IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v275y2019i2p659-665.html
   My bibliography  Save this article

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

Author

Listed:
  • Algaba, Encarnación
  • Fragnelli, Vito
  • Llorca, Natividad
  • Sánchez-Soriano, Joaquin

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.

Suggested Citation

  • Algaba, Encarnación & Fragnelli, Vito & Llorca, Natividad & Sánchez-Soriano, Joaquin, 2019. "Horizontal cooperation in a multimodal public transport system: The profit allocation problem," European Journal of Operational Research, Elsevier, vol. 275(2), pages 659-665.
    • Handle: RePEc:eee:ejores:v:275:y:2019:i:2:p:659-665
    DOI: 10.1016/j.ejor.2018.11.050
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718309913
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.11.050?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Joaquín Sánchez-Soriano & Natividad Llorca & Ana Meca & Elisenda Molina & Manuel Pulido, 2002. "An Integrated Transport System for Alacant's Students. UNIVERCITY," Annals of Operations Research, Springer, vol. 109(1), pages 41-60, January.
    2. Norde, Henk & Fragnelli, Vito & Garcia-Jurado, Ignacio & Patrone, Fioravante & Tijs, Stef, 2002. "Balancedness of infrastructure cost games," European Journal of Operational Research, Elsevier, vol. 136(3), pages 635-654, February.
    3. Serguei Netessine & Robert A. Shumsky, 2005. "Revenue Management Games: Horizontal and Vertical Competition," Management Science, INFORMS, vol. 51(5), pages 813-831, May.
    4. Xing Hu & René Caldentey & Gustavo Vulcano, 2013. "Revenue Sharing in Airline Alliances," Management Science, INFORMS, vol. 59(5), pages 1177-1195, May.
    5. Çetiner, D. & Kimms, A., 2013. "Assessing fairness of selfish revenue sharing mechanisms for airline alliances," Omega, Elsevier, vol. 41(4), pages 641-652.
    6. Demet Çetiner, 2013. "Selfish Revenue Sharing Mechanisms for Airline Alliances," Lecture Notes in Economics and Mathematical Systems, in: Fair Revenue Sharing Mechanisms for Strategic Passenger Airline Alliances, edition 127, chapter 0, pages 111-132, Springer.
    7. Ginsburgh, Victor & Zang, Israel, 2003. "The museum pass game and its value," Games and Economic Behavior, Elsevier, vol. 43(2), pages 322-325, May.
    8. Grauberger, Waldemar & Kimms, Alf, 2016. "Revenue management under horizontal and vertical competition within airline alliances," Omega, Elsevier, vol. 59(PB), pages 228-237.
    9. Bergantiños, G. & Gómez-Rúa, M. & Llorca, N. & Pulido, M. & Sánchez-Soriano, J., 2014. "A new rule for source connection problems," European Journal of Operational Research, Elsevier, vol. 234(3), pages 780-788.
    10. Kuipers, Jeroen & Mosquera, Manuel A. & Zarzuelo, José M., 2013. "Sharing costs in highways: A game theoretic approach," European Journal of Operational Research, Elsevier, vol. 228(1), pages 158-168.
    11. Vito Fragnelli & Ignacio García-Jurado & Luciano Méndez-Naya, 2000. "On shortest path games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 251-264, November.
    12. Vito Fragnelli & Anna Iandolino, 2004. "A cost allocation problem in urban solid wastes collection and disposal," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 447-463, July.
    13. Andrea Lodi & Enrico Malaguti & Nicolás E. Stier-Moses & Tommaso Bonino, 2016. "Design and Control of Public-Service Contracts and an Application to Public Transportation Systems," Management Science, INFORMS, vol. 62(4), pages 1165-1187, April.
    14. Sanchez-Soriano, Joaquin, 2006. "Pairwise solutions and the core of transportation situations," European Journal of Operational Research, Elsevier, vol. 175(1), pages 101-110, November.
    15. Marie Karen Anderson & Otto Anker Nielsen & Carlo Giacomo Prato, 2017. "Multimodal route choice models of public transport passengers in the Greater Copenhagen Area," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 221-245, September.
    16. Sanchez-Soriano, Joaquin, 2003. "The pairwise egalitarian solution," European Journal of Operational Research, Elsevier, vol. 150(1), pages 220-231, October.
