Existence of independent random matching

By Darrell Duffie, Yeneng Sun. 2007

125 citations recorded by the source corpus.

This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, suitable for applications of the exact law of large numbers for random matching that have been popular in the economics and genetics literatures. We construct a joint agent-probability space, and randomized mutation, partial matching, and match-induced type-changing functions that satisfy appropriate independence conditions. The proofs are achieved via nonstandard analysis. The proof for the dynamic setting relies on a new Fubini-type theorem for Loeb transition probabilities and their products, based on which a continuum of independent Markov chains is derived from random mutation, random partial matching and random type changing.

Subfields: Economics and Econometrics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f0f5a57bf7509a82bea3b9cb99436c0c418925b0

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In Economics and Econometrics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Matching and anonymity (2006, background): “A second strand of literature comprises research directed at building solid mathematical foundations for random matching models; examples include studies on random meetings between agents drawn from countable or uncountable populations, as in [3], [11], or [2], and work on the exact law of large num”
Information Percolation (2008, background): “…chosen at random from the population, without replacement, with the uniform distribution, which we can take to be the agentspace measure γ. Duffie and Sun (2007) provide a complete construction for independent random matching from a large set (a non-atomic measure space) of agents, for the case…”
An Economic Model of Friendship: Homophily, Minorities and Segregation (2007, background): “44See also Duffie and Sun (2007).”
Liquidity in asset markets with search frictions (2007, background): “The expressions (24), (25) and (26) are the steady-state counterparts of (12), (17) and (13), respectively.”
Information Percolation in Large Markets (2007, methodology): “…random matching model is provided by Duffie and Sun (2005a), and the associated exact law of large numbers for the matching results is provided by Duffie and Sun (2005b). letting subscripts denote partial derivatives as usual, we have (almost everywhere) gt(x, t) = −λg(x, t) + ∫ +∞ −∞ λg(y,…”
Presidential Address: Social Transmission Bias in Economics and Finance (2020, unknown): “This allows a law of large numbers to be applied to matching outcomes (see Duffie and Sun (2007)).”
A Search-Based Theory of the On-the-Run Phenomenon (2006, unknown): “If the parameter δ is an (8)See also Ellison and Fudenberg (2003) for a general analysis of the coexistence of markets, and Economides and Siow (1988) for a spatial model of market formation.”