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Sequential Bargaining Mechanisms

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Abstract

The introductory discussion presented in this chapter considers the simplest type of sequential bargaining games in which the players' time preferences are described by known and fixed discount rates. I begin by characterizing the class of perfect bargaining mechanisms, which satisfy the desirable properties of incentive compatibility (i.e., each player reports his type truthfully), individual rationality (i.e., every potential player wishes to play the game), and sequential rationality (i.e., it is never common knowledge that the mechanism induced over time is dominated by an alternative mechanism). It is shown that ex post efficiency is unobtainable by any incentive-compatible and individually rational mechanism when the bargainers are uncertain about whether or not they should trade immediately. I conclude by finding those mechanisms that maximize the players' ex ante utility, and show that such mechanisms violate sequential rationality. Thus, the bargainers would be better off ex ante if they could commit to a mechanism before they knew their private information. In terms of their ex ante payoffs, if the seller's delay costs are higher than those of the buyer, then the bargainers are better off adopting a sequential bargaining game rather than a static mechanism; however, when the buyer's delay costs are higher, then a static mechanism is optimal.

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  • Peter Cramton, 1985. "Sequential Bargaining Mechanisms," Papers of Peter Cramton 85roth, University of Maryland, Department of Economics - Peter Cramton, revised 09 Jun 1998.
    • Handle: RePEc:pcc:pccumd:85roth
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    References listed on IDEAS

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    1. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    2. Kalyan Chatterjee & William Samuelson, 1983. "Bargaining under Incomplete Information," Operations Research, INFORMS, vol. 31(5), pages 835-851, October.
    3. Drew Fudenberg & Jean Tirole, 1983. "Sequential Bargaining with Incomplete Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(2), pages 221-247.
    4. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    5. Ausubel, Lawrence M. & Cramton, Peter & Deneckere, Raymond J., 2002. "Bargaining with incomplete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 50, pages 1897-1945, Elsevier.
    6. Joel Sobel & Takahashi, 1983. "A Multi-stage Model of Bargaining," Levine's Working Paper Archive 255, David K. Levine.
    7. Peter C. Cramton, 1984. "Bargaining with Incomplete Information: An Infinite-Horizon Model with Two-Sided Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(4), pages 579-593.
    8. Thomas A. Gresik & Mark A. Satterthwaite, 1983. "The Number of Traders Required to Make a Market Competitive: The Beginnings of a Theory," Discussion Papers 551, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Fishburn, Peter C & Rubinstein, Ariel, 1982. "Time Preference," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 677-694, October.
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    Cited by:

    1. Vincent, Daniel R., 1989. "Bargaining with common values," Journal of Economic Theory, Elsevier, vol. 48(1), pages 47-62, June.
    2. Peter C. Cramton, 1984. "Bargaining with Incomplete Information: An Infinite-Horizon Model with Two-Sided Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(4), pages 579-593.
    3. Lawrence M. Ausubel & Raymond J. Deneckere, 1988. "Stationary Sequential Equilibria in Bargaining With Two-Sided Incomplete Information," Discussion Papers 784, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Lawrence M. Ausubel & Raymond J. Deneckere, 1988. "Efficient Sequential Bargaining," Discussion Papers 804, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Lawrence M. Ausubel & Raymond J. Deneckere, 1987. "A Direct Mechanism Characterization of Sequential Bargaining With One-Sided Incomplete Information," Discussion Papers 728, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. McAfee, R. Preston & Vincent, Daniel, 1997. "Sequentially Optimal Auctions," Games and Economic Behavior, Elsevier, vol. 18(2), pages 246-276, February.
    7. Aviad Heifetz & Ella Segev & Eric Talley, "undated". "Market Design with Endogenous Preferences," University of Southern California Legal Working Paper Series usclwps-1001, University of Southern California Law School.
    8. Cramton Peter C. & Palfrey Thomas R., 1995. "Ratifiable Mechanisms: Learning from Disagreement," Games and Economic Behavior, Elsevier, vol. 10(2), pages 255-283, August.

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    More about this item

    Keywords

    Bargaining; Bargaining Mechanisms; Delay; Private Information;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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