Random Matching Model Research Articles

Random Matching of Several Infinite Populations

Random matching models with infinite populations present formal difficulties due to the lack of a law of large numbers for a continuum of random variables. In a previous paper (Alos-Ferrer, 1999), random matching processes for a continuum of agents were studied, proving their existence. The present work extends the analysis to the case of several populations, which includes general equilibrium buyers–sellers models, and evolutionary models with underlying asymmetric games.

Private money, settlement, and discounts

We construct a random matching model to study the effects of clearing arrangements for private money on the prices at which private monies trade, the volume of exchange, and welfare. In a model with full information, clearing arrangements eliminate discounts on private monies issued in other locations, the volume of exchange increases, and welfare increases. However, with private information about the quality of non-local monies, clearing arrangements may discourage the circulation of high-quality monies, and there may exist welfare-dominated equilibria with low-quality monies.

Another Example in which Lump-sum Money Creation is Beneficial

Abstract A probabilistic version of lump-sum money creation is studied in a random matching model with indivisible money and individual holdings bounded at 2 units. Sufficient conditions are obtained for an ex ante optimum from among implementable steady states to involve lump-sum creation of money. The role of that creation is to change the distribution of money holdings to permit more trade to occur. Beneficial money creation is impossible in a version with a 1 unit upper bound on individual holdings, but can almost certainly happen for all higher bounds.

ON RANDOM MATCHING, MONETARY EQUILIBRIA, AND SUNSPOTS

We study comparative statics results for the steady-state monetary equilibria of a simple random matching model of money with endogenous prices and no extrinsic uncertainty. Some of the results appear counterintuitive (both when take-it-or-leave-it offer or when Nash–Rubinstein bargaining is used in the model). Consistency of the equilibrium expectations causes the partial equilibrium intuitions to be reversed. We then proceed to apply the new insights to the analysis of sunspot equilibria in these type of models of bilateral trade with money.

A model of random matching and price formation

We study a model where buyers and sellers meet randomly. The meeting probabilities are endogenous and are derived from the basics of the model. The agents can decide to either search or wait, and the searchers are distributed on the waiters. Prices are determined by bargaining if exactly two agents are matched. If more than one agent of one type are matched with an agent of another type an auction ensues. There exist at most three equilibria, and when the numbers of buyers and sellers differ greatly one can argue that the equilibrium where the agents on the short side wait is the plausible one. We also study the relation of the model to the Walrasian markets, as well as to random matching models with bargaining only or auction only.

Money, Search and Costly Matchmaking

I examine the robustness of monetary equilibria in a random matching model where a more efficient mechanism for trade is available. Agents choose between two trading sectors: the search and the intermediated sector. In the former, trade partners arrive randomly and there is a trading externality. In the latter a costly matching technology provides deterministic double-coincidence matches. Multiple equilibria exist with the extent of costly matching endogenously determined. Money and “mediated” trade may coexist. This depends on the size of the probability of a trade, relative to the cost of deterministic matching. This outcome is inferior for an increasing returns externality. Under certain conditions regimes with only costly matching are welfare superior to monetary regimes with random matching.

MONEY, SEARCH, AND COSTLY MATCHMAKING

I examine the robustness of monetary equilibria in a random-matching model, where a more efficient mechanism for trade is available. Agents choose between two trading sectors: the search and the intermediated sector. In the former, trade partners arrive randomly and there is a trading externality. In the latter, a costly matching technology provides deterministic double-coincidence matches. Multiple equilibria exist with the extent of costly matching endogenously determined. Money and “mediated” trade may coexist. This depends on the size of the probability of a trade, relative to the cost of deterministic matching. This outcome is inferior for an increasing-returns externality. Under certain conditions, regimes with only costly matching are welfare superior to monetary regimes with random matching.

Knowledge of Individual Histories and Optimal Payment Arrangements

This article reviews recent work that generalizes a random matching model of money to permit there to be a mix of transactions: some accomplished through the use of tangible media of exchange and the rest through some form of credit. The generalizations are accomplished by specifying assumptions about common knowledge of individual histories that are intermediate between no common knowledge and complete common knowledge. One of the specifications permits a simple representation of the sense in which more common knowledge is beneficial. The other permits a comparison between using outside money and using inside money as a medium of exchange.

Exact solution of the random bipartite matching model

In this paper we present the exact solution for the average minimum energy of the random bipartite matching model with an arbitrary finite number of elements where random paired interactions are described by independent exponential distribution. This solution confirms the Parisi conjecture proposed for this model earlier, as well as the result of the replica solution of this model in the thermodynamic limit.

Social Norms and Monetary Trading

Random matching models have been used in Monetary Economics to argue that money can increase the well being of all agents in the economy. If the model features a finite number of agents it will be shown that there is an equilibrium, analogous to the contagious equilibria described in Kandori (1992), that Pareto dominates the monetary one. However it will be shown also that monetaty equilibria have two important advantages: firstly, they are more plausible in large economies in the sense that the lowest discount factor compatible with monetary equilibria doesn’t depend on the population size, which is not the case with contagious equilibria; secondly, it is more stable to finite deviations in the following sense: no matter what the past has been, future play of the equilibrium strategies will give players the same payo

A Matching Model with Bounded Holdings of Indivisible Money

Recent versions of pairwise random matching models of money with divisible and perishable goods are amended to allow individuals to hold more than one unit of an indivisible asset. The asset resembles a fiat asset, except that nominal holdings of it yield a small amount of utility. There is a general upper bound on the number of units of the asset that individuals can hold. A steady state with trade is shown to exist. The model is applied to study numerically the effect on welfare of the degree to which the asset is divisible.

