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Some Impossibility Results on the Converse Consistency Principle in Bargaining

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  • Youngsub Chun

    (Seoul National University)

Abstract

We investigate the existence of solutions satisfying converse consistency together with other well-known axioms in the context of bargaining. Our results are negative. First, we show that there is no solution satisfying converse consistency together with Pareto optimality and contraction independence. Second, we show that there is no solution satisfying converse consistency together with Pareto optimality and individual monotonicity.

Suggested Citation

  • Youngsub Chun, 2020. "Some Impossibility Results on the Converse Consistency Principle in Bargaining," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 59-65, November.
    • Handle: RePEc:spr:homoec:v:37:y:2020:i:1:d:10.1007_s41412-020-00099-5
    DOI: 10.1007/s41412-020-00099-5
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    References listed on IDEAS

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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038.
    3. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    4. Thomson, William, 1980. "Two characterizations of the Raiffa solution," Economics Letters, Elsevier, vol. 6(3), pages 225-231.
    5. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
    6. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
    7. Chun, Youngsub, 2002. "The Converse Consistency Principle in Bargaining," Games and Economic Behavior, Elsevier, vol. 40(1), pages 25-43, July.
    8. Hans Peters & Dries Vermeulen, 2012. "WPO, COV and IIA bargaining solutions for non-convex bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 851-884, November.
    9. Youngsub Chun, 2005. "The replacement principle in bargaining," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 141-154, October.
    10. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    11. Peters, H.J.M. & Tijs, S.H., 1985. "Characterization of all individually monotonic bargaining solutions," Other publications TiSEM 52f5a6d5-dcac-4fec-9b8e-9, Tilburg University, School of Economics and Management.
    12. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
    13. 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.
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    Cited by:

    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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    More about this item

    Keywords

    Bargaining problem; Axiomatic approach; Impossibility results; Converse consistency; Contraction independence; Individual monotonicity;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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