Mikhail Nediak

Dynamic Pricing in the Presence of Strategic Consumers and Oligopolistic Competition

We present a dynamic pricing model for oligopolistic firms selling differentiated perishable goods to multiple finite segments of strategic consumers who are aware that pricing is dynamic and may time their purchases accordingly. This model encompasses strategic behavior by both firms and consumers in a unified stochastic dynamic game in which each firms objective is to maximize its total expected revenues, and each consumer responds according to a shopping-intensity-allocation consumer choice model. We prove the existence of a unique subgame-perfect equilibrium, provide equilibrium optimality conditions, and prove monotonicity results for special cases. The model provides insights about equilibrium price dynamics under different levels of competition, asymmetry between firms, and multiple market segments with varying properties. We demonstrate that strategic behavior by consumers can have serious impacts on revenues if firms ignore that behavior in their dynamic pricing policies. Moreover, ideal equilibrium responses to consumer strategic behavior can recover only a portion of the lost revenues. A key conclusion is that firms may benefit more from limiting the information available to consumers than from allowing full information and responding to the resulting strategic behavior in an optimal fashion.

The Maximum Box Problem and its Application to Data Analysis

AbstractGiven two finite sets of points X+ and X− in

Risk in Revenue Management and Dynamic Pricing

\mathbb{R}^n

Dynamic Pricing with Online Learning and Strategic Consumers: An Application of the Aggregating Algorithm

n, the maximum box problem consists of finding an interval (“box”) B = {x : l ≤ x ≤ u} such that B ∩ X− = ∅, and the cardinality of B ∩ X+ is maximized. A simple generalization can be obtained by instead maximizing a weighted sum of the elements of B ∩ X+. While polynomial for any fixed n, the maximum box problem is

Cargo Capacity Management with Allotments and Spot Market Demand

{\mathcal{N}}{\mathcal{P}}

A direct Newton method for calculus of variations

-hard in general. We construct an efficient branch-and-bound algorithm for this problem and apply it to a standard problem in data analysis. We test this method on nine data sets, seven of which are drawn from the UCI standard machine learning repository.