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Optimal Value Commitment in Bilateral Bargaining

  • Britz Volker

    (METEOR)

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    We propose a new model to study the role of commitment as a sourceof strategic bargaining power. Two impatient players bargain aboutthe division of a pie under a standard bargaining protocol indiscrete time with time-invariant recognition probabilities.Instantaneous utility is linear, but players discount the future bya constant factor. Before bargaining starts, a player can commit notto enter into any agreement which gives him less than some utilitylevel. This commitment is perfectly binding initially. However, onceso much time has passed that even receiving the entire pie wouldyield less than the committed level of utility, then the commitmentbecomes void. Intuitively, this simply means that no player canremain committed to something which has become impossible. We use aslight refinement of subgame-perfect equilibrium as a solutionconcept. If only one player can commit, then we find an immediateand efficient agreement on a division which gives the committedplayer (strictly) between one half and the entire pie, the exactallocation being determined uniquely by the recognitionprobabilities. If both players can commit sequentially before thebargaining starts, we find a unique equilibrium division with afirst--mover advantage. Finally, we consider a version of the gamewhere both players commit simultaneously before the bargainingstarts. In this case, there is a range of equilibrium divisions.However, in the limit as the discount factor goes to one, no playerobtains less than one third of the pie, even with arbitrarily smallproposal power. Somewhat surprisingly, the equal split emerges asthe only division supported by an equilibrium for any choice of thediscount factor and the recognition probabilities.

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    Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 056.

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    Date of creation: 2010
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    Handle: RePEc:unm:umamet:2010056
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    1. Kambe, Shinsuke, 1999. "Bargaining with Imperfect Commitment," Games and Economic Behavior, Elsevier, vol. 28(2), pages 217-237, August.
    2. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 661465000000000387, David K. Levine.
    3. Antoni Cunyat, 2004. "The optimal degree of commitment in a negotiation with a deadline," Economic Theory, Springer, vol. 23(2), pages 455-465, January.
    4. 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.
    5. Li, Duozhe, 2007. "Bargaining with history-dependent preferences," Journal of Economic Theory, Elsevier, vol. 136(1), pages 695-708, September.
    6. 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.
    7. 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.
    8. Muthoo, Abhinay, 1992. "Revocable Commitment and Sequential Bargaining," Economic Journal, Royal Economic Society, vol. 102(411), pages 378-87, March.
    9. D. Abreu & F. Gul, 1998. "Bargaining and Reputation," Princeton Economic Theory Papers 00s9, Economics Department, Princeton University.
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