Existence of independent random matching

• 成果类型: Article
• 署名作者: Duffie, Darrell; Sun, Yeneng
• 署名单位: Stanford University; National University of Singapore
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000673
• 发表日期: 2007
• 页码: 386-419
• 关键词: large numbers; equilibrium selection; price adjustment; search; LAW; unemployment; nonstandard; COMPETITION; EFFICIENCY; pairwise

摘要

This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, which has 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 an infinite product of Loeb transition probabilities, based on which a continuum of independent Markov chains is derived from random mutation, random partial matching and random type changing.