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A theory of unstructured bargaining using distribution-valued solution concepts

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  • David H. Wolpert
  • James Bono

Abstract

In experiments it is typically found that many joint utility outcomes arise in any given unstructured bargaining game. This suggests using a positive unstructured bargaining concept that maps a bargaining game to a probability distribution over outcomes rather than to a single outcome. We show how to "translate" Nash's bargaining axioms to apply to such distributional bargaining concepts. We then prove that a subset of those axioms forces the distribution over outcomes to be a power-law. Unlike Nash's original result, our result holds even if the feasible set is finite. When the feasible set is convex and comprehensive, the mode of the power law distribution is the Harsanyi bargaining solution, and if we require symmetry it is the Nash bargaining solution. However in general these modes of the joint utility distribution are not Bayes-optimal predictions for the joint uitlity, nor are the bargains corresponding to those outcomes the most likely bargains. We then show how an external regulator can use distributional solution concepts to optimally design an unstructured bargaining scenario. Throughout we demonstrate our analysis in computational experiments involving flight rerouting negotiations in the National Airspace System.

Suggested Citation

  • David H. Wolpert & James Bono, 2010. "A theory of unstructured bargaining using distribution-valued solution concepts," Working Papers 2010-14, American University, Department of Economics.
  • Handle: RePEc:amu:wpaper:2010-14
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    References listed on IDEAS

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    1. David H. Wolpert & James Bono, 2010. "Distribution-Valued Solution Concepts," Working Papers 2010-13, American University, Department of Economics.
    2. Özgür Kıbrıs & Murat Sertel, 2007. "Bargaining over a finite set of alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(3), pages 421-437, April.
    3. Rubinstein, Ariel & Safra, Zvi & Thomson, William, 1992. "On the Interpretation of the Nash Bargaining Solution and Its Extension to Non-expected Utility Preferences," Econometrica, Econometric Society, vol. 60(5), pages 1171-1186, September.
    4. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    6. Conley, John P. & Wilkie, Simon, 1996. "An Extension of the Nash Bargaining Solution to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 13(1), pages 26-38, March.
    7. Peters Hans & Vermeulen Dries, 2006. "WPO, COV and IIA bargaining solutions," Research Memorandum 021, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. Smith, Vernon L & Suchanek, Gerry L & Williams, Arlington W, 1988. "Bubbles, Crashes, and Endogenous Expectations in Experimental Spot Asset Markets," Econometrica, Econometric Society, vol. 56(5), pages 1119-1151, September.
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