The Coarse Nash Bargaining Solutions

TL;DR

This paper introduces coarse Nash bargaining solutions, a new class of solutions that are coarser than the classical Nash solution, characterized by modified rationality axioms related to independence of irrelevant alternatives.

Contribution

It proposes a novel class of bargaining solutions and characterizes them through new rationality axioms, extending Nash's and Arrow's axioms.

Findings

Coarse Nash solutions are coarser than classical Nash solutions.

They can be characterized by modified independence axioms.

The solutions satisfy standard axioms alongside new rationality conditions.

Abstract

This paper studies the axiomatic bargaining problem and proposes a new class of bargaining solutions, called coarse Nash solutions. These solutions assign to each problem a set of outcomes coarser than that chosen by the classical Nash solution (Nash, 1950). Our main result shows that these solutions can be characterized by new rationality axioms for choice correspondences, which are modifications of Nash's independence of irrelevant alternatives (or more precisely, Arrow's (1959) choice axiom), when combined with standard axioms.