Stochastic Optimal Control for Online Seller under Reputational Mechanisms

TL;DR

This paper develops a stochastic optimal control model for online sellers that captures pulsing behavior driven by reputation, providing analytical solutions and insights into optimal reputation levels for profit maximization.

Contribution

It introduces a novel stochastic model linking seller reputation with optimal switching behavior, including a closed-form solution for simplified cases.

Findings

Optimal reputation levels for profit maximization identified

Closed-form solution derived for simplified model

Model validated through empirical reputation effects

Abstract

In this work we propose and analyze a model which addresses the pulsing behavior of sellers in an online auction (store). This pulsing behavior is observed when sellers switch between advertising and processing states. We assert that a seller switches her state in order to maximize her profit, and further that this switch can be identified through the seller's reputation. We show that for each seller there is an optimal reputation, i.e., the reputation at which the seller should switch her state in order to maximize her total profit. We design a stochastic behavioral model for an online seller, which incorporates the dynamics of resource allocation and reputation. The design of the model is optimized by using a stochastic advertising model from (16) and used effectively in the Stochastic Optimal Control of Advertising (12). This model of reputation is combined with the effect of online reputation on sales price empirically verified in (9). We derive the Hamilton-Jacobi-Bellman (HJB) differential equation, whose solution relates optimal wealth level to a seller's reputation. We formulate both a full model, as well as a reduced model with fewer parameters, both of which have the same qualitative description of the optimal seller behavior. Coincidentally, the reduced model has a closed form analytical solution that we construct.