On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms
AbstractConsider 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.
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Bibliographic InfoArticle provided by Econometric Society in its journal Econometrica.
Volume (Year): 69 (2001)
Issue (Month): 2 (March)
Other versions of this item:
- Govindan, S & McLennan, A, 1997. "On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms," Papers 299, Minnesota - Center for Economic Research.
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
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