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International Journal of Game Theory

, Volume 19, Issue 3, pp 237–267 | Cite as

Perfect equilibria in simultaneous-offers bargaining

  • K. Chatterjee
  • L. Samuelson
Article

Abstract

A generalization of the Nash demand game is examined. Agents make simultaneous offers in each period as to how a pie is to be divided. Incompatible offers send the game to the next period, while compatible offers end the game with a split-the-difference trade. The set of perfect equilibria of this game includes any individually rational outcome, including inefficient outcomes and even including the outcome of perpetual disagreement. We suggest a stronger equilibrium concept of universal perfection, which requires robustness against every rather than just one sequence of perturbed games. The set of universally perfect equilibria also includes all individually rational outcomes. The results provide useful insights into both simultaneous-offers bargaining and the nature of the perfect equilibrium and similar concepts (such as stability and hyperstability) in infinite games.

Keywords

Economic Theory Game Theory Rational Outcome Similar Concept Equilibrium Concept 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bagnoli M, Lipman BL (1987) Provision of Public Goods: Fully Implementing the Core Through Private Contributions, mimeo, Carnegie-Mellon UniversityGoogle Scholar
  2. Bernheim D (1984) Rationalizable Strategic Behavior, Econometrica 52, 1007–1028Google Scholar
  3. Billingsley P (1968) Convergence of Probability Measures, John Wiley and Sons, NYGoogle Scholar
  4. Binmore KG (1981) Nash Bargaining and Incomplete Information, STICERD Discussion Paper, London School of EconomicsGoogle Scholar
  5. Binmore KG (1987) Nash Bargaining and Incomplete Information. In: Binmore KG, Dasgupta P (eds), Economics of Bargaining, Basil Blackwell, 155–192Google Scholar
  6. Binmore KG, Herrero MJ (1985) Matching and Bargaining in Dynamic Markets I, Review of Economic Studies, 55, 33–48Google Scholar
  7. Dunford N, Schwartz JT (1967) Linear Operators, Part I, John Wiley & Sons, NYGoogle Scholar
  8. Fudenberg D, Levine D (1986) Limit Games and Limit Equilibria, Journal of Economic Theory 38, 261–279Google Scholar
  9. Harsanyi JC (1982) Solutions for Some Bargaining Games under the Harsanyi-Selten Solution Theory Part I, Mathematical Social Sciences 3, 179–191Google Scholar
  10. Hellwig M, Leininger W (1986) A Note on the Relation Between Discrete and Continuous Frames of Perfect Information, Discussion Paper No. A-92, University of BonnGoogle Scholar
  11. Jansen MJM (1981) Regularity and Stability of Equilibrium Point of Bimatrix Games, Mathematics of Operations Research 6, 530–550Google Scholar
  12. Kalai E, Samet D (1984) Persistent Equilibria in Strategic Games, International Journal of Game Theory 13, 129–144Google Scholar
  13. Kojima M, Okada A, and Shindoh S (1985) Strongly Stable Equilibrium Points ofN-Person Non-cooperative Game, Mathematics of Operations Research 10, 650–663Google Scholar
  14. Kohlberg E, Mertens J-F (1986) On the Strategic Stability of Equilibria, Econometrica 54, 1003–1038Google Scholar
  15. Kreps D, Wilson R (1982) Sequential Equilibria, Econometrica 50, 863–894Google Scholar
  16. Myerson RB (1978) Refinements of the Nash Equilibrium Concept, International Journal of Game Theory 7, 73–80Google Scholar
  17. Nash JF (1950) The Bargaining Problem, Econometrica 18, 155–162Google Scholar
  18. Nash JF (1953) Two-Person Cooperative Games, Econometrica 21, 128–140Google Scholar
  19. Parthasarathy KR (1967) Probability Measures on Metric Spaces, Academic Press, NYGoogle Scholar
  20. Pearce D (1984) Rationalizable Strategic Behavior and the Problem of Perfection, Econometrica 52, 1029–1050Google Scholar
  21. Rubinstein A (1982) Perfect Equilibrium in a Bargaining Model, Econometrica 50, 97–110Google Scholar
  22. Samuelson L (1986) On the Restrictiveness of Monotonic Scalable Choice in Probabilistic Choice Models, Mathematical Social Sciences, forthcomingGoogle Scholar
  23. Selten R (1975) Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, International Journal of Game Theory 4, 25–55Google Scholar
  24. Simon LK (1987) Local Perfection, Journal of Economic Theory 43, 134–156Google Scholar
  25. Tan TC, Werlang SRDC (1988) A Guide to Knowledge and Games. In: Vardi MY (ed), Theoretical Aspects of Reasoning about Knowledge, Morgan Kaufmann Publishers, 163–177Google Scholar
  26. van Damme E (1983) Refinements of the Nash Equilibrium Concept, Springer-Verlag, NYGoogle Scholar
  27. Wen-Tsün W, Jin-He J (1962) Essential Equilibrium Points ofN-person Noncooperative Games, Sci. Sinica 11, 1307–1322Google Scholar

Copyright information

© Physica-Verlag 1990

Authors and Affiliations

  • K. Chatterjee
    • 1
  • L. Samuelson
    • 2
  1. 1.Department of Management ScienceThe Pennsylvania State UniversityUniversity Park
  2. 2.Department of EconomicsUniversity of WisconsinMadisonUSA

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