Aggregate Stable Matching with Money Burning

TL;DR

This paper introduces a new stability concept for decentralized matching markets using money burning, establishing existence, uniqueness, and an algorithm for equilibrium computation.

Contribution

It extends NTU stability models by incorporating money burning, relating to classical stability, and providing a convergent algorithm for equilibrium.

Findings

Existence and uniqueness of equilibrium are proven.

A generalized deferred acceptance algorithm is developed and shown to converge.

Money burning decentralizes stable outcomes in aggregate matching models.

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.