A Game-based Model for Pricing and Timetabling in Liberalised Passenger Railway Markets

Abstract

We propose a game-theoretic model for pricing and timetabling in liberalised passenger rail markets under vertical separation. Railway undertakings compete for train paths (on-rail competition) and subsequently set fares facing passenger demand (off-rail competition). Passenger choice is modelled through a nested logit structure. The resulting bi-level equilibrium model determines path bids and ticket prices. A column generation algorithm is developed and validated using data from the Spanish HSR Madrid–Barcelona corridor.