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Interdependent Bargains

Author

Listed:
  • Zhou, Yihang
  • Sibley, David

Abstract

A seller bargains with two buyers to make a deal with each of them, using an alternating-offer protocol (“AO”). The bargaining begins with one buyer, with the second entering at a future date. The seller has a concave utility function, defined over total payments made by the two buyers. Hence, the bargain made with one buyer affects the outcome of the bargain made with the second buyer. The curvature properties of the seller utility and the arrival date of the second buyer decide how bargains affect each other. We derive dynamic properties of the negotiated prices. These prices exhibit unusual comparative statics. The price paid by the first buyer can be non-monotone in the discount factor used in the AO bargaining. This is because the bargaining between the seller and the first buyer anticipates the arrival of the second buyer. We extend the model to include downstream competition between the two buyers. We obtain results on first-mover and second-mover advantage.

Suggested Citation

  • Zhou, Yihang & Sibley, David, 2026. "Interdependent Bargains," Journal of Mathematical Economics, Elsevier, vol. 122(C).
    • Handle: RePEc:eee:mateco:v:122:y:2026:i:c:s0304406826000017
    DOI: 10.1016/j.jmateco.2026.103213
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    References listed on IDEAS

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    1. Capps, Cory & Dranove, David & Satterthwaite, Mark, 2003. "Competition and Market Power in Option Demand Markets," RAND Journal of Economics, The RAND Corporation, vol. 34(4), pages 737-763, Winter.
    2. Roth, Alvin E, 1985. "A Note on Risk Aversion in a Perfect Equilibrium Model of Bargaining," Econometrica, Econometric Society, vol. 53(1), pages 207-211, January.
    3. Taylor, John B, 1979. "Staggered Wage Setting in a Macro Model," American Economic Review, American Economic Association, vol. 69(2), pages 108-113, May.
    4. Molina, Hugo & Wang, Ao, 2024. "Vertical Bargaining under Uncertain Retailer Responsiveness : A Structural Approach," The Warwick Economics Research Paper Series (TWERPS) 1534, University of Warwick, Department of Economics.
    5. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    6. Volij, Oscar & Winter, Eyal, 2002. "On risk aversion and bargaining outcomes," Games and Economic Behavior, Elsevier, vol. 41(1), pages 120-140, October.
    7. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    8. Kate Ho & Robin S. Lee, 2019. "Equilibrium Provider Networks: Bargaining and Exclusion in Health Care Markets," American Economic Review, American Economic Association, vol. 109(2), pages 473-522, February.
    9. Gautam Gowrisankaran & Aviv Nevo & Robert Town, 2015. "Mergers When Prices Are Negotiated: Evidence from the Hospital Industry," American Economic Review, American Economic Association, vol. 105(1), pages 172-203, January.
    10. Fershtman, Chaim, 2000. "A Note on Multi-Issue Two-Sided Bargaining: Bilateral Procedures," Games and Economic Behavior, Elsevier, vol. 30(2), pages 216-227, February.
    11. repec:bla:scandj:v:88:y:1986:i:2:p:383-400 is not listed on IDEAS
    12. In-Koo Cho, 1990. "Uncertainty and Delay in Bargaining," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(4), pages 575-595.
    13. Fershtman, Chaim, 1990. "The importance of the agenda in bargaining," Games and Economic Behavior, Elsevier, vol. 2(3), pages 224-238, September.
    14. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
    15. Henrick Horn & Asher Wolinsky, 1988. "Bilateral Monopolies and Incentives for Merger," RAND Journal of Economics, The RAND Corporation, vol. 19(3), pages 408-419, Autumn.
    16. Rey, Patrick & Vergé, Thibaud, 2016. "Secret contracting in multilateral relations," TSE Working Papers 16-744, Toulouse School of Economics (TSE), revised Dec 2020.
    17. 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.
    18. Chae Suchan & Yang Jeong-Ae, 1994. "An N-Person Pure Bargaining Game," Journal of Economic Theory, Elsevier, vol. 62(1), pages 86-102, February.
    19. Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 52(6), pages 1351-1364, November.
    20. Kate Ho & Robin S. Lee, 2017. "Insurer Competition in Health Care Markets," Econometrica, Econometric Society, vol. 85, pages 379-417, March.
    21. Crawford, Vincent P. & Varian, Hal R., 1979. "Distortion of preferences and the Nash theory of bargaining," Economics Letters, Elsevier, vol. 3(3), pages 203-206.
    22. White, Lucy, 2008. "Prudence in bargaining: The effect of uncertainty on bargaining outcomes," Games and Economic Behavior, Elsevier, vol. 62(1), pages 211-231, January.
    23. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(1), pages 61-80.
    24. Gregory S. Crawford & Ali Yurukoglu, 2012. "The Welfare Effects of Bundling in Multichannel Television Markets," American Economic Review, American Economic Association, vol. 102(2), pages 643-685, April.
    25. Peter C. Cramton, 1992. "Strategic Delay in Bargaining with Two-Sided Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 205-225.
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