Optimal monopoly pricing with congestion and random utility via partial mass transport

Guillaume Carlier (1) , Lina Mallozzi (2)

1 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
2 Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”

We consider a bilevel optimization framework corresponding to a monopoly spatial pricing problem: the price for a set of given facilities maximizes the profit (upper level problem) taking into account that the demand is determined by consumers' cost minimization (lower level problem). In our model, both transportation costs and congestion costs are considered, and the lower level problem is solved via partial transport mass theory. The partial transport aspect of the problem comes from the fact that each consumer has the possibility to remain out of the market. We also generalize the model and our variational analysis to the stochastic case where utility involves a random term.

Mots clés: monopoly spatial pricing; partial optimal mass transport; congestion; random utility

Domaines: Optimisation et contrôle [math.OC]

Guillaume Carlier, Lina Mallozzi. Optimal monopoly pricing with congestion and random utility via partial mass transport. Journal of Mathematical Analysis and Applications, 2018. ⟨hal-01420707⟩