Econometrica Vol. 69 No. 2 2001
On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms
Abstract
Consider nonempty finite pure strategy sets S1,…,Sn, let S=S1×⋅⋅⋅×Sn, let Ω be a finite space of “outcomes,” let Δ(Ω) be the set of probability distributions on Ω, and let θ: S→Δ(Ω) be a function. We study the conjecture that for any utility in a generic set of n-tuples of utilities on Ω there are finitely many distributions on Ω induced by the Nash equilibria of the game given by the induced utilities on S. We give a counterexample refuting the conjecture for n≥3. Several special cases of the conjecture follow from well known theorems, and we provide some generalizations of these results.
- DOI
- 10.1111/1468-0262.00198
- Volume
- 69
- Issue
- 2
- Pages
- 455-471
- Language
- en
- Sources
- bibtex:phds-export.bib openalex crossref