Inside and Outside Money as Alternative Media of Exchange

We study a random matching model of money in which a subset of people, called bankers, have known histories and the rest, called nonbankers, have unknown histories. Earlier, we showed that if there are no outside assets, then an optimal arrangement has bankers issuing objects, banknotes, that are used in trades involving nonbankers. Here, the same model is used to compare such exclusive use of inside money to the exclusive use of outside money. We show that the set of implementable outcomes using outside money is a strict subset of the set using inside money.

Credit in a Random Matching Model with Private Information

We consider a random matching model where agents have complete access to each others' histories. Exchange is motivated by risk sharing, given random unobservable incomes. There is capital accumulation and an endogenous interest rate. The key feature of this environment is that information is mobile across locations, while there are frictions associated with transporting goods. Optimal allocations in the dynamic private information environment resemble real-world credit arrangements in that there are credit balances, credit limits, and installment payments. The steady state has the property that there is a limiting distribution of expected utility entitlements with mobility and a positive fraction of agents who are credit constrained.Journal of Economic LiteratureClassification Numbers: D8, E1.

A Model of Private Bank-Note Issue

A random-matching model (of money) is formulated in which there is complete public knowledge of the trading histories of a subset of the population, called the banking sector, and no public knowledge of the trading histories of the complement of that subset, called the nonbank sector. Each person, whether a banker or a nonbanker, is assumed to have the technological capability to create indivisible, distinct, and durable objects called notes. If outside money is indivisible and sufficiently scarce, then an optimal mechanism is shown to have note issue and note redemption (destruction) by members of the banking sector.Journal of Economic LiteratureClassification Numbers: E40, E42.

A Dictum for Monetary Theory

This essay argues that monetary theories should not contain an undefined object labeled money. Among existing theories that do not satisfy that dictum are models which assume that real balances are arguments of utility or production functions and models which assume cash-in-advance constraints. A main weakness of theories that do not satisfy the dictum is that they cannot address questions about which objects constitute money. Theories that do satisfy the dictum are those which specify assets by their physical properties and which permit the assets’ role in exchange to be endogenous. The essay briefly describes one such theory, a random matching model with assets that differ according to whether they throw off real dividends. This essay is reprinted, with permission, from the book Foundations of Research in Economics: How Do Economists Do Economics? (ed. Steven Medema and Warren Samuels), Cheltenham, U.K.: Edward Elgar Publishing, 1996.

Contacts with agreements: Towards face-to-face communication modelingContacts with agreements

In this paper a random matching model is elaborated to characterize bilateral interregional human face-to-face contacts. The bilateral contacts can be realized only when both parties agree to meet each other. Thus, mutual agreement is the core of our contact modeling. Spatial distribution of bilateral contacts can be described as the results of random matching by potential meeting partners. The failure in agreement of meeting is the major source of inefficiency in human contacts among regions. The paper provides a random matching scheme to describe the generation mechanism of inter-regional human contacts. The paper concludes by illustrating some numerical examples showing how changes in transportation costs can modify the inter-regional interactability in terms of the face-to-face contacts.

A Rudimentary Random-Matching Model with Divisible Money and Prices

We consider a version of Kiyotaki and Wright's monetary search model in which agents can hold arbitrary amounts of divisible money. A continuum of stationary equilibria, indexed by the aggregate real money stock, exists with all trading occurring at a single price. There is always a maximum level of the real money stock consistent with existence of such an equilibrium. In the limit as trading becomes faster relative to discounting, any real money stock becomes feasible in such an equilibrium. In contrast to the original Kiyotaki–Wright model, higher equilibrium real money stocks unambiguously correspond to higher welfare in this costless-production environment.Journal of Economic LiteratureClassification Numbers: D51, E40.

Efficiency of Investment in Human and Physical Capital in a Model of Bilateral Search and Bargaining

A matching model is used to analyze the effect of search frictions on incentives to invest in human and physical capital. Equilibrium involves inefficient (low) levels of investment. The source of the inefficiency cannot be attributed solely to either search or bargaining. Schemes that assist matching are Pareto-improving. While the ratio of workers to firms remains fixed, intermediaries that pay owners according to the amount of capital carried into the market are able to generate efficient outcomes. Such intervention may not eliminate inefficiencies when the ratio is endogenized. Policy implications include encouragement of investment (even while abstracting from growth). This paper examines investment in human and physical capital in an environment with explicit frictions. In particular, I analyze a random matching model, where workers must search for employers and vice versa, but one that is generalized beyond the previous literature to include ex ante investments on both sides of the market.2 The model generates equilibria with inefficiently low levels of investment. To identify the source of the inefficiency, its robustness to variations in the environment is considered. I also analyze a generalized version of the model, in which individuals can choose whether to invest in physical or human capital (i.e., whether to become employers or workers). The model predicts that the

Scale returns of a random matching model

This note considers a random matching model in which the meeting probabilities can be derived from the basics of the model. We determine conditions for the matching technology to exhibit decreasing, constant, and increasing returns to scale.

A model of a currency shortage

Until the mid-19th century, shortages of currency were common. Moreover, a frequent policy response was a prohibition on the export of coins. We use a random matching model with indivisible money to explain a shortage and to judge the desirability of a prohibition on the export of coins. The model, although extreme in many regards, represents better than earlier models a demand for outside money and the problems that arise when that money is indivisible. It can also rationalize a prohibition on the export of money.