Horizontal cooperation in a multimodal public transport system: The profit allocation problem

Abstract We analyse the situation involving several transport companies in an intermodal public transport system. It is assumed that they cooperate by offering travel cards which can be used on all available means of transport. In order to solve the problem of profit allocation among the companies involved, we first introduce a coloured graph which describes the transport network and then propose a game theoretical approach to share the profit among the companies. Two new allocation rules, called the Coloured Egalitarian Solution and the Coloured Cost Proportional Solution, are introduced and axiomatically characterised. Furthermore, it is shown that both solutions provide stable allocations in the sense that they cannot be improved upon by any coalition of players.

[1]  Alf Kimms,et al.  Revenue management under horizontal and vertical competition within airline alliances , 2016 .

[2]  Joaquín Sánchez-Soriano,et al.  An Integrated Transport System for Alacant's Students. UNIVERCITY , 2002, Ann. Oper. Res..

[3]  Jeroen Kuipers,et al.  Sharing costs in highways: A game theoretic approach , 2013, Eur. J. Oper. Res..

[4]  Joaquín Sánchez-Soriano,et al.  Pairwise solutions and the core of transportation situations , 2006, Eur. J. Oper. Res..

[5]  Sylvain Béal,et al.  Règles d'allocation pour les programmes de pass culturel , 2010 .

[6]  Joaquín Sánchez-Soriano,et al.  The pairwise egalitarian solution , 2003, Eur. J. Oper. Res..

[7]  Andrea Lodi,et al.  Design and Control of Public-Service Contracts and an Application to Public Transportation Systems , 2013 .

[8]  G. Owen,et al.  A Simple Expression for the Shapley Value in a Special Case , 1973 .

[9]  Vito Fragnelli,et al.  Balancedness of infrastructure cost games , 2002, Eur. J. Oper. Res..

[10]  Serguei Netessine,et al.  Revenue Management Games: Horizontal and Vertical Competition , 2005, Manag. Sci..

[11]  Peter Sudhölter,et al.  Characterizations of highway toll pricing methods , 2017, Eur. J. Oper. Res..

[12]  Ana S. Camanho,et al.  Estimation of Origin-Destination matrices under Automatic Fare Collection: the case study of Porto transportation system , 2017 .

[13]  Alf Kimms,et al.  Assessing fairness of selfish revenue sharing mechanisms for airline alliances , 2013 .

[14]  Gustavo Bergantiños,et al.  A new rule for source connection problems , 2014, Eur. J. Oper. Res..

[15]  L. Shapley.  Cores of convex games , 1971 .

[16]  Wei Wang,et al.  Bus Passenger Origin-Destination Estimation and Related Analyses , 2011 .

[17]  Otto Anker Nielsen,et al.  Multimodal route choice models of public transport passengers in the Greater Copenhagen Area , 2017, EURO J. Transp. Logist..

[18]  Shing Chung Josh Wong,et al.  Estimation of origin-destination matrices for a multimodal public transit network , 2010 .

[19]  Vito Fragnelli,et al.  A cost allocation problem in urban solid wastes collection and disposal , 2004, Math. Methods Oper. Res..

[20]  L. Shapley.  A Value for n-person Games , 1988 .

[21]  William Thomson,et al.  Cost allocation and airport problems , 2007 .

[22]  Michael Maschler,et al.  The nucleolus of a standard tree game revisited: a study of its monotonicity and computational properties , 2010, Int. J. Game Theory.

[23]  Vito Fragnelli,et al.  On shortest path games , 2000, Math. Methods Oper. Res..

[24]  Victor Ginsburgh,et al.  The museum pass game and its value , 2003, Games Econ. Behav..

[25]  Xing Hu,et al.  Revenue Sharing in Airline Alliances , 2013, Manag. Sci..

[26]  Leo Kroon,et al.  Capacity, information and minority games in public transport , 2016 .