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with Assaf Zeevi
This paper investigates how the presence of the product review system affects a dynamic-pricing monopolist who is operating without knowing the demand model. A salient feature of our problem is that the demand function evolves over time in conjunction with the dynamics of the review system. We find the optimal pricing policy in a closed-form using fluid, mean-field model, which is a good approximation when the sales volume is large.
We first assume that sellers are relatively well-informed about the parameters of the demand function, in which case we show that a certain form of myopic policy works well. Then we consider a case with more significant uncertainty, where the myopic policy’s performance is strictly suboptimal, because the sellers need to implement price experimentation to counter the added uncertainty in the demand model.
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.
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.