Non-cooperative mobility network pricing: an application of bilevel optimization with generalized Nash equilibrium problems
In: Journée Programmation mathématique non linéaire (axe PMNL du GDR ROD), 2023, Toulouse
Optimization, Transportation
Abstract
This talk explores a mobility network pricing problem in a competitive environment. We consider a transportation network where the links are operated by multiple profit-maximizing, mobility service providers (MSPs). We take the perspective of a network regulator that aims to increase the total flow in a target mobility network by providing non-additive, path-based subsidies to travelers. MSPs are non-cooperative and adjust link fares according to the subsidy policy implemented by the regulator. This sets the basis for a bilevel optimization problem wherein the leader player represents the network regulator and multiple follower players represent the MSPs. This game-theoretical framework is known as a single-leader multi-follower game (SLMFG). We conduct a theoretical analysis of this SLMFG and of the parameterized generalized Nash equilibrium problem (GNEP) that is played amongst MSPs. We show that this GNEP is jointly convex, and we use this property to develop an exact numerical approach to solve the SLMFG based on customized branch-and-bound algorithms.