Learning to Price with Reference Effects

TL;DR

This paper introduces a reinforcement learning approach using Thompson sampling to optimize pricing strategies in markets where consumer demand depends on both current and past prices, balancing revenue and information gathering.

Contribution

It formulates the dynamic pricing problem with reference effects as a reinforcement learning task and provides a tractable solution with theoretical regret guarantees.

Findings

The proposed method effectively balances exploration and exploitation in pricing.

Simulation results demonstrate improved revenue performance.

Theoretical bounds show performance improves with more data.

Abstract

As a firm varies the price of a product, consumers exhibit reference effects, making purchase decisions based not only on the prevailing price but also the product's price history. We consider the problem of learning such behavioral patterns as a monopolist releases, markets, and prices products. This context calls for pricing decisions that intelligently trade off between maximizing revenue generated by a current product and probing to gain information for future benefit. Due to dependence on price history, realized demand can reflect delayed consequences of earlier pricing decisions. As such, inference entails attribution of outcomes to prior decisions and effective exploration requires planning price sequences that yield informative future outcomes. Despite the considerable complexity of this problem, we offer a tractable systematic approach. In particular, we frame the problem as one of reinforcement learning and leverage Thompson sampling. We also establish a regret bound that provides graceful guarantees on how performance improves as data is gathered and how this depends on the complexity of the demand model. We illustrate merits of the approach through simulations.