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Optimal Value Commitment in Bilateral Bargaining

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  • Britz Volker

    (METEOR)

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    Abstract

    Two impatient players bargain about the division of a pie under a standard bargaining protocol in discrete time with time-invariant recognition probabilities. Instantaneous utility is linear, but players discount the future by a constant factor. Before bargaining starts, a player can commit to a utility level. This commitment is perfectly binding initially. However, once so much time has passed that even receiving the entire pie would yield less than thecommitted level of utility, then the commitment becomes void. Intuitively, this simply means that no player can remain committed to something which has become impossible. If only one player can commit, his subgame--perfect equilibrium payoff varies between one half and the entire pie, depending on the distribution of proposal power. If both players commit sequentially before the bargaining starts, we find a unique perfect equilibrium division. If both players commit simultaneously, there is a range of perfect equilibrium divisions. However, no player obtains less than one third of the pie, even with arbitrarily small proposal power. The equal split is the only division supported by a perfect equilibrium for any choice of the discount factor and the recognition probabilities.

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    Bibliographic Info

    Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 013.

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    Date of creation: 2010
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    Handle: RePEc:unm:umamet:2010013

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    Keywords: microeconomics ;

    References

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Dilip Abreu & Faruk Gul, 2000. "Bargaining and Reputation," Econometrica, Econometric Society, vol. 68(1), pages 85-118, January.
    3. Kambe, Shinsuke, 1999. "Bargaining with Imperfect Commitment," Games and Economic Behavior, Elsevier, vol. 28(2), pages 217-237, August.
    4. Fershtman Chaim & Seidmann Daniel J., 1993. "Deadline Effects and Inefficient Delay in Bargaining with Endogenous Commitment," Journal of Economic Theory, Elsevier, vol. 60(2), pages 306-321, August.
    5. Muthoo, Abhinay, 1992. "Revocable Commitment and Sequential Bargaining," Economic Journal, Royal Economic Society, vol. 102(411), pages 378-87, March.
    6. Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 52(6), pages 1351-64, November.
    7. Vicent Calabuig & Antoni Cunyat & Gonzalo Olcina, 2002. "Commitment and choice of partner in a negotiation with a deadline," Spanish Economic Review, Springer, vol. 4(1), pages 61-78.
    8. Antoni Cunyat, 2004. "The optimal degree of commitment in a negotiation with a deadline," Economic Theory, Springer, vol. 23(2), pages 455-465, January.
    9. Li, Duozhe, 2007. "Bargaining with history-dependent preferences," Journal of Economic Theory, Elsevier, vol. 136(1), pages 695-708, September.
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