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A projected gradient dynamical system modeling the dynamics of bargaining

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Author Info

  • 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.

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File URL: http://cemapre.iseg.utl.pt/archive/preprints/472.pdf
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Bibliographic Info

Paper provided by Centre for Applied Mathematics and Economics (CEMAPRE), School of Economics and Management (ISEG), Technical University of Lisbon in its series CEMAPRE Working Papers with number 1101.

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Length: 31 pages
Date of creation: Oct 2011
Date of revision:
Handle: RePEc:cma:wpaper:1101

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Keywords: Discrete time projected dynamical systems; optimization; bargaining;

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  1. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475, 9.
  2. 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.
  3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, Econometric Society, vol. 18(2), pages 155-162, April.
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