Kostas Bimpikis

Optimal Pricing in Networks with Externalities

We study the optimal pricing strategies of a monopolist selling a divisible good (service) to consumers who are embedded in a social network. A key feature of our model is that consumers experience a (positive) local network effect. In particular, each consumers usage level depends directly on the usage of her neighbors in the social network structure. Thus, the monopolists optimal pricing strategy may involve offering discounts to certain agents who have a central position in the underlying network. Our results can be summarized as follows. First, we consider a setting where the monopolist can offer individualized prices and derive a characterization of the optimal price for each consumer as a function of her network position. In particular, we show that it is optimal for the monopolist to charge each agent a price that consists of three components: (i) a nominal term that is independent of the network structure, (ii) a discount term proportional to the influence that this agent exerts over the rest of the social network (quantified by the agents Bonacich centrality), and (iii) a markup term proportional to the influence that the network exerts on the agent. In the second part of the paper, we discuss the optimal strategy of a monopolist who can only choose a single uniform price for the good and derive an algorithm polynomial in the number of agents to compute such a price. Third, we assume that the monopolist can offer the good in two prices, full and discounted, and we study the problem of determining which set of consumers should be given the discount. We show that the problem is NP-hard; however, we provide an explicit characterization of the set of agents who should be offered the discounted price. Next, we describe an approximation algorithm for finding the optimal set of agents. We show that if the profit is nonnegative under any feasible price allocation, the algorithm guarantees at least 88% of the optimal profit. Finally, we highlight the value of network information by comparing the profits of a monopolist who does not take into account the network effects when choosing her pricing policy to those of a monopolist who uses this information optimally.

Optimal pricing in the presence of local network effects

We study the optimal pricing strategies of a monopolist selling a divisible good (service) to consumers that are embedded in a social network. A key feature of our model is that consumers experience a (positive) local network effect. In particular, each consumers usage level depends directly on the usage of her neighbors in the social network structure. Thus, the monopolists optimal pricing strategy may involve offering discounts to certain agents1, who have a central position in the underlying network. Our results can be summarized as follows. First, we consider a setting where the monopolist can offer individualized prices and derive an explicit characterization of the optimal price for each consumer as a function of her network position. In particular, we show that it is optimal for the monopolist to charge each agent a price that is proportional to her Bonacich centrality in the social network. In the second part of the paper, we discuss the optimal strategy of a monopolist that can only choose a single uniform price for the good and derive an algorithm polynomial in the number of agents to compute such a price. Thirdly, we assume that the monopolist can offer the good in two prices, full and discounted, and study the problem of determining which set of consumers should be given the discount. We show that the problem is NP-hard, however we provide an explicit characterization of the set of agents that should be offered the discounted price. Finally, we describe an approximation algorithm for finding the optimal set of agents. We show that if the profit is nonnegative under any feasible price allocation, the algorithm guarantees at least 88 % of the optimal profit.

Competitive Targeted Advertising Over Networks

Recent advances in information technology have allowed firms to gather vast amounts of data regarding consumers’ preferences and the structure and intensity of their social interactions. This paper examines a game-theoretic model of competition between firms that can target their marketing budgets to individuals embedded in a social network. We provide a sharp characterization of the optimal targeted advertising strategies and highlight their dependence on the underlying social network structure. Furthermore, we provide conditions under which it is optimal for the firms to asymmetrically target a subset of the individuals and establish a lower bound on the ratio of their payoffs in these asymmetric equilibria. Finally, we find that at equilibrium firms invest inefficiently high in targeted advertising and the extent of the inefficiency is increasing in the centralities of the agents they target. Taken together, these findings shed light on the effect of the network structure on the outcome of marketing competition between the firms.

Designing Dynamic Contests

Innovation contests have emerged as a viable alternative to the standard research and development process. They are particularly suited for settings that feature a high degree of uncertainty regarding the actual feasibility of the end goal. The objective of the contest designer is to maximize the probability of reaching the innovation goal while minimizing the time it takes to complete the project. Obviously here the important question is how to best design these contests. This paper departs from prior literature through three key modeling features. First, in our model, an agents progress towards the goal is not a deterministic function of effort. As is typically the case in real-world settings, progress is positively correlated with effort but the mapping involves a stochastic component. Secondly and quite importantly, it is possible that the innovation in question is not attainable, either because the goal is actually infeasible or because it requires too much effort and resources that it makes little economic sense to pursue. We model such a scenario by having an underlying state of the world (whether the innovation is attainable or not) over which participants have some prior belief. Taken together, these two features imply that an agents lack of progress may be attributed to either an undesirable underlying state (the innovation is not attainable) or simply to the fact that the agent was unlucky in how her effort was stochastically mapped to progress. Thirdly, we consider a dynamic framework that captures how competition between agents evolves over time and incorporates the fact that agents learn from each others partial progress to discern the underlying reason for their own lack of progress. In particular, our modeling setup includes well-defined intermediate milestones that constitute partial progress towards the end goal.

