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Stability, fairness and random walks in the bargaining problem

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  • Kapeller, Jakob
  • Steinerberger, Stefan

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.

Suggested Citation

  • Kapeller, Jakob & Steinerberger, Stefan, 2017. "Stability, fairness and random walks in the bargaining problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 60-71.
    • Handle: RePEc:eee:phsmap:v:488:y:2017:i:c:p:60-71
    DOI: 10.1016/j.physa.2017.07.008
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