Convergence in models with bounded expected relative hazard rates

• 成果类型: Article
• 署名作者: Oyarzun, Carlos; Ruf, Johannes
• 署名单位: University of Queensland; University of London; University College London
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2014.09.014
• 发表日期: 2014
• 页码: 229-244
• 关键词: Hazard rate; individual learning; social learning; Two-armed bandit algorithm; dynamic system; stochastic approximation; Submartingale; CONVERGENCE

摘要

We provide a general framework to study stochastic sequences related to individual learning in economics, learning automata in computer sciences, social learning in marketing, and other applications. More precisely, we study the asymptotic properties of a class of stochastic sequences that take values in [0, 1] and satisfy a property called bounded expected relative hazard rates. Sequences that satisfy this property and feature small step-size or shrinking step-size converge to 1 with high probability or almost surely, respectively. These convergence results yield conditions for the learning models in [13,35,7] to choose expected payoff maximizing actions with probability one in the long run. (c) 2014 Elsevier Inc. All rights reserved.