    17. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    18. Michael Maschler & Jos Potters & Hans Reijnierse, 2010. "The nucleolus of a standard tree game revisited: a study of its monotonicity and computational properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 89-104, March.
    19. Sudhölter, Peter & Zarzuelo, José M., 2017. "Characterizations of highway toll pricing methods," European Journal of Operational Research, Elsevier, vol. 260(1), pages 161-170.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rick K. Acosta-Vega & Encarnaci'on Algaba & Joaqu'in S'anchez-Soriano, 2022. "On proportionality in multi-issue problems with crossed claims," Papers 2202.09877, arXiv.org.
    2. Wu, Hao & van den Brink, René & Estévez-Fernández, Arantza, 2024. "Highway toll allocation," Transportation Research Part B: Methodological, Elsevier, vol. 180(C).
    3. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2022. "Monotonicity in sharing the revenues from broadcasting sports leagues," European Journal of Operational Research, Elsevier, vol. 297(1), pages 338-346.
    4. Nassim Mrabti & Nadia Hamani & Laurent Delahoche, 2022. "A Comprehensive Literature Review on Sustainable Horizontal Collaboration," Sustainability, MDPI, vol. 14(18), pages 1-38, September.
    5. Heydari, Jafar & Momeni, Behnam, 2021. "Retailers’ coalition and quantity discounts under demand uncertainty," Journal of Retailing and Consumer Services, Elsevier, vol. 61(C).
    6. Schlicher, L. & Dietzenbacher, Bas & Musegaas, Marieke, 2023. "Stable streaming platforms: a cooperative game approach," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
    7. Juan Carlos Gonc{c}alves-Dosantos & Ricardo Mart'inez & Joaqu'in S'anchez-Soriano, 2024. "Measures of relevance to the success of streaming platforms," Papers 2403.08421, arXiv.org.
    8. Jiawei Gui & Qunqi Wu, 2020. "Multiple Utility Analyses for Sustainable Public Transport Planning and Management: Evidence from GPS-Equipped Taxi Data in Haikou," Sustainability, MDPI, vol. 12(19), pages 1-46, September.
    9. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2020. "Allocating extra revenues from broadcasting sports leagues," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 65-73.
    10. G. Bergantiños & Juan D. Moreno-Ternero, 2024. "Anonymity in sharing the revenues from broadcasting sports leagues," Annals of Operations Research, Springer, vol. 336(3), pages 1395-1417, May.
    11. Rick K. Acosta & Encarnación Algaba & Joaquín Sánchez-Soriano, 2022. "Multi-issue bankruptcy problems with crossed claims," Annals of Operations Research, Springer, vol. 318(2), pages 749-772, November.
    12. Algaba, Encarnación & Béal, Sylvain & Fragnelli, Vito & Llorca, Natividad & Sánchez-Soriano, Joaquin, 2019. "Relationship between labeled network games and other cooperative games arising from attributes situations," Economics Letters, Elsevier, vol. 185(C).
    13. Song, Zhuzhu & Tang, Wansheng & Zhao, Ruiqing, 2020. "A simple game theoretical analysis for incentivizing multi-modal transportation in freight supply chains," European Journal of Operational Research, Elsevier, vol. 283(1), pages 152-165.
    14. Acosta-Vega, Rick K. & Algaba, Encarnación & Sánchez-Soriano, Joaquín, 2023. "Design of water quality policies based on proportionality in multi-issue problems with crossed claims," European Journal of Operational Research, Elsevier, vol. 311(2), pages 777-788.
    15. Xiaohui Wu & Ren He & Meiling He, 2021. "Chaos Analysis of Urban Low-Carbon Traffic Based on Game Theory," IJERPH, MDPI, vol. 18(5), pages 1-12, February.
    16. Hao Wu & Rene van den Brink & Arantza Estevez-Fernandez, 2022. "Highway toll allocation," Tinbergen Institute Discussion Papers 22-036/II, Tinbergen Institute.
    17. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2020. "Manipulability in the cost allocation of transport systems," ThE Papers 20/08, Department of Economic Theory and Economic History of the University of Granada..
    18. Liu, Jia-Cai & Sheu, Jiuh-Biing & Li, Deng-Feng & Dai, Yong-Wu, 2021. "Collaborative profit allocation schemes for logistics enterprise coalitions with incomplete information," Omega, Elsevier, vol. 101(C).
