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Two-party Bargaining Processes Based on Subjective Expectations: A Model and a Simulation Study

Author

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  • Luis C. Dias

    (University of Coimbra)

  • Rudolf Vetschera

    (University of Vienna)

Abstract

This work presents a model for a two-party bargaining process in which multiple offers are exchanged as the negotiation goes on, under a risk of breakdown. Typical game theoretical analyses of such settings assume the breakdown risk is known and the parties are able to calculate an initial offer that is immediately accepted by the other party, ending the negotiation. Aiming to develop a model that is closer to real-life situations, in which parties do exchange many offers in a bargaining process, we consider the parties are unable to compute the far-reaching consequences of their offers, and are guided by their subjective expectations of the outcome of the negotiation. This introduces a new perspective to the analysis of two-party bargaining processes: the confidence of the bargainers in terms of what they hope to achieve by bargaining with each other. The resulting model can be seen as an extension of the Zeuthen-Hicks bargaining model. We show analytically that under the assumption of concave utilities of both parties, the bargaining process converges to the nonsymmetric Nash bargaining solution, where the asymmetry is caused by differences in expectations. This result provides a new interpretation of the parameters of the nonsymmetric Nash bargaining solution, linking them to behavior in the bargaining process. As an additional contribution, we perform a simulation study to examine the role of confidence and to analyze the outcomes for non-concave utility functions.

Suggested Citation

  • Luis C. Dias & Rudolf Vetschera, 2022. "Two-party Bargaining Processes Based on Subjective Expectations: A Model and a Simulation Study," Group Decision and Negotiation, Springer, vol. 31(4), pages 843-869, August.
    • Handle: RePEc:spr:grdene:v:31:y:2022:i:4:d:10.1007_s10726-022-09786-x
    DOI: 10.1007/s10726-022-09786-x
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Hwang, Ilwoo, 2018. "A theory of bargaining deadlock," Games and Economic Behavior, Elsevier, vol. 109(C), pages 501-522.
    3. Sebastian Schweighofer†Kodritsch, 2018. "Time Preferences and Bargaining," Econometrica, Econometric Society, vol. 86(1), pages 173-217, January.
    4. Svejnar, Jan, 1986. "Bargaining Power, Fear of Disagreement, and Wage Settlements: Theory and Evidence from U.S. Industry," Econometrica, Econometric Society, vol. 54(5), pages 1055-1078, September.
    5. Luis C. Dias & Rudolf Vetschera, 2019. "Multiple local optima in Zeuthen–Hicks bargaining: an analysis of different preference models," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 7(1), pages 33-53, May.
    6. John Sutton, 1986. "Non-Cooperative Bargaining Theory: An Introduction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 709-724.
    7. Howard, J. V., 1992. "A social choice rule and its implementation in perfect equilibrium," Journal of Economic Theory, Elsevier, vol. 56(1), pages 142-159, February.
    8. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475, January.
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    10. Dias, Luis C. & Vetschera, Rudolf, 2019. "On generating utility functions in Stochastic Multicriteria Acceptability Analysis," European Journal of Operational Research, Elsevier, vol. 278(2), pages 672-685.
    11. N.R. Jennings & P. Faratin & A.R. Lomuscio & S. Parsons & M.J. Wooldridge & C. Sierra, 2001. "Automated Negotiation: Prospects, Methods and Challenges," Group Decision and Negotiation, Springer, vol. 10(2), pages 199-215, March.
    12. Schweighofer-Kodritsch, Sebastian, 2018. "Time Preferences and Bargaining," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 86(1), pages 173-217.
    13. Lorenzo Bastianello & Marco LiCalzi, 2019. "The Probability to Reach an Agreement as a Foundation for Axiomatic Bargaining," Econometrica, Econometric Society, vol. 87(3), pages 837-865, May.
    14. Kjell Hausken, 1997. "Game-theoretic and Behavioral Negotiation Theory," Group Decision and Negotiation, Springer, vol. 6(6), pages 511-528, December.
    15. Claus-Jochen Haake & Sonja Recker, 2018. "The Generalized Nash Bargaining Solution for Transfer Price Negotiations Under Incomplete Information," Group Decision and Negotiation, Springer, vol. 27(6), pages 905-932, December.
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    Cited by:

    1. Rudolf Vetschera & Luis C. Dias, 2024. "Confidence and Outcome Expectations in Bilateral Negotiations–A Dynamic Model," Group Decision and Negotiation, Springer, vol. 33(4), pages 775-803, August.
    2. Katrin Zulauf & Ralf Wagner, 2023. "Countering Negotiation Power Asymmetries by Using the Adjusted Winner Algorithm," SN Operations Research Forum, Springer, vol. 4(1), pages 1-20, March.

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