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Computing the Bargaining Approach for Equalizing the Ratios of Maximal Gains in Continuous-Time Markov Chains Games

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Abstract

This paper presents a novel approach for computing the Kalai–Smorodinsky bargaining equilibrium for continuous time and discrete states Markov chains games. To solve the bargaining situation we set the disagreement point as the Nash equilibrium of the problem, then to find the new agreement point we follow the bargaining model presented by Kalai–Smorodinsky employing the utopia point concept. We exemplify the game formulation in terms of nonlinear programming equations implementing the Lagrange principle. The Tikhonov’s regularization method is applied to ensure the convergence of the cost-functions to an equilibrium point. For solving the problem we use a programming method implemented by the extraproximal optimization approach. The proposed method is validated by a numerical example related to the labor market problem for a three-person bargaining problem.

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Authors and Affiliations

  1. Department of Automatic Control, Center for Research and Advanced Studies CINVESTAV-IPN, Av. Instituto Politécnico Nacional 2508, San Pedro Zacatenco, Gustavo A. Madero, 07360, Mexico City, Mexico

    Kristal K. Trejo & Alexander S. Poznyak

  2. Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, School of Physics and Mathematics, National Polytechnic Institute, Building 9, Av. Instituto Politécnico Nacional, San Pedro Zacatenco, Gustavo A. Madero, 07738, Mexico City, Mexico

    Julio B. Clempner

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  1. Kristal K. Trejo
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  2. Julio B. Clempner
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  3. Alexander S. Poznyak
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Correspondence to Kristal K. Trejo.

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Trejo, K.K., Clempner, J.B. & Poznyak, A.S. Computing the Bargaining Approach for Equalizing the Ratios of Maximal Gains in Continuous-Time Markov Chains Games. Comput Econ 54, 933–955 (2019). https://doi.org/10.1007/s10614-018-9859-9

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  • DOI: https://doi.org/10.1007/s10614-018-9859-9

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