On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms

Srihari Govindan and Andrew McLennan ()

Econometrica, 2001, vol. 69, issue 2, 455-71

Abstract: Consider nonempty finite pure strategy sets S[subscript 1], . . . , S[subscript n], let S = S[subscript 1] times . . . times S[subscript n], let Omega be a finite space of "outcomes," let Delta(Omega) be the set of probability distributions on Omega, and let theta: S approaches Delta(Omega) be a function. We study the conjecture that for any utility in a generic set of n-tuples of utilities on Omega there are finitely many distributions on Omega 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.

Date: 2001
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Working Paper: On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms (1997)
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