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Repeated Bargaining with Persistent Private Information

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  • John Kennan

Abstract

The paper analyses repeated contract negotiations involving the same buyer and seller where the contracts are linked because the buyer has persistent (but not fully permanent) private information. The size of the surplus being divided is specified as a two-state Markov chain with transitions that are synchronized with contract negotiation dates. Equilibrium involves information cycles triggered by the success or failure of aggressive demands made by the seller. Because there is persistence in the Markov chain generating the surplus, a successful demand induces the seller to make another aggressive demand in the next negotiation, since the buyer's acceptance reveals that the current surplus is large. Rejection of an aggressive demand, on the other hand, leads the seller to be pessimistic about the size of the surplus in the next contract, so the seller makes a "soft" offer that is sure to be accepted. Then, after several such offers have been accepted, the seller is optimistic enough to again make an aggressive demand, creating an information cycle. An interesting feature of this cycle is that the soft price is not constant, but declines as the cycle continues, so as to offset the buyer's option value of re-starting the cycle when the current state is bad. An explicit mapping is given for the relationship between the basic parameters and the equilibrium prices and quantities; in particular, there is a closed-form solution for the threshold belief that makes the seller indifferent between hard and soft offers.

Suggested Citation

  • John Kennan, 2001. "Repeated Bargaining with Persistent Private Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(4), pages 719-755.
    • Handle: RePEc:oup:restud:v:68:y:2001:i:4:p:719-755.
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    File URL: http://hdl.handle.net/10.1111/1467-937X.00188
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    Cited by:

    1. Huan Xie, 2013. "Bargaining with uncertain value distributions," Economics Bulletin, AccessEcon, vol. 33(2), pages 1047-1066.
    2. Battaglini, Marco, 2007. "Optimality and renegotiation in dynamic contracting," Games and Economic Behavior, Elsevier, vol. 60(2), pages 213-246, August.
    3. Bita Hajihashemi & Amin Sayedi & Jeffrey D. Shulman, 2022. "The Perils of Personalized Pricing with Network Effects," Marketing Science, INFORMS, vol. 41(3), pages 477-500, May.
    4. Richard Chung & Bryan Byung-Hee Lee & Woo-Jong Lee & Byungcherl Charlie Sohn, 2016. "Do Managers Withhold Good News from Labor Unions?," Management Science, INFORMS, vol. 62(1), pages 46-68, January.
    5. Susan Athey & Kyle Bagwell, 2008. "Collusion With Persistent Cost Shocks," Econometrica, Econometric Society, vol. 76(3), pages 493-540, May.
    6. J. Benjamin & P. Chinloy & G. Jud & D. Winkler, 2007. "Do Some People Work Harder than Others? Evidence from Real Estate Brokerage," The Journal of Real Estate Finance and Economics, Springer, vol. 35(1), pages 95-110, July.
    7. Phelan, Christopher, 2006. "Public trust and government betrayal," Journal of Economic Theory, Elsevier, vol. 130(1), pages 27-43, September.
    8. Elizabeth Hemphill, 2007. "Factors Affecting Real Estate Broker Selection: What Really Counts?," International Real Estate Review, Global Social Science Institute, vol. 10(1), pages 1-25.
    9. Raphael Boleslavsky & Maher Said, 2013. "Progressive Screening: Long-Term Contracting with a Privately Known Stochastic Process," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(1), pages 1-34.
    10. Amit Mehra & Ram Bala & Ramesh Sankaranarayanan, 2012. "Competitive Behavior-Based Price Discrimination for Software Upgrades," Information Systems Research, INFORMS, vol. 23(1), pages 60-74, March.
    11. Dutta, Prajit K., 2021. "Compromise is key in infinitely repeated bargaining with an Evergreen Clause," Journal of Economic Theory, Elsevier, vol. 193(C).
    12. James M. Malcomson, 2016. "Relational Incentive Contracts With Persistent Private Information," Econometrica, Econometric Society, vol. 84, pages 317-346, January.
    13. Martino Banchio & Frank Yang, 2021. "Dynamic Pricing with Limited Commitment," Papers 2102.07742, arXiv.org, revised Dec 2021.
    14. Ortner, Juan, 2023. "Bargaining with evolving private information," Theoretical Economics, Econometric Society, vol. 18(3), July.
    15. Loginova, Oksana & Taylor, Curtis, 2003. "Price Experimentation with Strategic Buyers," Working Papers 03-02, Duke University, Department of Economics.
    16. Jia, Kunhao & Liao, Xiuwu & Feng, Juan, 2018. "Selling or leasing? Dynamic pricing of software with upgrades," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1044-1061.
    17. Cantillon, Estelle & Asker, John, 2005. "Optimal Procurement When Both Price and Quality Matter," CEPR Discussion Papers 5276, C.E.P.R. Discussion Papers.
    18. Marco Battaglini, 2005. "Long-Term Contracting with Markovian Consumers," American Economic Review, American Economic Association, vol. 95(3), pages 637-658, June.
    19. Lemke, Robert J., 2004. "Dynamic bargaining with action-dependent valuations," Journal of Economic Dynamics and Control, Elsevier, vol. 28(9), pages 1847-1875, July.

    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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