Reetabrata Mookherjee

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

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.

Formulating and Solving Service Network Pricing and Resource Allocation Games as Differential Variational Inequalities

In this chapter we show how certain noncooperative Cournot-Nash dynamic games arising in service pricing and resource allocation may be articulated as differential variational inequalities. We show how such problems may be solved using a fixed point algorithm having continuous time optimal control subproblems.

Modeling Large Scale and Complex Infrastructure Systems as Computable Games

Infrastructure systems for generalized transportation – such as goods, passengers and water – take the form of networks. These networks typically have interdependencies which are not addressed in engineering practice. In order to make efficient policy regarding an infrastructure system, the impacts of that policy on other interdependent infrastructure systems must be understood. The combination of the different layers of the interconnected infrastructure network may be thought of as a system of systems representing the grand infrastructure system. Users of the system of systems may be thought of as agents competing for the limited capacities of the network layers. Dynamic game theory is a natural method for modeling systems of systems in an effort to make better infrastructure decisions. However, to be of use, these models must be computable and thus some different solution techniques for general equilibrium models are discussed.