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Bargaining with revoking costs

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  • Dutta, Rohan

Abstract

A simple two stage bilateral bargaining game is analyzed. The players simultaneously demand shares of a unit size pie. If the demands add up to more than one, the players simultaneously choose whether to stick to their demand or accept the otherʼs offer. While both parties sticking to their offers leads to an impasse, accepting a lower share than the original demand is costly for each party. The set of pure strategy subgame perfect equilibria of the game is characterized for continuously differentiable payoff and cost functions, strictly increasing in the pie share and the amount conceded, respectively. Higher cost functions are shown to improve bargaining power. The limit equilibrium prediction of the model, as the cost functions are made arbitrarily high, selects a unique equilibrium in the Nash Demand Game that corresponds to a Proportional Bargaining Solution of Kalai (1977).

Suggested Citation

  • Dutta, Rohan, 2012. "Bargaining with revoking costs," Games and Economic Behavior, Elsevier, vol. 74(1), pages 144-153.
    • Handle: RePEc:eee:gamebe:v:74:y:2012:i:1:p:144-153
    DOI: 10.1016/j.geb.2011.06.006
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    Cited by:

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    2. Nejat Anbarci & Kang Rong & Jaideep Roy, 2019. "Random-settlement arbitration and the generalized Nash solution: one-shot and infinite-horizon cases," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 21-52, July.
    3. Rohan Dutta & David K Levine & Salvatore Modica, 2018. "Peer Monitoring, Ostracism and the Internalization of Social Norms," Levine's Working Paper Archive 786969000000001449, David K. Levine.
    4. Rohan Dutta & David K Levine & Salvatore Modica, 2018. "Interventions when Social Norms are Endogenous: A Critique," Levine's Bibliography 786969000000001479, UCLA Department of Economics.
    5. Liu, Haiyang, 2014. "The Unbalanced Physical Movements of International Trade," MPRA Paper 54163, University Library of Munich, Germany.
    6. Burdett, Kenneth & Trejos, Alberto & Wright, Randall, 2017. "A new suggestion for simplifying the theory of money," Journal of Economic Theory, Elsevier, vol. 172(C), pages 423-450.
    7. Hu, Tai-Wei & Rocheteau, Guillaume, 2020. "Bargaining under liquidity constraints: Unified strategic foundations of the Nash and Kalai solutions," Journal of Economic Theory, Elsevier, vol. 189(C).
    8. Lotz, Sébastien & Zhang, Cathy, 2016. "Money and credit as means of payment: A new monetarist approach," Journal of Economic Theory, Elsevier, vol. 164(C), pages 68-100.
    9. Rohan Dutta & David K. Levine & Salvatore Modica, 2021. "The whip and the Bible: Punishment versus internalization," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(5), pages 858-894, October.
    10. Chao He & Randall Wright, 2019. "On Complicated Dynamics in Simple Monetary Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 51(6), pages 1433-1453, September.
    11. Yu Zhu & Scott Hendry, 2019. "A Framework for Analyzing Monetary Policy in an Economy with E-money," Staff Working Papers 19-1, Bank of Canada.
    12. Zhang, Cathy, 2014. "An information-based theory of international currency," Journal of International Economics, Elsevier, vol. 93(2), pages 286-301.
    13. Jeon, Haejun & Nishihara, Michi, 2018. "Optimal patent policy in the presence of vertical separation," European Journal of Operational Research, Elsevier, vol. 270(2), pages 682-697.
    14. Noriaki Matsushima & Fumitoshi Mizutani, 2014. "How Does Market Size Affect Vertical Structure When Considering Vertical Coordination? Application to the Railway Industry," Pacific Economic Review, Wiley Blackwell, vol. 19(5), pages 657-676, December.
    15. Zachary Bethune & Guillaume Rocheteau & Peter Rupert, 2015. "Aggregate Unemployment and Household Unsecured Debt," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(1), pages 77-100, January.
    16. John Duffy & Lucie Lebeau & Daniela Puzzello, 2021. "Bargaining Under Liquidity Constraints: Nash vs. Kalai in the Laboratory," Working Papers 2113, Federal Reserve Bank of Dallas.
    17. Guillaume Rocheteau & Lucie Lebeau & Tai-Wei Hu & Younghwan In, 2018. "Gradual Bargaining in Decentralized Asset Markets," Working Papers 181904, University of California-Irvine, Department of Economics.
    18. Emin Karagözoğlu & Kerim Keskin & Çağrı Sağlam, 2023. "(In)efficiency and equitability of equilibrium outcomes in a family of bargaining games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 175-193, March.
    19. Shiran Rachmilevitch, 2020. "Rewarding moderate behavior in a dynamic Nash Demand Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 639-650, June.

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    More about this item

    Keywords

    Nash demand game; Proportional bargaining solution; Bargaining; Commitment;
    All these keywords.

    JEL classification:

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

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