Stability, fairness and random walks in the bargaining problem

Jakob Kapeller and Stefan Steinerberger

Physica A: Statistical Mechanics and its Applications, 2017, vol. 488, issue C, 60-71

Abstract: We study the classical bargaining problem and its two canonical solutions, (Nash and Kalai–Smorodinsky), from a novel point of view: we ask for stability of the solution if both players are able distort the underlying bargaining process by reference to a third party (e.g. a court). By exploring the simplest case, where decisions of the third party are made randomly we obtain a stable solution, where players do not have any incentive to refer to such a third party. While neither the Nash nor the Kalai–Smorodinsky solution are able to ensure stability in case reference to a third party is possible, we found that the Kalai–Smorodinsky solution seems to always dominate the stable allocation which constitutes novel support in favor of the latter.

Keywords: Bargaining problem; Nash solution; Kalai–Smorodinsky solution; Stability; Brownian motion; Feynman–Kac formula; Partial differential equation (search for similar items in EconPapers)
Date: 2017
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Related works:
Working Paper: Stability, Fairness and Random Walks in the Bargaining Problem (2017)
Working Paper: Stability, Fairness and Random Walks in the Bargaining Problem (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:488:y:2017:i:c:p:60-71

DOI: 10.1016/j.physa.2017.07.008

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