Inventory Pooling Under Heavy-Tailed Demand

Risk pooling has been studied extensively in the operations management literature as the basic driver behind strategies such as transshipment, manufacturing flexibility, component commonality, and drop shipping. This paper explores the benefit of risk pooling in the context of inventory management using the canonical model first studied in Eppen [Eppen GD (1979) Effects of centralization on expected costs in a multi-location newsboy problem. Management Sci. 25(5):498–501]. Specifically, we consider a single-period, multilocation newsvendor model, where n different locations face independent and identically distributed demands and linear holding and backorder costs. We show that Eppen’s celebrated result, i.e., that the expected cost savings from centralized inventory management scale with the square root of the number of locations, depends critically on the “light-tailed” nature of the demand uncertainty. In particular, we establish that the benefit from pooling relative to the decentralized case, in term...

Dynamic Learning of Patient Response Types: An Application to Treating Chronic Diseases

Currently available medication for treating many chronic diseases is often effective only for a subgroup of patients, and biomarkers accurately assessing whether an individual belongs to this subgroup typically do not exist. In such settings, physicians learn about the effectiveness of a drug primarily through experimentation, i.e., by initiating treatment and monitoring the patients response. Precise guidelines for discontinuing treatment are often lacking or left entirely to the physicians discretion. We introduce a framework for developing adaptive, personalized treatments for such chronic diseases. Our model is based on a continuous-time, multi-armed bandit setting where drug effectiveness is assessed by aggregating information from several channels: by continuously monitoring the state of the patient, but also by (not) observing the occurrence of particular infrequent health events, such as relapses or disease flare-ups. Recognizing that the timing and severity of such events provides critical information for treatment decisions is a key point of departure in our framework compared with typical (bandit) models used in healthcare. We show that the model can be analyzed in closed form for several settings of interest, resulting in optimal policies that are intuitive and may have practical appeal. We illustrate the effectiveness of the methodology by developing a set of efficient treatment policies for multiple sclerosis, which we then use to benchmark several existing treatment guidelines.

Optimal pricing in social networks

We consider the pricing strategies of a monopolist selling a divisible good (service) to consumers who are embedded in a social network. We assume that each consumers usage level depends directly on the usage of her neighbors in the social network, and investigate the optimal pricing policies of the monopolist. We show that if the monopolist can perfectly price discriminate the agents, then the price offered to each agent has three components: a nominal price, a discount term due to the agents influence on her neighbors, and a markup term due to the influence of her neighbors on the agent. We also characterize the optimal pricing strategies in settings where the monopolist is constrained to offering a single price, and where she can choose two distinct prices (a discounted and a full price). For the former setting we provide a polynomial time algorithm for the solution of the pricing problem. On the other hand, we show that in the latter setting the optimal pricing problem is NP-hard, and we provide an approximation algorithm, which, under some conditions, achieves at least 88% of the maximum profit.

Multisourcing and Miscoordination in Supply Chain Networks

This paper studies sourcing decisions of firms in a multitier supply chain when procurement is subject to disruption risk. We argue that features of the production process that are commonly encountered in practice (including differential production technologies and financial constraints) may result in the formation of inefficient supply chains, owing to the misalignment of the sourcing incentives of firms at different tiers. We provide a characterization of the conditions under which upstream suppliers adopt sourcing strategies that are suboptimal from the perspective of firms further downstream. Our analysis highlights that a focus on optimizing procurement decisions in each tier of the supply chain in isolation may not be sufficient for mitigating risks at an aggregate level. Rather, we argue that a holistic view of the entire supply network is necessary to properly assess and secure against disruptive events. Importantly, the misalignment we identify does not originate from cost or reliability asymmetr...

Learning and Hierarchies in Service Systems

Motivated by diverse application areas such as healthcare, call centers, and crowdsourcing, we consider the design and operation of service systems that process tasks with types that are ex ante unknown, and employ servers with different skill sets. Our benchmark model involves two types of tasks, Easy and Hard, and servers that are either Junior or Senior in their abilities. The service provider determines a resource allocation policy, i.e., how to assign tasks to servers over time, with the goal of maximizing the system’s long-term throughput. Information about a task’s type can only be obtained while serving it. In particular, the more time a Junior server spends on a task without service completion, the higher her belief that the task is Hard and thus needs to be rerouted to a Senior server. This interplay between service time and task-type uncertainty implies that the system’s resource allocation policy and staffing levels implicitly determine how the provider prioritizes between learning and actuall...