Events & Seminars

When only the moments of the underline distribution are known, many max-min optimization models can be interpreted as zero-sum games, in which the firm chooses actions to maximize her expected profit while Nature chooses a distribution subject to the moment conditions to minimize the firm’s expected profit. For single-period models, we reformulate the zero-sum game as a robust moral hazard, in which Nature chooses both the distribution and actions to minimize the firm’s expected profit subject to incentive compatibility (IC) constraints. Under quasi-concavity, these IC constraints are replaced by the firm’s first-order conditions, which give rise to additional moment constraints and an extended reformulation of the dual problem in a higher dimensional space, facilitating the search for the closed-form solution. In the equilibrium, the additional moment constraints are binding but have zero Lagrangian multipliers. This property enables us to derive closed-form solutions for several distributionally robust inventory models that the extant literature is unable to solve. For multi-period models, we apply subgame perfect conditions to eliminate Nature’s dominated strategies so that we can conveniently compute the firm’s time-average cost under Adverse Nature’s undominated strategy. We then solve the robustly optimal base-stock level with positive lead time and lost sales (or backorder). The theme of this ambitious research program is to combine both zero-sum games and semi-infinite programming tools.

We explore a new model of bandit experiments where a potentially nonstationary sequence of contexts influences arms' performance. Context-unaware algorithms risk confounding while those that perform correct inference face information delays. Our main insight is that an algorithm we call deconfounted Thompson sampling strikes a delicate balance between adaptivity and robustness. Its adaptivity leads to optimal efficiency properties in easy stationary instances, but it displays surprising resilience in hard nonstationary ones which cause other adaptive algorithms to fail.

We study an assortment optimization problem under a multi-purchase choice model in which customers choose a bundle of up to one product from each of two product categories. Different bundles have different utilities and the bundle price is the summation of the prices of products in it. For the uncapacitated setting where any set of products can be offered, we prove that this problem is strongly NP-hard. We show that an adjusted-revenue-ordered assortment provides a 1/2-approximation. Furthermore, we develop an approximation framework based on a linear programming relaxation of the problem and obtain a 0.74-approximation algorithm. This approximation ratio almost matches the integrality gap of the linear program, which is proven to be at most 0.75. For the capacitated setting, we prove that there does not exist a constant-factor approximation algorithm assuming the Exponential Time Hypothesis. The same hardness result holds for settings with general bundle prices or more than two categories. Finally, we conduct numerical experiments on randomly generated problem instances. The average approximation ratios of our algorithms are over 99%.

We consider a platform marketplace with both third-party and platform-owned sellers. The platform charges commissions to third-party sellers and buyers for their transactions in the marketplace. Meanwhile, it also directly determines the transaction prices for platform-owned sellers in their sales to buyers. Sellers and buyers are divided into different types with their compatibility captured by a bipartite network. Different types of sellers and buyers are heterogeneous in their cost and utility functions. Given the platform's choices of prices and commissions, third-party sellers/buyers maximize their own payoffs from supplying/demanding products, and market-clearing conditions are satisfied in the networked market. Facing the complexity with non-convex equilibrium constraints in the network, we develop a method of determining the platform's price-commission vector for profit maximization purposes. Based on the characterization of the platform's profit-optimal equilibrium, we investigate three other aspects of the revenue management problem. First, under fairness consideration between the platform and its market participants, we develop an efficient approximation algorithm to obtain a price-commission vector such that an allocation of surplus with a fairness level between the platform and its market participants is guaranteed in the equilibrium trades. Next, we shed light on how the platform should determine the optimal mixture of third-party sellers and platform-owned ones in the networked market. Lastly, we establish how the platform's profit-optimal price-commission decision depends on the network structure and demonstrate the impact of network structure on the platform's optimal profit.

This paper considers integrated information-sharing and financing services for a retail platform on which sellers sell products. Online marketplaces such as Amazon and Tmall have been expanding services to boost the growth of their ecosystems. One is information service on sharing privately gathered massive consumer data that is not available to their sellers, and the other is financing service, e.g., Amazon Lending and Ant Financial, aiming to provide accessible and cheap financial support for small and medium sized sellers. We develop a game-theoretical model to examine the impacts of financing on the platform’s information-sharing strategy when sellers are financially constrained. The platform charges a commission fee for each transaction and determines how to share the privately observed demand information which may be contingent on seller’s financing choice. The platform and bank then simultaneously set the loan interest rates, followed by the seller’s selection of loan provider and production quantity. We characterize the equilibrium finance-operations and the optimal information-sharing strategy for the platform. We find that although the seller selects loan provider based on relative financing cost under exogenously given interest rates, she always selects the platform financing under equilibrium. The platform should always share information, but may make it contingent on his financing service which causes double-marginalization in the capital market and hurts supply chain efficiency. We show that such inefficiency could be resolved by charging a fixed-payment for the information-sharing service which leads to a ‘win-win’ outcome. We also examine the impacts of the capital market composition and extend these analytical results and managerial insights to general settings to ensure the robustness. Our findings could provide useful guidance for platform practitioners to design integrated services on the financing and information provision.

