Ian A. Hanlon

October 14th 2025

Abstract

This paper develops a model of bilateral exchange with bounded monetary trans-ferability. Agents hold heterogeneous goods and engage in direct swaps, with optional cash top-ups that bridge valuation gaps. Valuations are expressed in a common nu-meraire (USD) to anchor preferences, but transfers are capped to preserve the identity of barter. This structure defines a regime of hybrid barter that lies between non-transferable and fully transferable utility. We show that bounded transfers expand the feasible set of trades and weakly improve welfare relative to pure barter when transfer frictions are small. The model generalizes the transferable-utility assignment game of Shapley and Shubik (1971) by imposing bounded transferability, creating a continuum between barter and full monetary exchange. It connects search-and-matching theory with assignment games, offering a tractable framework for analyzing decentralized ex-change under costly liquidity.

1 Introduction

Barter systems have long provided the conceptual baseline for decentralized exchange. Their classic limitation is the double coincidence of wants: two agents must simultaneously desire each other’s goods for trade to occur. This coincidence constraint leaves surplus unrealized and sharply restricts the size of the feasible set. Partial monetary exchange relaxes this by introducing a limited medium of exchange and a common unit of account (Kiyotaki and Wright, 1989), while still preserving direct relational exchange alongside price-based adjustment.

This paper proposes a theoretical framework that lies between those extremes: a Hybrid Barter Regime (HBR) in which trades are primarily item-for-item, but small cash top-ups are allowed to reconcile valuation gaps. Agents express valuations in a common numeraire, but cash plays only an auxiliary role—its use incurs increasing inconvenience as transfer size grows. The result is an exchange environment that blends the bilateral structure of barter with the liquidity advantages of money, without collapsing into full market trade.

The contributions are threefold. First, we formalize the hybrid barter regime as a bilateral matching model with bounded transferability. Second, we establish welfare dominance of bounded-transfer equilibria over pure barter and derive comparative statics with respect to

1

the transfer cap. Third, we connect this structure to classical matching theory, showing that the model generalizes both pure barter and the transferable-utility assignment game (Shapley and Shubik, 1971).

Positioning. While the transferable-utility assignment game of Shapley and Shubik (1971) characterizes the fully monetary limit of bilateral exchange, it leaves open what occurs when transfers are possible but constrained. This paper formalizes that intermediate region by introducing bounded transferability as a primitive friction, thereby defining a new class of matching environments that interpolate between barter and full monetary exchange. The framework generalizes pure barter, where transfers are prohibited, and the transferable-utility assignment game, where transfers are unrestricted. By imposing a finite cap on side payments, the model embeds monetary search frictions (Kiyotaki and Wright, 1989; Trejos and Wright, 1995) within a matching structure that preserves the identity of barter. The ap-proach is conceptually related to search-and-matching models of bilateral trade (Mortensen and Pissarides, 1994; Rogerson et al., 2005) and to market-design frameworks with con-strained transferability (Echenique and Oviedo, 2004; Hatfield and Milgrom, 2005). It there-fore bridges decentralized exchange theory and matching with transfers, defining an interme-diate regime of bounded transferability that is tractable, welfare-comparable, and empirically testable.

2 The Model

There is a finite set of agents i ∈I. Each agent i is endowed with a finite set of heterogeneous, indivisible goods

Gi ⊂G, with {Gi}i∈I pairwise disjoint at the initial allocation.

For any item x ∈G, agent i has a valuation vi(x) ∈R expressed in a common numeraire. Utility is quasi-linear in money and additive over the items an agent holds after trade:

ui(Ai, ti) = vi(x) + ti,

x∈Ai

where Ai ⊆G is i’s post-trade item set and ti ∈R is the net monetary transfer to i. Feasibility requires that goods are merely reassigned and money is conserved:

Ai = Gi, Ai ∩Aj = ∅for all i ̸= j, ti = 0*. i∈I* i∈I i∈I

Bilateral match (realized trade). exactly one good from each side,