Continuous-Time Random Matching

41 Pages Posted: 24 Aug 2023

See all articles by Darrell Duffie

Darrell Duffie

Stanford University - Graduate School of Business; National Bureau of Economic Research (NBER); Canadian Derivatives Institute

Lei Qiao

National University of Singapore (NUS)

Yeneng Sun

National University of Singapore

Date Written: August 23, 2023

Abstract

Continuous-time random matching with a large (continuum) population is widely exploited in the literature, but has not had a rigorous formulation, nor a demonstration of its key assumed properties. This paper provides the first probabilistic foundation for this approach by presenting a mathematical model of continuous-time random matching and showing its existence and properties. The agents' types, which can change due to random matching and random mutation, form a continuum of independent continuous-time Markov chains. Using the exact law of large numbers, we show how the cross-sectional distribution of agent types evolves deterministically according to an explicit ordinary differential equation. Nonstandard analysis is used in proving the main theorem.

Keywords: Independent dynamic random matching, Markov chain, exact law of large numbers, continuous-time, random mutation.

JEL Classification: C78, D50, D53, D83

Suggested Citation

Duffie, James Darrell and Qiao, Lei and Sun, Yeneng, Continuous-Time Random Matching (August 23, 2023). Stanford University Graduate School of Business Research Paper No. 4549798, Available at SSRN: https://ssrn.com/abstract=4549798 or http://dx.doi.org/10.2139/ssrn.4549798

James Darrell Duffie (Contact Author)

Stanford University - Graduate School of Business ( email )

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National Bureau of Economic Research (NBER)

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Canadian Derivatives Institute ( email )

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Lei Qiao

National University of Singapore (NUS) ( email )

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Singapore, 119228
Singapore

Yeneng Sun

National University of Singapore ( email )

Departments of Economics and Mathematics
Singapore, 119076
Singapore

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