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The Nash product is a utility representation of the Pareto ordering

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  • Trockel, W.

Abstract

The paper deals with different completions of partial orderings on finite dimensional compact sets and an application to bargaining games. In particular, the Nash product turns out to be a continuous utility representation of the Pareto ordering in the sense of [Peleg, B., Econometrica 38 (1970) 93-96.] and [Sondermann, D., Journal of Economic Theory 23 (1980) 183-188.]. This provides an interesting "straightforward interpretation" that the Nash product according to [Osborne, M.J. and A. Rubinstein, A Course in Game Theory (1994), MIT Press: Cambridge, Massachusetts., p. 303] is lacking. For each payoff allocation admissible in the bargaining problem, it measures the set of admissible allocations Pareto dominated by it. The two sets of resulting maximal elements of the two completions are the Pareto efficient boundary and the Nash bargaining solution, respectively.

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  • Trockel, W., 2008. "The Nash product is a utility representation of the Pareto ordering," Economics Letters, Elsevier, vol. 99(2), pages 220-222, May.
    • Handle: RePEc:eee:ecolet:v:99:y:2008:i:2:p:220-222
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    References listed on IDEAS

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    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. NEUEFEIND, Wilhellm, 1972. "On continuous utility," LIDAM Reprints CORE 113, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Trockel, Walter, 2017. "Rationalizability of the Nash bargaining solution," Center for Mathematical Economics Working Papers 291, Center for Mathematical Economics, Bielefeld University.
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    5. Anke Gerber, 1999. "The Nash Solution and the Utility of Bargaining: A Corrigendum," Econometrica, Econometric Society, vol. 67(5), pages 1239-1240, September.
    6. Sondermann, Dieter, 1980. "Utility representations for partial orders," Journal of Economic Theory, Elsevier, vol. 23(2), pages 183-188, October.
    7. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
    8. Lee, Lung-Fei, 1972. "The Theorems of Debreu and Peleg for Ordered Topological Spaces," Econometrica, Econometric Society, vol. 40(6), pages 1151-1153, November.
    9. Neuefeind, Wilhelm, 1972. "On continuous utility," Journal of Economic Theory, Elsevier, vol. 5(1), pages 174-176, August.
    10. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
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    Cited by:

    1. Claus-Jochen Haake & Walter Trockel, 2020. "Introduction to the Special Issue “Bargaining”," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 1-6, November.
    2. Lorenzo Bastianello & Marco LiCalzi, 2015. "Target-based solutions for Nash bargaining," Working Papers 5, Department of Management, Università Ca' Foscari Venezia.
    3. Lorenzo Bastianello & Marco LiCalzi, 2019. "The Probability to Reach an Agreement as a Foundation for Axiomatic Bargaining," Econometrica, Econometric Society, vol. 87(3), pages 837-865, May.

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