Yiwei Chen

Simple Policies for Dynamic Pricing with Imperfect Forecasts

We consider the “classical” single-product dynamic pricing problem allowing the “scale” of demand intensity to be modulated by an exogenous “market size” stochastic process. This is a natural model of dynamically changing market conditions. We show that for a broad family of Gaussian market-size processes, simple dynamic pricing rules that are essentially agnostic to the specification of this market-size process perform provably well. The pricing policies we develop are shown to compensate for forecast imperfections (or a lack of forecast information altogether) by frequent reoptimization and reestimation of the “instantaneous” market size.

Robust Dynamic Pricing With Strategic Customers

We consider the canonical problem of revenue management (RM) wherein a seller must sell an inventory of some product over a finite horizon via an anonymous, posted price mechanism. Unlike typical models in RM, we assume that customers are forward looking. In particular, customers arrive randomly over time, and strategize about their time of purchase. The private valuations of these customers decay over time and the customers incur monitoring costs; both the rate of decay and these monitoring costs are private information. Moreover, customer valuations and monitoring costs are potentially correlated. This setting has proven to be a difficult one for the design of optimal dynamic mechanisms heretofore. Optimal pricing schemes -- an almost necessary mechanism format for practical RM considerations -- have been similarly elusive. We propose a class of pricing policies, and a simple to compute policy within this class, that is guaranteed to achieve expected revenues that are at least within 29% of those under an optimal (not necessarily posted price) dynamic mechanism. Moreover, the seller can compute this pricing policy without any knowledge of the distribution of customer discount factors and monitoring costs. Our scheme can be interpreted as solving a dynamic pricing problem for myopic customers with the additional requirement of a novel --restricted submartingale constraint on prices. Numerical experiments suggest that the policy is, for all intents, near optimal.

Pricing and Matching with Forward-Looking Buyers and Sellers

Problem definition: We study a dynamic market over a finite horizon for a single product or service in which buyers with private valuations and sellers with private supply costs arrive following Po...

Joint Pricing and Inventory Management with Strategic Customers

We consider a joint pricing and inventory management problem wherein a seller sells a single product over an infinite horizon via dynamically determining anonymous posted prices and inventory replenishment quantities. Customers arrive over time with a deterministic arrival rate but heterogeneous product valuations. A customers arrival time and product valuation are his private information. Customers are forward-looking, who can strategize their times of purchases. Customer unsatisfied demand is backlogged. A customer incurs disutility from delaying making the purchasing decision and incurring product delivery delay. The seller incurs fixed ordering cost and inventory holding cost. The seller seeks a joint pricing and inventory policy that maximizes her long-run average profit. We show that the optimal policy is cyclic, i.e., the seller repeats the pricing and ordering decisions over cycles of the same length. Under the optimal policy, strategic customer equilibrium behaviors are proven to be myopic. The sellers optimal long-run average profit in the presence of strategic customers is the same as her optimal profit in an auxiliary classical backlogging model wherein customers are myopic that they make their purchasing decisions immediately upon their arrivals. We adopt a mechanism design approach to prove the optimality of our proposed policy in the presence of strategic customers.

Fair Resource Allocation in A Volatile Marketplace

We consider the setting where a seller must allocate a collection of goods to budgeted buyers, as exemplified by online advertising systems where platforms decide which impressions to serve to various advertisers. Such resource allocation problems are challenging for two reasons: (a) the seller must strike a balance between optimizing her own revenues and guaranteeing fairness to her (repeat) buyers and (b) the problem is inherently dynamic due to the uncertain, time-varying supply of goods available with the seller. We propose a stochastic approximation scheme akin to a dynamic market equilibrium. Our scheme relies on frequent re-solves of an Eisenberg-Gale convex program, and does not require the seller to have any knowledge about how goods arrival processes evolve over time. The scheme fully extracts buyer budgets (thus maximizing seller revenues), while at the same time provides a 0.47 approximation of the proportionally fair allocation of goods achievable in the offline case, as long as the supply of goods comes from a wide family of (possibly non-stationary) Gaussian processes. We then extend our results to a more general family of metrics called \alpha-fairness. Finally, we deal with a multi-objective problem where the seller is concerned with both the proportional fairness and efficiency of the allocation, and propose a hybrid algorithm which achieves a 0.27 bi-criteria guarantee against fairness and efficiency.

Why are Fairness Concerns so Important? Lessons from Pricing a Shared Last-Mile Transportation System

The Last-Mile Problem refers to the provision of travel service for passengers from the nearest public transportation node to the final destination. The Last-Mile Transportation System (LMTS), which has recently emerged, provides on-demand shared last-mile transportation service for passengers. We consider an LMTS that consists of two types of passengers, regular-type passengers and special-type passengers (e.g., seniors, disabled people). The valuation of the last-mile service for special-type passengers is statistically higher than the one for regular-type passengers. Passengers incur disutility from waiting for the last-mile service. In this paper, we explore two fairness guarantees on special-type passengers: (1) the fare for special-type passengers is restricted to be no higher than a given fraction of the fare for regular-type passengers; (2) special-type passengers cannot be served after regular-type passengers. We aim at understanding the role of these two fairness constraints on the LMTS operators pricing and service priority policies, with the objective of maximizing either profit or social welfare. Our theoretical analysis and numerical experiments using real public transport data show that if passenger waiting disutility is negatively correlated with the last-mile service valuation, i.e., regular-type passengers are more sensitive to waiting time, then with both objectives, the LMTS operator always has incentive to charge special-type passengers no less than regular-type passengers and serve special-type passengers after regular-type passengers. This entails the necessity of enforcing the two fairness guarantees. In addition, even if passenger waiting disutility is positively correlated with the last-mile service valuation, i.e., special-type passengers are more sensitive to waiting time, the two fairness guarantees are still necessary under some market environments. These findings demonstrate the importance of fairness concerns in shared transportation systems.

Robust Dynamic Pricing with Strategic Customers

We consider the canonical revenue management (RM) problem wherein a seller must sell an inventory of some product over a finite horizon via an anonymous, posted price mechanism. Unlike typical mode...

On the Efficacy of Static Prices for Revenue Management in the Face of Strategic Customers

The present paper considers a canonical revenue management problem wherein a monopolist seller seeks to maximize revenues from selling a fixed inventory of a product to customers who arrive over time. We assume that customers are forward looking and strategize on the timing of their purchase, an empirically confirmed aspect of modern customer behavior. In the event that customers were myopic, foundational work by Gallego and van Ryzin [1994] established that static prices were asymptotically optimal for this problem. In stark contrast, for the case where customers are forward looking, available results in mechanism design and dynamic pricing offer no such simple solution and are also constrained by restrictive assumptions on customer type. The present paper studies the revenue management problem while assuming forward looking customers. We demonstrate that for a broad class of customer utility models, static prices surprisingly continue to remain asymptotically optimal in the scaling regime where inventory and demand grow large. We further show that irrespective of regime, an optimally set static price guarantees the seller revenues that are within at least 63.2% of that under an optimal dynamic mechanism. The class of customer utility models we consider is parsimonious and enjoys empirical support. It also subsumes many of the utility models considered for this problem in existing mechanism design research; we allow for multi-dimensional customer types. We also allow for a customers disutility from waiting to be positively correlated with his valuation. Our conclusions are thus robust and provide a simple solution to what is considered a challenging problem of dynamic mechanism design.