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

Kristal K. Trejo (), Julio B. Clempner () and Alexander S. Poznyak ()
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Kristal K. Trejo: Center for Research and Advanced Studies CINVESTAV-IPN
Julio B. Clempner: National Polytechnic Institute
Alexander S. Poznyak: Center for Research and Advanced Studies CINVESTAV-IPN

Computational Economics, 2019, vol. 54, issue 3, No 5, 933-955

Abstract: 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.

Keywords: Bargaining; Kalai–Smorodinsky solution; Markov chains; Game theory (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10614-018-9859-9

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