CONTINUOUS TIME RANDOM MATCHING

• 成果类型: Article
• 署名作者: Duffie, Darrell; Qiao, Lei; Sun, Yeneng
• 署名单位: Stanford University; Shanghai University of Finance & Economics; National University of Singapore
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/25-AAP2156
• 发表日期: 2025
• 页码: 1755-1790
• 关键词: search; nonstandard; EXISTENCE; EVOLUTION; games

摘要

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 crosssectional distribution of agent types evolves deterministically according to an explicit ordinary differential equation. Nonstandard analysis is used in proving the main theorem.