We consider a monopolist who sells a set of products over a time horizon of T periods. The seller initially does not know the parameters of the products' linear demand curve, but can estimate them based on demand observations. We first assume that the seller knows nothing about the parameters of the demand curve, and then consider the case where the seller knows the expected demand under an incumbent price. It is shown that the smallest achievable revenue loss in T periods, relative to a clairvoyant who knows the underlying demand model, is of order √ T in the former case and of order log T in the latter case. To derive pricing policies that are practically implementable, we take as our point of departure the widely used policy called greedy iterated least squares (ILS), which combines sequential estimation and myopic price optimization. It is known that the greedy ILS policy itself suffers from incomplete learning, but we show that certain variants of greedy ILS achieve the minimum asymptotic loss rate. To highlight the essential features of well-performing pricing policies, we derive sufficient conditions for asymptotic optimality.

Motivated by applications in financial services, we consider a seller who offers prices sequentially to a stream of potential customers, observing either success or failure in each sales attempt. The parameters of the underlying demand model are initially unknown, so each price decision involves a trade-off between learning and earning. Attention is restricted to the simplest kind of model uncertainty, where one of two demand models is known to apply, and we focus initially on performance of the myopic Bayesian policy (MBP), variants of which are commonly used in practice. Because learning is passive under the MBP (that is, learning only takes place as a by-product of actions that have a different purpose), it can lead to incomplete learning and poor profit performance. However, under one additional assumption, a constrained variant of the myopic policy is shown to have the following strong theoretical virtue: the expected performance gap relative to a clairvoyant who knows the underlying demand model is bounded by a constant as the number of sales attempts becomes large. This paper was accepted by Gérard P. Cachon, stochastic models and simulation.

We consider a seller who can dynamically adjust the price of a product at the individual customer level, by utilizing information about customers’ characteristics encoded as a d-dimensional feature vector. We assume a personalized demand model, parameters of which depend on s out of the d features. The seller initially does not know the relationship between the customer features and the product demand but learns this through sales observations over a selling horizon of T periods. We prove that the seller’s expected regret, that is, the revenue loss against a clairvoyant who knows the underlying demand relationship, is at least of order [Formula: see text] under any admissible policy. We then design a near-optimal pricing policy for a semiclairvoyant seller (who knows which s of the d features are in the demand model) who achieves an expected regret of order [Formula: see text]. We extend this policy to a more realistic setting, where the seller does not know the true demand predictors, and show that this policy has an expected regret of order [Formula: see text], which is also near-optimal. Finally, we test our theory on simulated data and on a data set from an online auto loan company in the United States. On both data sets, our experimentation-based pricing policy is superior to intuitive and/or widely-practiced customized pricing methods, such as myopic pricing and segment-then-optimize policies. Furthermore, our policy improves upon the loan company’s historical pricing decisions by 47% in expected revenue over a six-month period. This paper was accepted by Noah Gans, stochastic models and simulation.

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Problem definition: This paper explores the impact of competition between platforms in the sharing economy. Examples include the cases of Uber and Lyft in the context of ride-sharing platforms. In particular, we consider competition between two platforms that offer a common service (e.g., rides) through a set of independent service providers (e.g., drivers) to a market of customers. Each platform sets a price that is charged to customers for obtaining the service provided by a driver. A portion of that price is paid to the driver who delivers the service. Both customers’ and drivers’ utilities are sensitive to the payment terms set by the platform and are also sensitive to congestion in the system (given by the relative number of customers and drivers in the market). We consider two possible settings. The first one, termed “single-homing,” assumes that drivers work through a single platform. In the second setting, termed “multihoming” (or “multiapping,” as it is known in practice), drivers deliver their service through both platforms. Academic/practical relevance: This is one of the first papers to study competition and multihoming in the presence of congestion effects typically observed in the sharing economy. We leverage the model to study some practical questions that have received significant press attention (and stirred some controversies) in the ride-sharing industry. The first involves the issue of surge pricing. The second involves the increasingly common practice of drivers choosing to operate on multiple platforms (multihoming). Methodology: We formulate our problem as a pricing game between two platforms and employ the concept of a Nash equilibrium to analyze equilibrium outcomes in various settings. Results: In both the single-homing and multihoming settings, we study the equilibrium prices that emerge from the competitive interaction between the platforms and explore the supply and demand outcomes that can arise at equilibrium. We build on these equilibrium results to study the impact of surge pricing in response to a surge in demand and to examine the incentives at play when drivers engage in multihoming. Managerial implications: We find that raising prices in response to a surge in demand makes drivers and customers better off than if platforms were constrained to charge the same prices that would arise under normal demand levels. We also compare drivers’ and customers’ performance when all drivers either single-home or multihome. We find that although individual drivers may have an incentive to multihome, all players are worse off when all drivers multihome. We conclude by proposing an incentive mechanism to discourage multihoming.