Solidarity to achieve stability

TL;DR

This paper demonstrates that sharing rules satisfying a solidarity axiom can induce stable coalition formations among agents, linking fairness principles to stability in cooperative settings.

Contribution

It characterizes sharing rules based on solidarity that guarantee stability in coalition formation problems, providing a formal axiomatic foundation.

Findings

Solidarity-based sharing rules induce stable coalitions.

A natural axiom formalizes the principle of solidarity.

Solidarity is sufficient for stability in coalition formation.

Abstract

Agents may form coalitions. Each coalition shares its endowment among its agents by applying a sharing rule. The sharing rule induces a coalition formation problem by assuming that agents rank coalitions according to the allocation they obtain in the corresponding sharing problem. We characterize the sharing rules that induce a class of stable coalition formation problems as those that satisfy a natural axiom that formalizes the principle of solidarity. Thus, solidarity becomes a sufficient condition to achieve stability.