In this paper, we propose a Deep-DiD method that incorporates two deep neural networks in a difference-in-difference (DiD) framework to estimate heterogeneous treatment effects (HTEs). The dual-network architecture contains one neural network modeling HTEs as a nonparametric function of pretreatment features and another neural network capturing individual and time fixed effects. Through a series of simulations, we show that our method can uncover the true HTEs with high accuracy under various settings and demonstrates more robust estimation performance compared with existing methods like linear models and random forests. We apply this method to an empirical setting where a large video-sharing platform introduced a “Creator Signing Program” aimed at signing creators and motivating them to generate more high-quality video content. Leveraging a matched data set of signed and unsigned creators, we employ our Deep-DiD method to estimate the HTEs of the signing program. Our method can help the platform optimize creator selection by identifying creators with the highest-estimated treatment effects. Through out-of-sample tests, we show that creators selected by the Deep-DiD method experience substantially larger actual performance jumps than those selected by the platform. Creator selection based on the Deep-DiD method also consistently outperforms that based on linear models.
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This work examines the behaviors of the online projected gradient ascent (OPGA) algorithm and its variant in a repeated oligopoly price competition under reference effects. In particular, we consider that multiple firms engage in a multiperiod price competition, where consecutive periods are linked by the reference price update and each firm has access only to its own first-order feedback. Consumers assess their willingness to pay by comparing the current price against the memory-based reference price, and their choices follow the multinomial logit (MNL) model. We use the notion of stationary Nash equilibrium (SNE), defined as the fixed point of the equilibrium pricing policy, to simultaneously capture the long-run equilibrium and stability. We first study the loss-neutral reference effects and show that if the firms employ the OPGA algorithm—adjusting the price using the first-order derivatives of their log-revenues—the price and reference price paths attain last-iterate convergence to the unique SNE, thereby guaranteeing the no-regret learning and market stability. Moreover, with appropriate step-sizes, we prove that this algorithm exhibits a convergence rate of ̃ 𝒪 (1/𝑡2) in terms of the squared distance and achieves a constant dynamic regret. Despite the simplicity of the algorithm, its convergence analysis is challenging due to the model lacking typical properties such as strong monotonicity and variational stability that are ordinarily used for the convergence analysis of online games. The inherent asymmetry nature of reference effects motivates the exploration beyond loss-neutrality. When loss-averse reference effects are introduced, we propose a variant of the original algorithm named the conservative-OPGA (C-OPGA) to handle the nonsmooth revenue functions and show that the price and reference price achieve last-iterate convergence to the set of SNEs with the rate of 𝒪(1/√𝑡) . Finally, we demonstrate the practicality and robustness of OPGA and C-OPGA by theoretically showing that these algorithms can also adapt to firm-differentiated step-sizes and inexact gradients.
Problem definition: As digitization transforms the service sector and empowers service platforms, questions arise about utilizing and disseminating customer information captured by digitization to enhance platform operations. We contribute by investigating how providing customer-related information at the start of a service encounter impacts both service supply and demand in the context of entertainment service platforms. Methodology/results: We conducted a field experiment on a live-streaming platform that connects hundreds of millions of viewers with individual broadcasters. For broadcasters randomly assigned to the treatment condition (but not for broadcasters in the control condition), when a viewer entered their shows, information about the viewer appeared on the screen. Our analyses, involving a random sample of 49,998 broadcasters, demonstrate that relative to control broadcasters, treatment broadcasters expanded service supply by 12.62% by increasing both show frequency (3.31%) and show length (7.10%), thus earning 10.44% more income, based on our conservative estimate. Moreover, our intervention increased service demand (measured by viewer watch time) by 4.51%. Additional analyses and surveys in our field setting and online experiments (n = 3,115) shed light on the potential mechanisms. Viewer-related information enables broadcasters to offer personalized service and vividly perceive viewers. On the demand side, viewers appreciate personalized service and interact with broadcasters more, which collectively boost demand. On the supply side, broadcasters not only enjoy the increased interaction with viewers but also feel a stronger sense of appreciation due to the more vivid mental image of viewers, which collectively lifts service supply. Managerial implications: This research suggests that providing customer-related information at the beginning of a service encounter can increase both service demand and supply. This low-cost, information-based intervention has important implications for digital service platforms that have little control over service providers’ work schedules and service quality.
The rapid development of blockchain has inspired many traditional centralized intermediaries to transform their transaction models, especially for the peer-to-peer market. Lately, the token-based (blockchain) system (with cryptocurrency) is gaining popularity. However, little is known about the (comparative) performance of different operating types. In this study, we build an analytical framework to find the optimal strategies for the token-based and nontoken-based blockchain (as a special application scenario) platforms and derive the essential model properties and characteristics. We analytically show how the optimal mining bonus depends on the fraction of reserved tokens sold to customers and on the price-to-sales ratio. Furthermore, we obtain several actionable findings for choosing suitable platform types under different scenarios. The shift from the nontoken-based platform to the token-based platform may yield greater social welfare unless the nontoken-based system operates with a much larger ride price, which we show to be unrealistic for the considered Beijing case through numerical studies. Moreover, we find that the matching probability for the token-based platform is predominantly higher than that for the nontoken-based one. Besides, government interventions may encourage a path toward a fair consensus mechanism or a high decentralization level in order to enhance social welfare. One unanticipated finding is that a higher decentralization level may lead to a lower mining capacity shortage and so to a more efficient system, indicating that the combination of blockchain and the sharing economy has much potential.
