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International Journal of Game Theory

, Volume 26, Issue 4, pp 501–524 | Cite as

Multiple-issue bargaining and axiomatic solutions

  • Clara Ponsati
  • Joel Watson
Article

Abstract

We study two-person, multiple-issue bargaining problems and identify four procedures by which the bargaining may take place. Drawing on some logic from non-cooperative game theory, we propose axioms which relate the outcomes of the procedures. We also promote a weak monotonicity axiom on solutions, called issue-by-issue monotonicity, which is geared toward multiple-issue bargaining. Our main result concerns the relationship between a sequential bargaining procedure — with the rule that agreements are implemented only after all issues are resolved — and global bargaining (in which all issues are negotiated simultaneously). If a bargaining solution predicts the same outcome with these two procedures, then we say that it satisfiesagenda independence. We prove that a solution satisfies axioms of efficiency, symmetry, scale invariance, issue-by-issue monotonicity, and agenda independence if and only if it is the Nash solution. This result provides new intuition for Nash's independence of irrelevant alternatives axiom. Among other results, we show that a solution is invariant to all four of the procedures and satisfies efficiency and symmetry if and only if it is the utilitarian solution with equal weights. We comment on the results of other authors who address multiple-issue bargaining.

Keywords

Economic Theory Game Theory Equal Weight Scale Invariance Bargaining Solution 
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. [1]
    Chun Y (1988) Nash solution and timing of bargaining. Economics Letters 28: 27–31Google Scholar
  2. [2]
    Fershtman C (1986) The importance of agenda in bargaining. Games and Economic Behavior 2: 224–238Google Scholar
  3. [3]
    Herrero MJ (1993) Two issue bargaining, mimeoGoogle Scholar
  4. [4]
    Kalai E (1977) Proportional solutions to bargaining situations: Intertemporal utility comparisons. Econometrica 45: 1623–1630Google Scholar
  5. [5]
    Kalai E, Smorodinsky M (1975) Other solutions to the Nash bargaining problem. Econometrica 43: 513–518Google Scholar
  6. [6]
    De Koster R, Peters H, Tijs S, Wakker P (1983) Risk sensitivity, independence of irrelevant alternatives and continuity of bargaining solutions. Mathematical Social Sciences 4: 295–300Google Scholar
  7. [7]
    Luce RD, Raiffa, H (1957), Games and decisions. Wiley, New YorkGoogle Scholar
  8. [8]
    Myerson RB (1977) Two-person bargaining problems and comparable utility. Econometrica 45: 1631–1637Google Scholar
  9. [9]
    Myerson RB (1981) Utilitarianism, egalitarianism, and the timing effect in social choice problems. Econometrica 49: 883–897Google Scholar
  10. [10]
    Nash JF (1950) The Bargaining Problem. Econometrica 18: 155–162Google Scholar
  11. [11]
    Perles MA, Maschler M (1981) The super-additive solution for the Nash bargaining game. International journal of Game Theory 10: 163–193Google Scholar
  12. [12]
    Peters H (1985) A note on additive utility and bargaining.Economics Letters 17: 219–222Google Scholar
  13. [13]
    Peters H (1986) Simultaneity of issues and additivity in bargaining. Econometrica 54: 153–169Google Scholar
  14. [14]
    Ponsati C (1992) Unique equilibrium in a model of bargaining over many issues.” Annales d'Economie et de Statistique 25/26: 81–100Google Scholar
  15. [15]
    Thomson W (1994) Cooperative models of bargaining. to appear in: Aumann R, Hart S (eds) The handbook of game theoryGoogle Scholar
  16. [16]
    Thomson W (forthcoming) Bargaining theory: The axiomatic approach. Academic Press, San DiegoGoogle Scholar
  17. [17]
    Thomson W, Myerson RB (1980) Monotonicity and independence axioms. International Journal of Game Theory 9: 37–49Google Scholar

Copyright information

© Physica-Verlag 1997

Authors and Affiliations

  • Clara Ponsati
    • 1
  • Joel Watson
    • 2
  1. 1.Departament d'Economia i Historia EconoicaUniversitat AutonomaBarcelonaSpain
  2. 2.Department of Economics, 0508University of CaliforniaSan Diego, La JollaUSA

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