Stable Matching with Payoff Guarantees

2026-08-04

AI Summary

This study addresses Shapley-Shubik assignment games under information constraints, where agents cannot observe others’ pairings or surplus divisions. To tackle this setting, the paper introduces two novel solution concepts: the self-stable set and the Stable Payoff Guarantee (SPG) set, both requiring that every participant receives at least their guaranteed payoff level, which is common knowledge. Theoretical analysis shows that, for general surplus matrices, the SPG set contains only efficient allocations; under generic conditions, it uniquely corresponds to the efficient allocation and yields a payoff vector that spans the minimal interval encompassing both worker-optimal and firm-optimal stable payoffs, thereby simultaneously ensuring stability and individual rationality.

Abstract

We consider a variant of the Assignment Game of Shapley and Shubik (1971), where agents do not observe the assignment or the surplus division of other matched pairs. We propose a set-valued solution concept (Self-Stabilizing Set) and characterize the largest such set. This leads to the formulation of the Stable Payoff Guarantee (SPG) set, which assumes that agents receive at least their payoff guarantees and that this is common knowledge. Our main result is that, for generic surplus matrices, the SPG set consists only of the efficient assignment. The associated payoff vectors are given by the smallest interval that contains the worker-optimal and firm-optimal stable payoffs.

Problem

• Stable Matching
• Assignment Game
• Payoff Guarantees
• Self-Stabilizing Set
• Surplus Division

Innovation

• Stable Matching
• Payoff Guarantees
• Assignment Game
• Self-Stabilizing Set
• Stable Payoff Guarantee