Allocation of Railroad Capacity Under Competition: A Game Theoretic Approach to Track time Pricing

Generalized Nash equilibrium problems

“…But GNEPs have also been employed to model more technical problems that do not fit any of the categories listed above, and it just seems likely that now that the model is winning more and more popularity, many other applications will be uncovered in the near future. It is impossible to list here all relevant references for these applications; we limit ourselves to a few that, in our view, are either particularly interesting or good entry points to the literature (Adida and Perakis 2006a,b;Altman and Wynter 2004;Arrow and Debreu 1954;Başar and Olsder 1989;Bassanini et al 2002;Breton et al 2005;Contreras et al 2004;Ehrenmann 2004;Gabriel et al 2005;Gabriel and Smeers 2006;Harker 1991;Harker and Hong 1994;Haurie and Krawczyk 1997;Hobbs et al 2001;Hobbs and Pang 2007;Jiang 2007;Kesselman et al 2005;Krawczyk 2000Krawczyk , 2007Outrata et al 1998;Pang et al 2007;Puerto et al 2005;Sun and Gao 2007;Tidball and Zaccour 2005;Wei and Smeers 1999;Zhou et al2005). …”

Generalized Nash Equilibrium Problems

“…But GNEPs have also been employed to model more technical problems that do not fit any of the categories listed above, and it just seems likely that now that the model is winning more and more popularity, many other applications will be uncovered in the near future. It is impossible to list here all relevant references for these applications; we limit ourselves to a few that, in our view, are either particularly interesting or good entry points to the literature Perakis 2006a, 2006b;Altman and Wynter 2004;Arrow and Debreu 1954;Başar and Olsder 1989;Bassanini et al 2002;Breton et al 2005;Contreras et al 2004;Ehrenmann 2004;Gabriel et al 2005;Gabriel and Smeers 2006;Harker 1991;Harker and Hong 1994;Haurie and Krawczyk 1997;Hobbs et al 2001;Hobbs and Pang 2007;Jiang 2007;Kesselman et al 2005;Krawczyk 2000Krawczyk , 2007Outrata et al 1998;Pang et al 2008;Pang et al 2009;Puerto et al 2005;Scutari et al 2009;Sun and Gao 2007;Tidball and Zaccour 2005;Wei and Smeers 1999;Zhou et al 2005). We finally mention that the very recent reference ) presents a rather comprehensive and sophisticated treatment of the GNEP based on a variational inequality approach that allows to establish some interesting new results.…”

The effect of train formation length and service frequency on the determination of train schedules

“…11 proposed a method for optimizing the schedule on the basis of the behaviour of passengers in choosing which train to board. At the same time, many studies 4,9–10,13,14 have verified the influence of demand flexibility and ticket price on train schedules.…”