A Central Limit Theorem, Loss Aversion and Multi-Armed Bandits

TL;DR

This paper explores how loss aversion influences long-term decision-making in multi-armed bandit problems, introducing a new central limit theorem to analyze asymptotic behaviors under complex variance conditions.

Contribution

It presents a novel central limit theorem applicable to loss-averse bandit problems with history-dependent variances, advancing understanding of asymptotic properties in such settings.

Findings

Loss aversion affects asymptotic bandit strategies.

A new CLT for measures with variable variances.

Analytical results on large horizon behaviors.

Abstract

This paper studies a multi-armed bandit problem where the decision-maker is loss averse, in particular she is risk averse in the domain of gains and risk loving in the domain of losses. The focus is on large horizons. Consequences of loss aversion for asymptotic (large horizon) properties are derived in a number of analytical results. The analysis is based on a new central limit theorem for a set of measures under which conditional variances can vary in a largely unstructured history-dependent way subject only to the restriction that they lie in a fixed interval.