Kiyotaki–Wright Search-Theoretic Model of Money

The Kiyotaki–Wright search-theoretic model of money is a microfounded model of exchange in business and economics theory that explains why agents hold and accept an object they do not consume. Introduced by Nobuhiro Kiyotaki and Randall Wright in the 1989 Journal of Political Economy article "On Money as a Medium of Exchange", the model replaces the Walrasian auctioneer of general equilibrium theory with decentralized, pairwise, random meetings. Because trade requires a double coincidence of wants, direct barter is often impossible, and an agent may rationally accept a good she does not want in order to trade it onward. Money is therefore an equilibrium outcome, not an assumption: the model derives which goods circulate as media of exchange, and why, from primitives of preferences, technology, and beliefs.

Time is continuous or discrete and the horizon is infinite. The economy contains a continuum of agents of three types, indexed i = 1, 2, 3, and three indivisible goods, also indexed 1, 2, 3. A type i agent derives utility u > 0 only from consuming good i, but cannot produce it directly. Immediately after consuming, she produces one unit of a good according to the specialization pattern: type i produces good i + 1 (modulo 3). Each agent stores at most one unit of one good at a time, which is an indivisibility that rules out credit and barter chains of unlimited length.

Agents meet in pairs at a Poisson rate β, with partners drawn uniformly at random. A trade occurs only if both agents agree. Because type i produces good i + 1 while type i + 1 wants good i + 1, but a type i agent wants good i, which is produced by type i − 1, no pair of agents has a double coincidence of wants in the baseline cyclic specification. Trade therefore requires indirect exchange, in which an agent accepts a good she will not consume.

Goods differ in storage cost. Holding good j costs c_j per period, with 0 ≤ c₁ < c₂ < c₃. Agents discount future payoffs at rate r. These storage costs create a reason to prefer a durable inventory, but they also interact with the probability of trading the held good onward.

Let V_ij be the value to a type i agent of holding good j, and let π_j be the fraction of the population holding good j. A strategy specifies, for every pair of goods, whether the agent is willing to swap. The value function satisfies a flow condition of the form

r V_ij = −c_j + β Σ_k π_k · max over trades of [ V_ik − V_ij + u · 1(k = i) ] weighted by partner acceptance.

An equilibrium is a set of strategies and a stationary distribution of inventories such that each agent's strategy is optimal given the others' strategies, and the distribution of holdings is invariant under the induced trading flows. The setup is a Nash equilibrium of a dynamic game, with beliefs about partner acceptance pinned down by the population strategy.

Kiyotaki and Wright distinguish two classes of acceptance behavior. In a fundamental equilibrium, an agent accepts a good as a medium of exchange only if it has a lower storage cost than the good she currently holds. Under this rule the cheapest-to-store good emerges as money, since accepting it never costs more in storage than holding the original item, and it raises the chance of eventually obtaining the consumption good.

In a speculative equilibrium, agents accept a good with a higher storage cost than their own holding, because they expect it to be acceptable to many more trading partners. Speculation is rational when the higher acceptability outweighs the extra holding cost. Whether such equilibria exist depends on the ratio of the cost differential to the trade surplus u and on the proportions of agents holding each good. The key force is a strategic complementarity: a good is accepted widely because others are expected to accept it, which produces multiple equilibria and a role for coordination. This is a feature shared with the general models of coordination failure in game theory.

When the accepted object has intrinsic value, the model describes commodity money. The equilibrium can be inefficient because acceptance of a high-cost good reduces net welfare through storage expenditure even as it raises the trade rate. Consequently, Pareto efficiency can fail, and a fiat object with zero storage cost would deliver higher welfare than any commodity money. A cooperative planner would choose the lowest-storage-cost good as the universal medium. The decentralized outcome is therefore a second-best trade-off between exchange frequency and holding costs.

The model also shows that the identity of money is endogenous and sensitive to parameters. Raising the arrival rate β or the trade utility u tends to push the economy toward fundamental equilibria, while larger storage-cost gaps can support speculative acceptance of a costlier good. An increase in the fraction of agents who hold a good raises its acceptability, since a random partner is more likely to want to trade it.

Experiments by Ramon Marimon, Edward Prescott, and Randall Wright (1990) and later by John Duffy and Jack Ochs (1999) placed human subjects in the Kiyotaki–Wright environment. Subjects frequently converged to the fundamental equilibrium and used the lowest-storage-cost good as money. Evidence for speculative behavior was weaker: agents usually did not accept a costlier good unless the cost gap was small and the benefit visible. Duffy and Ochs found that learning dynamics favored simple, myopic rules about storage cost, which explains why fundamental equilibria were the more common outcome. These results suggest that the equilibrium selection problem is tied to adaptive learning rather than to full rational-expectations coordination.

Kiyotaki and Wright (1991, 1993) extended the framework to fiat money, a good with zero intrinsic value, zero consumption utility, and negligible storage cost. A fiat object is accepted because agents believe others will accept it, so a monetary equilibrium exists alongside the non-monetary equilibrium in which the object is rejected. The model thereby formalizes the idea that money is a social convention supported by beliefs. Later generations of search models gave money a role of memory in an environment without record-keeping, a perspective developed by Narayana Kocherlakota (1998). Indivisible goods and money prevented analysis of prices and inflation, which motivated the Lagos–Wright monetary model and its divisible-money variant with tractable distributions of money holdings.

The baseline model is limited by the one-unit storage constraint, which makes money holdings and prices trivial: every trade swaps one indivisible item for another, so no price level or quantity theory emerges. The assumption of random matching also abstracts from relationships and enforcement. Despite these simplifications, the framework established the modern New Monetarist approach, which asks what frictions (limited commitment, information asymmetry, and spatial separation) make an exchange medium essential. Its central lesson is that the medium of exchange is a self-fulfilling equilibrium institution whose existence, identity, and welfare cost depend on the frictions of the trading environment.

1. Kiyotaki, N., & Wright, R. (1989). On Money as a Medium of Exchange. Journal of Political Economy, 97(4), 927–954. https://doi.org/10.1086/261634
2. Kocherlakota, N. R. (1998). Money Is Memory. Journal of Economic Theory, 81(2), 232–251. https://doi.org/10.1006/jeth.1997.2357
3. Lagos, R., & Wright, R. (2005). A Unified Framework for Monetary Theory and Policy Analysis. Journal of Political Economy, 113(3), 463–484. https://doi.org/10.1086/429804
4. Lagos, R., Rocheteau, G., & Wright, R. (2017). Liquidity: A New Monetarist Perspective. Journal of Economic Literature, 55(2), 371–440. https://doi.org/10.1257/jel.20141195