Independent random matching

Abstract

Random matching models with a continuum population are widely used in economics to study environments where agents interact in small coalitions. This paper provides foundations to such models. In particular, the paper establishes an existence result for random matchings that are universal in the sense that certain desirable properties are satisfied for any assignment of types to agents. The result applies to infinitely many types of agents, thus covering random matching models which are currently used in the literature without a foundation. Furthermore, the paper provides conditions guaranteeing uniqueness of random matching. JEL classification: C00, C02, C73, C78Keywords: Random matching; Involution; Independence; Continuum population; Fubini extension * We thank an anonymous referee for valuable comments and for suggestions on how to improve the presentation of the material of this paper.

Imitation in heterogeneous populations

“…27 The outcomes 0.5 and 1 can be thought of as the physical payoff of "full symptoms" and "no symptoms," respectively. The expected physical heavily biased toward sampling individuals of their own type is not incompatible with uniform adoption.…”

“…More broadly, if we measure type B individuals' bias to sample their own type by B := ↵ B (1 ↵) 1 , it is easy to see that we can have uniform adoption even if B is very high: if we fix B , for sufficiently small (1 ↵) one obtains that B (1 ↵) < 0.54 and hence, uniform adoption of a (for high enough ↵ A ). 27 We normalize the physical payoffs to be in [0.5, 1] so that the total payoff of each choice, corresponding to the physical payoffs minus the price charged by the monopolist, fall in [0, 1], as in the benchmark model.…”

“…In the last decade, a number of papers deal with this issue and with independent random matching in particular, using Fubini Extensions introduced in Sun (2006) (see, e.g., Sun 2007, 2012). See also Podczeck and Puzzello (2012), who build on an earlier contribution by Alos-Ferrer (1999) to study independent random matching with a continuum of agents. We thank three anonymous referees for guiding us to this literature.…”

Independent random partial matching with general types

“…See also[3,4] for extensive references on biology, economics, mathematics and finance.2 In[20], the type space is [0, ∞). For independent random full matchings with a general type space,[3] and[4] established the mathematical foundation; see[22] for an alternative proof on the existence.3 The homogeneity is used in the nonstandard approach to stochastic analysis and mathematical economics; see[12,14]. For recent developments and applications of nonstandard analysis, see[1,5,13,16,17,21,25].…”

Separation of Unit of Account from Medium of Exchange

“…For mathematical foundations on the existence of random matching with a continuum of agents, see Alos‐Ferrer (), Aliprantis, Camera, and Puzzello (), Duffie and Sun (), and Podczeck and Puzzello ().…”