    19. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On how to allocate the fixed cost of transport systems," Annals of Operations Research, Springer, vol. 301(1), pages 81-105, June.
    20. Pantelidis, Theodoros P. & Chow, Joseph Y.J. & Rasulkhani, Saeid, 2020. "A many-to-many assignment game and stable outcome algorithm to evaluate collaborative mobility-as-a-service platforms," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 79-100.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On how to allocate the fixed cost of transport systems," Annals of Operations Research, Springer, vol. 301(1), pages 81-105, June.
    2. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2019. "On how to allocate the fixed cost of transport networks," ThE Papers 19/03, Department of Economic Theory and Economic History of the University of Granada..
    3. Grauberger, Waldemar & Kimms, Alf, 2016. "Revenue management under horizontal and vertical competition within airline alliances," Omega, Elsevier, vol. 59(PB), pages 228-237.
    4. W. Grauberger & A. Kimms, 2018. "Computing pure Nash equilibria in network revenue management games," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(2), pages 481-516, March.
    5. Clempner, Julio B., 2020. "Penalizing passenger’s transfer time in computing airlines revenue," Omega, Elsevier, vol. 97(C).
    6. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2020. "Manipulability in the cost allocation of transport systems," ThE Papers 20/08, Department of Economic Theory and Economic History of the University of Granada..
    7. Munich, Léa, 2024. "Schedule situations and their cooperative game theoretic representations," European Journal of Operational Research, Elsevier, vol. 316(2), pages 767-778.
    8. Gustavo Bergantiños & Juan Vidal-Puga, 2021. "A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 73-100, March.
    9. M. Fiestras-Janeiro & Ignacio García-Jurado & Manuel Mosquera, 2011. "Cooperative games and cost allocation problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-22, July.
    10. Léa Munich, 2023. "Schedule Situations and their Cooperative Game Theoretic Representations," Working Papers 2023-08, CRESE.
    11. O. Palancı & S. Z. Alparslan Gök & M. O. Olgun & G.-W. Weber, 2016. "Transportation interval situations and related games," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 119-136, January.
    12. Li, Tingting & Xie, Jinxing & Lu, Shengmin & Tang, Jiafu, 2016. "Duopoly game of callable products in airline revenue management," European Journal of Operational Research, Elsevier, vol. 254(3), pages 925-934.
    13. Rosenthal, Edward C., 2017. "A cooperative game approach to cost allocation in a rapid-transit network," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 64-77.
    14. Luo, Chunlin & Zhou, Xiaoyang & Lev, Benjamin, 2022. "Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management," Omega, Elsevier, vol. 110(C).
    15. Ding, Chengjin & Chen, Xinyuan & Wu, Weiwei & Wei, Wenbin & Xin, Zelin, 2023. "Game-theoretic analysis of the impact of crew overnight hotel cost on airlines’ fleet assignment and crew pairing," Journal of Air Transport Management, Elsevier, vol. 113(C).
    16. Bergantiños, Gustavo & Gómez-Rúa, María & Llorca, Natividad & Pulido, Manuel & Sánchez-Soriano, Joaquín, 2020. "Allocating costs in set covering problems," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1074-1087.
    17. Yuntong Wang, 2016. "Revenue Sharing in Airline Alliance Networks," Working Papers 1605, University of Windsor, Department of Economics.
    18. Mehmet Onur Olgun, 2022. "Collaborative airline revenue sharing game with grey demand data," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(3), pages 861-882, September.
    19. Bergantiños, Gustavo & Martínez, Ricardo, 2014. "Cost allocation in asymmetric trees," European Journal of Operational Research, Elsevier, vol. 237(3), pages 975-987.
    20. M. G. Fiestras-Janeiro & I. García-Jurado & A. Meca & M. A. Mosquera, 2020. "On benefits of cooperation under strategic power," Annals of Operations Research, Springer, vol. 288(1), pages 285-306, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:275:y:2019:i:2:p:659-665. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.