Aggregate Stable Matching with Money Burning

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.