Bortolomiol, S., Lurkin, V., and Bierlaire, M. (2021)

Price-based regulation of oligopolistic markets under discrete choice models of demand

We propose a framework to find optimal price-based policies to regulate markets characterized by oligopolistic competition and in which consumers make a discrete choice among a finite set of alternatives. With this framework, we can include general discrete choice models available in the literature to capture heterogeneous consumer behavior. In our work, consumers are utility maximizers and are modeled according to random utility theory. Suppliers are modeled as profit maximizers, according to the traditional microeconomic treatment. Market competition is modeled as a non-cooperative game, for which an epsilon-equilibrium solution is sought. Finally, the regulator can affect the behavior of all other agents by giving subsidies or imposing taxes to consumers. In transport markets, economic instruments might target specific alternatives, to reduce externalities such as congestion or emissions, or specific segments of the population, to achieve social welfare objectives. In public policy, different agents have different individual or social objectives, possibly conflicting, so value judgements are used to compare monetary and non-monetary objectives. We present a mixed integer optimization model to find optimal policies subject to supplier profit maximization and consumer utility maximization constraints. Then, we propose a model-based heuristic approach based on the fixed-point iteration algorithm that finds epsilon-equilibrium solutions for the market. Numerical experiments on an intercity travel case study show how the regulator can optimize its decisions for different policy instruments and for different objective functions.