: 08 Oct 2012
Published online: 31 Mar 2014 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article