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A projected gradient dynamical system modeling the dynamics of bargaining

Author

Listed:
  • Diogo Pinheiro

    (CEMAPRE, School of Economics and Management (ISEG), Technical University of Lisbon)

  • Alberto A. Pinto

    (Department of Mathematics, Faculty of Science, University of Porto)

  • S. Z. Xanthopoulos

    (University of the Aegean, Samos, Greece)

  • A. N. Yannacopoulos

    (Athens University of Economics and Business, Athens, Greece)

Abstract

We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations which do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world and the reservation prices are calculated using expected utility theory. The agents are not rigid concerning their subjective probabilities and are willing to update them under the pressure to reach finally an agreement concerning the asset. The proposed projected dynamical system, on the space of probability measures, provides a model for the evolution of the agents beliefs during the bargaining period and is constructed so that agreement is reached under the minimum possible deviation of both agents from their initial beliefs. The convergence results are shown using techniques from convex dynamics and Lyapunov function theory.

Suggested Citation

  • Diogo Pinheiro & Alberto A. Pinto & S. Z. Xanthopoulos & A. N. Yannacopoulos, 2011. "A projected gradient dynamical system modeling the dynamics of bargaining," CEMAPRE Working Papers 1101, Centre for Applied Mathematics and Economics (CEMAPRE), School of Economics and Management (ISEG), Technical University of Lisbon.
    • Handle: RePEc:cma:wpaper:1101
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    References listed on IDEAS

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    1. Lampros Boukas & Diogo Pinheiro & Alberto Pinto & Stylianos Xanthopoulos & Athanasios Yannacopoulos, 2009. "Behavioural and Dynamical Scenarios for Contingent Claims Valuation in Incomplete Markets," Papers 0903.3657, arXiv.org.
    2. Ken-ichi Inada, 1963. "On a Two-Sector Model of Economic Growth: Comments and a Generalization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(2), pages 119-127.
    3. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475.
    4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    5. Y. S. Xia & J. Wang, 2000. "On the Stability of Globally Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 129-150, July.
    6. Y. S. Xia, 2004. "Further Results on Global Convergence and Stability of Globally Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 627-649, September.
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    Cited by:

    1. N. Azevedo & D. Pinheiro & S. Z. Xanthopoulos & A. N. Yannacopoulos, 2018. "Contingent claim pricing through a continuous time variational bargaining scheme," Annals of Operations Research, Springer, vol. 260(1), pages 95-112, January.

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