Modelling competition in demand-based optimization models

This paper discusses some methodological approaches to model competition in a demand-based optimization framework which is particularly suitable for oligopolistic markets. Such approaches allow us to analyze oligopolies from three perspectives: at a customer level, by using discrete choice models to take into account preference heterogeneity and to model individual decisions; at an operator level, by solving a mixed integer linear program that maximizes any relevant objective function; and at a market level, by investigating the concept of Nash equilibrium in the resulting non-cooperative multi-leader-follower game. At the latter level, in order to find equilibrium solutions for this type of problem, we propose an algorithmic approach based on the fixed-point iteration method and a mixed integer linear program that enumerates the pure strategy Nash equilibria of a finite game.