Nash bargaining with a nondeterministic threat

TL;DR

This paper explores a bargaining model where two players face a nondeterministic threat, leading to a unique solution concept that accounts for random selection among players and feasible bargains.

Contribution

It introduces a novel bargaining framework with nondeterministic threats, expanding traditional models by incorporating probabilistic elements and arbitrary solutions.

Findings

The model characterizes bargaining outcomes under nondeterministic threats.

It demonstrates how random threats influence equilibrium solutions.

The approach generalizes classical bargaining solutions to stochastic threat scenarios.

Abstract

We consider bargaining problems which involve two participants, with a nonempty closed, bounded convex bargaining set of points in the real plane representing all realizable bargains. We also assume that there is no definite threat or disagreement point which will provide the default bargain if the players cannot agree on some point in the bargaining set. However, there is a nondeterministic threat: if the players fail to agree on a bargain, one of them will be chosen at random with equal probability, and that chosen player will select any realizable bargain as the solution, subject to a reasonable restriction.