Stability, Fairness and Random Walks in the Bargaining Problem

TL;DR

This paper investigates the stability of classical bargaining solutions when third-party interventions are possible, revealing that the Kalai-Smorodinsky solution often outperforms the Nash solution in stability scenarios involving random third-party decisions.

Contribution

It introduces a novel stability criterion for bargaining solutions considering third-party distortions and demonstrates the Kalai-Smorodinsky solution's dominance under this criterion.

Findings

Kalai-Smorodinsky solution generally more stable than Nash solution

Random third-party decisions lead to stable bargaining outcomes

Kalai-Smorodinsky solution dominates in stability when third-party influence is random

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.