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Stability, Fairness and Random Walks in the Bargaining Problem

Author

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  • Jakob Kapeller

    (Institute for Comprehensive Analysis of the Economy, Johannes Kepler University Linz, Austria)

  • Stefan Steinerberger

    (Department of Mathematics, Yale University, US)

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

  • Jakob Kapeller & Stefan Steinerberger, 2017. "Stability, Fairness and Random Walks in the Bargaining Problem," ICAE Working Papers 67, Johannes Kepler University, Institute for Comprehensive Analysis of the Economy.
    • Handle: RePEc:ico:wpaper:67
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