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On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms

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Author Info
Govindan, Srihari
McLennan, Andrew

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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.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 69 (2001)
Issue (Month): 2 (March)
Pages: 455-71
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Handle: RePEc:ecm:emetrp:v:69:y:2001:i:2:p:455-71

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  1. Francesco De Sinopoli & Giovanna Iannantuoni, 2003. "On the Generic Strategic Stability of Nash Equilibria if Voting is Costly," CEIS Research Paper 41, Tor Vergata University, CEIS. [Downloadable!]
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  2. Hans Haller & Roger Lagunoff, 1999. "Genericity and Markovian Behavior in Stochastic Games," Game Theory and Information 9901003, EconWPA, revised 03 Jun 1999. [Downloadable!]
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  3. Carlos Pimienta, 2007. "Generic Finiteness of Outcome Distributions for Two Person Game Forms with Three Outcomes," Discussion Papers 2007-20, School of Economics, The University of New South Wales. [Downloadable!]
  4. Carlos Pimienta, 2007. "Generic Determinacy of Nash Equilibrium in Network Formation Games," Discussion Papers 2007-31, School of Economics, The University of New South Wales. [Downloadable!]
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  5. DE SINOPOLI, Francesco, 1998. "Two results about generic non cooperative voting games with plurality rule," CORE Discussion Papers 1998034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  6. Andreu Mas-Colell, 2008. "Generic Finiteness of Equilibrium Payoffs for Bimatrix Games," Economics Working Papers 1103, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  7. In-Uck Park, 1993. "Generic Finiteness of Equilibrium Outcome Distributions in Sender-Received Cheap-Talk Games," Game Theory and Information 9310002, EconWPA. [Downloadable!]
  8. DE SINOPOLI, Francesco, 1999. "Further remarks on strategic stability in plurality games," CORE Discussion Papers 1999030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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