A Taste for Variety

TL;DR

This paper studies decision-making strategies in a repeated choice setting where payoffs depend on fixed action benefits and historical frequencies, analyzing optimal strategies under different evaluation schemes.

Contribution

It characterizes when stationary strategies are optimal under discounted, limit inferior, and limit superior evaluations of infinite payoffs.

Findings

Stationary strategies are optimal under discounted and limit inferior evaluations.

Stationary strategies are only optimal for the limit superior evaluation if all frequently chosen actions have equal payoffs.

The analysis provides conditions for the effectiveness of stationary strategies in dynamic decision problems.

Abstract

A decision maker repeatedly chooses one of a finite set of actions. In each period, the decision maker's payoff depends on fixed basic payoff of the chosen action and the frequency with which the action has been chosen in the past. We analyze optimal strategies associated with three types of evaluations of infinite payoffs: discounted present value, the limit inferior, and the limit superior of the partial averages. We show that when the first two are the evaluation schemes, a stationary strategy can always achieve the best possible outcome. However, for the latter evaluation scheme, a stationary strategy can achieve the best outcome only if all actions that are chosen with strictly positive frequency by an optimal stationary strategy have the same basic payoff.