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The bargaining correspondence: when Edgeworth meets Nash

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  • Sun, Ching-jen

Abstract

A new, more fundamental approach is proposed to the classical bargaining problem. The give-and-take feature in the negotiation process is explicitly modelled under the new framework. A compromise set consists of all allocations a player is willing to accept as agreement. We focus on the relationship between the rationality principles (arguments) adopted by players in making mutual concessions and the formation of compromise sets. The bargaining correspondence is then defined as the intersection of players’ compromise sets. We study the non-emptiness, symmetry, efficiency and single-valuedness of the bargaining correspondence, and establish its connection to the Nash solution. Our framework provides a rational foundation to Nash’s axiomatic approach.
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  • Sun, Ching-jen, 2015. "The bargaining correspondence: when Edgeworth meets Nash," Working Papers eco_2015_4, Deakin University, Department of Economics.
    • Handle: RePEc:dkn:econwp:eco_2015_4
    DOI: 10.1007/s00355-018-1119-3
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    References listed on IDEAS

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    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
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    6. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284, Elsevier.
    7. Duggan, John, 2017. "Existence of stationary bargaining equilibria," Games and Economic Behavior, Elsevier, vol. 102(C), pages 111-126.
    8. William Thomson, 2009. "Bargaining and the theory of cooperative games: John Nash and beyond," RCER Working Papers 554, University of Rochester - Center for Economic Research (RCER).
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    12. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "Non-cooperative support for the asymmetric Nash bargaining solution," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1951-1967, September.
    13. Roth, Alvin E & Murnighan, J Keith, 1982. "The Role of Information in Bargaining: An Experimental Study," Econometrica, Econometric Society, vol. 50(5), pages 1123-1142, September.
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    1. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.

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    Keywords

    Bargaining Correspondence; Compromise; Edgeworth-Nash Gap; Nash Solution;
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