Problem definition: How should retailers leverage aggregate (category) sales information for individual product demand prediction? Motivated by inventory risk pooling, we develop a new prediction framework that integrates category-product sales information to exploit the benefit of pooling. Methodology/results: We propose to combine data from different aggregation levels in a transfer learning framework. Our approach treats the top-level sales information as a regularization for fitting the bottom-level prediction model. We characterize the error performance of our model in linear cases and demonstrate the benefit of pooling. Moreover, our approach exploits a natural connection to regularized gradient boosting trees that enable a scalable implementation for large-scale applications. Based on an internal study with JD.com on more than 6,000 weekly observations between 2020 and 2021, we evaluate the out-of-sample forecasting performance of our approach against state-of-the-art benchmarks. The result shows that our approach delivers superior forecasting performance consistently with more than 9% improvement over the benchmark method of JD.com. We further validate its generalizability on a Walmart retail data set and through alternative pooling and prediction methods. Managerial implications: Using aggregate sales information directly may not help with product demand prediction. Our result highlights the value of transfer learning to demand prediction in retail with both theoretical and empirical support. Based on a conservative estimate of JD.com, the improved forecasts can reduce the operating cost by 0.01–0.29 renminbi (RMB) per sold unit on the retail platform, which implies significant cost savings for the low-margin e-retail business.
Problem definition: Inventory management problems with periodic and controllable resets occur in the context of managing water storage in the developing world and dynamically optimizing endcap promotion duration in retail outlets. In this paper, we consider a set of sequential decision problems in which the decision maker must not only balance holding and shortage costs but discard all inventory before a fixed number of decision epochs with the option for an early inventory reset. Methodology/results: Finding optimal policies for these problems through dynamic programming presents unique challenges because of the nonconvex nature of the resulting value functions. Moreover, this structure cannot be readily analyzed even with extended convexity definitions, such as K-convexity. Managerial implications: Our key contribution is to present sufficient conditions that ensure the optimal policy has an easily interpretable structure, which generalizes the well-known (𝑠,𝑆) policy from the operations management literature. Furthermore, we demonstrate that, under these rather mild conditions, the optimal policy exhibits a four-threshold structure. We then conclude with computational experiments, thereby illustrating the policy structures that can be extracted in various inventory management scenarios.
Problem definition: We consider the dynamic pricing problem of multiple products under (asymmetric) reference effects over an infinite horizon. Unlike existing literature, which is mostly focused on the single-product setting, our multiproduct setting takes into account the cross-product effects among substitutes and incorporates the memory-based reference prices into the multinomial logit (MNL) demand model. Even with the single-product logit demand, the structure of the optimal pricing policy is intractable. Therefore, we focus on the long-run patterns of the optimal pricing policy and also discuss the performance of the myopic pricing policy. Methodology/results: We first provide a comprehensive characterization of the myopic pricing policy, including its solution, long-run convergence behavior, and optimality gap. For the optimal pricing policy, we show an intricate connection between its long-run dynamics and types of reference effects. We demonstrate that the presence of any gain-seeking product renders a long-run constant pricing policy suboptimal. Conversely, the constant policy (or optimal steady state) can exist in both loss-neutral and loss-averse scenarios, where we provide a sufficient condition for such existence and give the analytical expression for the optimal steady state. We further show that when pricing perfect substitutes, the true optimal policy under the multiproduct framework is more likely to yield a long-run cyclic pattern than the policy derived from the single-product framework, a phenomenon that aligns well with the periodic discounts in real-world markets. Managerial implications: This discrepancy in the long-run behaviors between multi- and single-product-based policies highlights the importance of employing the multiproduct framework and addressing the cross-product effects, as sticking to the single-product framework while managing multiple substitutes can misrepresent long-run dynamics and result in suboptimality. In the multiproduct domain, our model suggests that retailers are more likely to benefit from appropriate price variations than maintaining a constant pricing policy.
We study the data-integrated, price-setting newsvendor problem in which the price–demand relationship is described by some parametric model with unknown parameters. We develop the operational data analytics (ODA) formulation of this problem that features a data-integration model and a validation model. The data-integration model consists of a class of functions called the operational statistics. Each operational statistic maps the available data to the ordering decision. The validation model finds, among the set of candidate operational statistics, the ordering decision that leads to the highest actual profit, which is unknown because of the unknown demand parameters. This ODA framework leads to a consistent estimate of the profit function with which we optimize the pricing decision. The derived quantity and price decisions demonstrate robust profit performance even when the sample size is very small in relation to the demand variability. Compared with the conventional approach with which the unknown parameters are estimated and then the decisions are optimized, the ODA framework produces significantly superior performance in the mean, standard deviation, and minimum of the profit, suggesting the robustness of the ODA solution especially in the small-sample regime.
We study the reliable (uncapacitated) facility location (RFL) problem in a data-driven environment where historical observations of random demands and disruptions are available. Owing to the combinatorial optimization nature of the RFL problem and the mixed-binary randomness of parameters therein, the state-of-the-art RFL models applied to the data-driven setting either suggest overly conservative solutions or become computationally prohibitive for large- or even moderate-size problems. In this paper, we address the RFL problem by presenting an innovative prescriptive model aiming to balance solution conservatism with computational efficiency. In particular, our model selects facility locations to minimize the fixed costs plus the expected operating costs approximated by a tractable data-driven estimator, which equals to a probabilistic upper bound on the intractable Kolmogorov distributionally robust optimization estimator. The solution of our model is obtained by solving a mixed-integer linear program that does not scale in the training data size. Our approach is proved to be asymptotically optimal, and offers a theoretical guarantee for its out-of-sample performance in situations with limited data. In addition, we discuss the adaptation of our approach when facing data with covariate information. Numerical results demonstrate that our model significantly outperforms several important RFL models with respect to both in-sample and out-of-sample performances as well as computational efficiency.