Aggregate Stable Matching with Money Burning

2026-05-08

AI Summary

This study addresses the challenge of achieving market clearing and stability in decentralized matching markets with fixed prices through one-sided "money burning"—such as waiting costs. The authors propose an aggregate non-transferable utility (NTU) stable matching framework that groups agents by observable types and defines equilibrium at the type level. They introduce, for the first time, a money-burning mechanism into the aggregate NTU model to capture waiting costs. This framework establishes a formal connection to Gale–Shapley stability and provides an NTU counterpart to the Choo–Siow model. Furthermore, they design a generalized deferred acceptance algorithm based on alternating constrained discrete choice problems. Theoretical analysis establishes the existence and uniqueness of equilibrium and demonstrates that the proposed algorithm converges to the unique stable equilibrium, thereby offering a decentralized implementation pathway.

Abstract

We propose an aggregate notion of non-transferable utility (NTU) stability for decentralized matching markets with fixed prices, where market clearing is achieved through one-sided money burning, which can be interpreted as waiting. Agents are grouped into observable types and are indifferent among individuals within type; equilibrium is defined at the type level and delivers equal indirect utility within each type. We introduce money burning into two types of NTU models: In a deterministic model, we relate our notion to classical Gale--Shapley stability and show how money burning decentralizes stable outcomes under aggregation. We then introduce separable random utility, obtaining an NTU counterpart to Choo and Siow (2006). We prove the existence and uniqueness of equilibrium and provide a stationary queueing interpretation. Finally, we develop a generalized deferred acceptance algorithm based on alternating constrained discrete-choice problems and prove its convergence to the unique equilibrium.

Problem

• aggregate stable matching
• non-transferable utility
• money burning
• decentralized matching markets
• type-level equilibrium

Innovation

• money burning
• aggregate stability
• non-transferable utility
• deferred acceptance algorithm
• random utility matching