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Dynamic Pricing with Online Product Reviews

with Assaf Zeevi

This paper investigates how the presence of product reviews affects a dynamic-pricing monopolist. A salient feature of our problem is that the demand function evolves over time in conjunction with the dynamics of the review system. The monopolist strives to maximize its total expected revenue over a finite horizon by adjusting prices in response to the review dynamics. To formulate the problem in tractable form, we study a fluid model, which is a good approximation when the volume of sales is large. This formulation lends itself to key structural insights, which are leveraged to design a well-performing pricing policy for the underlying revenue maximization problem. The proposed policy allows a closed-form expression for price and its performance is asymptotically near-optimal. We show via simulation and counterfactual analysis the effectiveness of the proposed policy in online markets with product reviews.

Tractable Sampling Strategies for Quantile-based Ordinal Optimization

with Mark Broadie and Assaf Zeevi

Given a certain number of stochastic alternatives (“systems”), the goal of our problem is to dynamically allocate a finite sampling budget to minimize the probability of falsely selecting non-best systems, where the selection is based on quantiles of their performances. This paper addresses two major aspects of the problem: (a) the probability of false selection does not possess an analytically tractable form and (b) the lack of knowledge on the underlying probability distributions prevents the exact implementation of optimal strategies since the sampling budget needs to be wasted on estimating those.

To formulate this problem in a tractable form, we introduce a function closely associated with the aforementioned objective using large deviations theory. To address the issue with unknown distributions, we suggest as our point of departure a policy that naively combines sequential estimation and myopic optimization, which is asymptotically optimal but exhibits poor finite-time performance. With the aim of improving finite-time performance, we propose alternative algorithms and show that they retain the asymptotic performance of the former algorithm in some cases, while dramatically improving its finite-time performance.

Tractable Dynamic Sampling Strategies for Ordinal Optimization

with Mark Broadie and Assaf Zeevi

We consider the problem of selecting the best of several competing alternatives (“systems”), where probability distributions of system performance are not known, but can be learned via sampling. The objective is to dynamically allocate a finite sampling budget to ultimately select the best system. We introduce a tractable performance criterion and a sampling policy that seeks to optimize it.

First, we characterize the optimal policy in an ideal “full information” setting where the means and variances of the underlying distributions are fully known. Then we construct a dynamic sampling policy which asymptotically attains the same performance as in the full information setting; this policy eventually allocates samples as if the underlying probability distributions are fully known. We characterize the efficiency of the proposed policy with respect to the probability of false selection, and show via numerical testing that it performs well compared to other benchmark policies.

Golf Analytics: A Random Putting Model and Its Applications to Optimal Targeting Strategy and Attribution Analysis

with Mark Broadie

The integration of a golf putting model and simulation & optimization techniques provides an analytical tool to develop the best strategy to win the game of golf. We calibrate a putting model to the PGA Tour data. Based on the calibrated model, we make two important implications on putting. First, we suggest the optimal targeting strategy and show that this tactic can significantly enhance putting score, without improving intrinsic putting skills. Second, we show via attribution analysis that green reading and direction control abilities are key for better putting performance, while the distance control ability has only minor impact.