This paper studies a simultaneous-search problem in which a player observes the outcomes sequentially, and must pay reservation fees to maintain eligibility for recalling the earlier offers. We use postgraduate program applications to illustrate the key ingredients of this family of problems. We develop a parsimonious model with two categories of schools: reach schools, which the player feels very happy upon joining, but the chance of getting into one is low; and safety schools, which are a safer choice but not as exciting. The player first decides on the application portfolio, and then the outcomes from the schools applied to arrive randomly over time. We start with the extreme case wherein the safety schools always admit the player. We show that it suffices to focus on the last safety school, which allows us to conveniently represent the player's value function by a product form of the probability of entering the last safety period and the expected payoff from then on.

We show that the player's payoff after applications is increasing and discrete concave in the number of safety schools. We also develop a recursive dynamic programming algorithm when admissions to safety schools are no longer guaranteed. We demonstrate instances in which the player applies to more safety schools when either the reservation fee gets higher or the admission probability drops lower, and articulate how these arise from the portfolio optimization consideration. This has strong managerial implications for service providers in devising their reservation fees and admission rates, especially for institutions that are not universally favored by prospective applicants.

Keywords: simultaneous search, dynamic programming, stochastic models, reservation fees

In many practical settings, learning algorithms can take a substantial amount of time to converge, thereby raising the need to understand the role of discounting in learning. We illustrate the impact of discounting on the performance of learning algorithms by examining two classic and representative
dynamic-pricing and learning problems studied in Broder and Rusmevichientong (2012) [BR] and Keskin and Zeevi (2014) [KZ]. In both settings, a seller sells a product with unlimited inventory over T periods. The seller initially does not know the parameters of the general choice model in BR (resp., the linear demand curve in KZ). Given a discount factor ρ, the retailer's objective is to determine a pricing policy to maximize the expected discounted revenue over T periods. In both settings, we establish lower bounds on the regret under any policy and show limiting bounds of Ω(√(1/(1-ρ))) and Ω(√T) when T → ∞ and ρ → 1, respectively. In the model of BR with discounting, we propose an asymptotically tight learning policy and show that the regret under our policy as well that under the MLE-CYCLE policy in BR is O(√(1/(1-ρ))) (resp., O(√T)) when T → ∞ (resp., ρ → 1). In the model of KZ with discounting, we present sufficient conditions for a learning policy to guarantee asymptotic optimality, and show that the regret under any policy satisfying these conditions is O(log(1/(1-ρ))√(1/(1-ρ))) (resp., O(log⁡T √T)) when T → ∞ (resp., ρ → 1). We show that three different policies - namely, the two variants of the greedy Iterated-Least-Squares policy in KZ and a different policy that we propose - achieve this upper bound on the regret. We numerically examine the behavior of the regret under our policies as well as those in BR and KZ in the presence of discounting. We also analyze a setting in which the discount factor per period is a function of the number of decision periods in the planning horizon.

We consider service competition between two platforms, who are assumed to be farsighted, i.e., they consider the chains of reactions following their initial deviation. We first investigate the one- sided competition where the supply-side capacities of two platforms are fixed and then proceed to the two-sided competition where the two platforms are competing on both the supply and demand sides. We aim to derive farsightedly stable outcomes referred as the von Neumann-Morgenstern farsighted stable set (vNM FSS), a problem boiling down to finding the Pareto efficient strategies which indirectly dominate other strategies. To that end, we construct auxiliary decision problems for each platform where they make price decisions for the customers and wage decisions for the workers, subject to a subgame workers-customers equilibrium. We obtain each platform’s price and wage decisions by analyzing the Karush-Kuhn-Tucker conditions. We show that, in sharp contrast to the “winner-take-all” outcome predicted by the Nash equilibrium (myopic) solution concept, both platforms can survive competition under the farsightedly stable outcomes. We also find that, in contrast to the myopic solution which may leave either customers or workers a positive surplus, farsightedness behaviour of platforms fully extracts the surplus from both customers and workers. Our analysis reveals that, in the one-sided competition, myopic stable outcome (i.e., Nash equilibrium) is consistent with the farsighted stable outcome in most of cases. However, in the two-sided competition, they are totally different. We also demonstrate that even though platforms are farsighted, the stable outcome cannot yield the monopolistic profit for the two platforms.