Non-cooperative competition among revenue maximizing service providers with demand learning

Abstract

This paper recognizes that in many decision environments in which revenue optimization is attempted, an actual demand curve and its parameters are generally unobservable. Herein we describe the dynamics of demand as a continuous time differential equation based on an evolutionary game theory perspective. We then observe realized sales data to obtain estimates of parameters that govern the evolution of demand; these are refined on a discrete time scale The resulting model takes the form of a differential variational inequality. We present an algorithm based on a gap function for the differential variational inequality and report its numerical performance for an example revenue optimization problem.

Demand Learning and Dynamic Pricing under Competition in a State-Space Framework

“…The random walk assumption in Kwon et al [18] implies that the historical price sensitivities provide no information about its future 5 changes, since it is assumed that the price sensitivity at time t equals to the price sensitivity at time t-1 plus Gaussian noise. Although this assumption provides analytical tractability, it may not be realistic in practice.…”

“…Kwon et al [18] considered dynamic games for demand learning, where the relationship between demand and price was characterized by evolutionary dynamics from the perspective of game theory. In their work, 4 underlying price sensitivities were assumed to follow a random walk.…”

Dynamic pricing and learning: Historical origins, current research, and new directions

“…The authors propose an algorithm to solve the resulting differential variational inequalities, and illustrate their method by a numerical example. Related to the set-up of Kwon et al (2009) is the recent study by Chung et al (2012), who consider a state-space model for dynamic pricing and learning in an oligopoly. They also assume that expected demand depends on the difference between a posted price and a reference price, which is computed as a weighted moving average of historical prices.…”

“…They also consider situations where the selling prices do neither converge to the Nash equilibrum nor to the cooperative solution, and where in addition the limit depends on the initial prices. Kwon et al (2009) formulate a finite-time finite-capacity oligopolistic pricing problem in the language of differential variational inequalities. They consider a demand model where the timederivative of demand is proportional to the difference between a firm's price and a moving average of prices used in the past.…”

Study on pricing strategy of hybrid distribution channels of Cruise Companies

“…So we should make a sensitivity analysis about the variable  . But there are many parameters in two game models, the best choice is to make a numerical analysis [8][9][10].…”