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Multiple-issue bargaining and axiomatic solutions

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.

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This paper was partially written while Watson was a Research Fellow at Nuffield College, Oxford, and while Ponsati was a visiting professor at UCSD. The authors are grateful to Ehud Kalai, William Thomson, and the associate editor for their generous and helpful comments. The authors also appreciate the comments of two anonymous referees and participants at the Second Social Choice and Welfare Meetings (Rochester, 1994). Ponsati acknowledges financial support from the Spanish Ministry of Education (project PB-DGCYT92-0590) and the Gaspar de Portola Catalonian Studies Program. Watson thanks the U.S. National Science Foundation for financial support (under SBR-9422196).

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Ponsati, C., Watson, J. Multiple-issue bargaining and axiomatic solutions. Int J Game Theory 26, 501–524 (1997). https://doi.org/10.1007/BF01813888

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Keywords

  • Economic Theory
  • Game Theory
  • Equal Weight
  • Scale Invariance
  • Bargaining Solution