# Convergence in models with bounded expected relative hazard rates

*Carlos Oyarzun* and
*Johannes Ruf*

*Journal of Economic Theory*, 2014, vol. 154, issue C, 229-244

**Abstract:**
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.

**Keywords:** Hazard rate; Individual learning; Social learning; Two-armed bandit algorithm; Dynamic system; Stochastic approximation; Submartingale; Convergence (search for similar items in EconPapers)

**JEL-codes:** D81 D83 (search for similar items in EconPapers)

**Date:** 2014

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:jetheo:v:154:y:2014:i:c:p:229-244

**DOI:** 10.1016/j.jet.2014.09.014

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