Generic finiteness of equilibrium distributions for bimatrix outcome game forms

  • Cristian Litan
  • Francisco Marhuenda
  • Peter Sudhölter
S.I.: Game theory and optimization
  • 7 Downloads

Abstract

We provide sufficient and necessary conditions for the generic finiteness of the number of distributions on outcomes, induced by the completely mixed Nash equilibria associated to a bimatrix outcome game form. These equivalent conditions are stated in terms of the ranks of two matrices constructed from the original game form.

Keywords

Outcome game form Completely mixed Nash equilibrium Generic finiteness 

Mathematics Subject Classification

91A12 

JEL Classification

C72 

References

  1. González-Pimienta, C. (2010). Generic finiteness of outcome distributions for two person game forms with three outcomes. Mathematical Social Sciences, 59, 364–365.CrossRefGoogle Scholar
  2. Govindan, S., & McLennan, A. (1998). Generic finiteness of outcome distributions for two person game forms with zero sum and common interest utilities. Mimeo: University of Western Ontario.Google Scholar
  3. Govindan, S., & McLennan, A. (2001). On the generic finiteness of equilibrium outcome distributions in game forms. Econometrica, 69, 455–471.CrossRefGoogle Scholar
  4. Harsanyi, J. C. (1973). Oddness of the number of equilibrium points: A new proof. International Journal of Game Theory, 2, 235–250.CrossRefGoogle Scholar
  5. Kreps, D. M., & Wilson, R. (1982). Sequential equilibria. Econometrica, 50, 863–894.CrossRefGoogle Scholar
  6. Kukushkin, N. S., Litan, C., & Marhuenda, F. (2008). On the generic finiteness of equilibrium outcome distributions in bimatrix game forms. Journal of Economic Theory, 139, 392–395.CrossRefGoogle Scholar
  7. Litan, C., Marhuenda, F., & Sudhölter, P. (2015). Determinacy of equilibrium in outcome game forms. Journal of Mathematical Economics, 60, 28–32.CrossRefGoogle Scholar
  8. Litan, C. M., & Marhuenda, F. (2012). Determinacy of equilibrium outcome distributions for zero sum and common utility games. Economics Letters, 115, 152–154.CrossRefGoogle Scholar
  9. Mas-Colell, A. (2010). Generic finiteness of equilibrium payoffs for bimatrix games. Journal of Mathematical Economics, 46, 382–383.CrossRefGoogle Scholar
  10. Park, I.-U. (1997). Generic finiteness of equilibrium outcome distributions for sender–receiver cheap-talk games. Journal of Economic Theory, 76, 431–448.CrossRefGoogle Scholar
  11. Rosenmüller, J. (1971). On a generalization of the Lemke–Howson algorithm to noncooperative n-person games. SIAM Journal on Applied Mathematics, 20, 73–79.CrossRefGoogle Scholar
  12. Wilson, R. (1971). Computing equilibria of n-person games. SIAM Journal on Applied Mathematics, 20, 80–87.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics, Forecasting, Mathematics, Faculty of Economics and Business AdministrationBabeş-Bolyai UniversityCluj-NapocaRomania
  2. 2.Department of EconomicsUniversity Carlos III of MadridGetafe, MadridSpain
  3. 3.Department of Business and Economics, and COHEREUniversity of Southern DenmarkOdense MDenmark

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