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Non-additive network pricing with non-cooperative mobility service providers

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  • Huang, Wentao
  • Jian, Sisi
  • Rey, David

Abstract

This study addresses a mobility network pricing problem in a competitive environment. We consider a multimodal 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 ridership in a target mobility network by providing non-additive, path-based subsidies to travelers. We model paths’ attractiveness using generalized cost functions that combine path travel time and path cost, and we use linear elastic travel demand functions to capture the proportion of demand served by a path. MSPs are non-cooperative and adjust link fares according to the subsidy policy implemented by the regulator. The goal of the network regulator is to solve a budget-constrained mobility network pricing problem under MSP competition. This game-theoretical framework is modeled as a single-leader multi-follower game (SLMFG) wherein the leader player represents the network regulator and multiple follower players represent the MSPs. We conduct a theoretical analysis of this SLMFG by identifying necessary and sufficient conditions for the existence of solutions to 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. Numerical results reveal the impact of MSP competition in this mobility network pricing problem and shed novel insights into the design of optimal path-based subsidy policies.

Suggested Citation

  • Huang, Wentao & Jian, Sisi & Rey, David, 2024. "Non-additive network pricing with non-cooperative mobility service providers," European Journal of Operational Research, Elsevier, vol. 318(3), pages 802-824.
    • Handle: RePEc:eee:ejores:v:318:y:2024:i:3:p:802-824
    DOI: 10.1016/j.ejor.2024.05.042
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    References listed on IDEAS

    as
    1. Christine Tawfik & Sabine Limbourg, 2019. "A Bilevel Model for Network Design and Pricing Based on a Level-of-Service Assessment," Transportation Science, INFORMS, vol. 53(6), pages 1609-1626, November.
    2. Martine Labbé & Patrice Marcotte & Gilles Savard, 1998. "A Bilevel Model of Taxation and Its Application to Optimal Highway Pricing," Management Science, INFORMS, vol. 44(12-Part-1), pages 1608-1622, December.
    3. Ramesh Johari & Gabriel Y. Weintraub & Benjamin Van Roy, 2010. "Investment and Market Structure in Industries with Congestion," Operations Research, INFORMS, vol. 58(5), pages 1303-1317, October.
    4. Economides, Nicholas & Salop, Steven C, 1992. "Competition and Integration among Complements, and Network Market Structure," Journal of Industrial Economics, Wiley Blackwell, vol. 40(1), pages 105-123, March.
    5. Sisi Jian & David Rey & Vinayak Dixit, 2019. "An Integrated Supply-Demand Approach to Solving Optimal Relocations in Station-Based Carsharing Systems," Networks and Spatial Economics, Springer, vol. 19(2), pages 611-632, June.
    6. Qian, Xinwu & Ukkusuri, Satish V., 2017. "Taxi market equilibrium with third-party hailing service," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 43-63.
    7. Ren-Yong Guo & Hai-Jun Huang & Hai Yang, 2019. "Tradable Credit Scheme for Control of Evolutionary Traffic Flows to System Optimum: Model and its Convergence," Networks and Spatial Economics, Springer, vol. 19(3), pages 833-868, September.
    8. Szeto, W.Y. & Wu, Yongzhong, 2011. "A simultaneous bus route design and frequency setting problem for Tin Shui Wai, Hong Kong," European Journal of Operational Research, Elsevier, vol. 209(2), pages 141-155, March.
    9. Zhang, Kenan & Nie, Yu (Marco), 2021. "Inter-platform competition in a regulated ride-hail market with pooling," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 151(C).
    10. Jorge, Diana & Molnar, Goran & de Almeida Correia, Gonçalo Homem, 2015. "Trip pricing of one-way station-based carsharing networks with zone and time of day price variations," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 461-482.
    11. Zhou, Yaqian & Yang, Hai & Ke, Jintao & Wang, Hai & Li, Xinwei, 2022. "Competition and third-party platform-integration in ride-sourcing markets," Transportation Research Part B: Methodological, Elsevier, vol. 159(C), pages 76-103.
    12. Szeto, W.Y. & Jiang, Y., 2014. "Transit route and frequency design: Bi-level modeling and hybrid artificial bee colony algorithm approach," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 235-263.
    13. Farahani, Reza Zanjirani & Miandoabchi, Elnaz & Szeto, W.Y. & Rashidi, Hannaneh, 2013. "A review of urban transportation network design problems," European Journal of Operational Research, Elsevier, vol. 229(2), pages 281-302.
    14. Borger Bruno De & Dunkerley Fay & Proost Stef, 2008. "The Interaction between Tolls and Capacity Investment in Serial and Parallel Transport Networks," Review of Network Economics, De Gruyter, vol. 7(1), pages 1-23, March.
    15. Long, Jiancheng & Szeto, W.Y. & Huang, Hai-Jun, 2014. "A bi-objective turning restriction design problem in urban road networks," European Journal of Operational Research, Elsevier, vol. 237(2), pages 426-439.
    16. Ke, Jintao & Yang, Hai & Li, Xinwei & Wang, Hai & Ye, Jieping, 2020. "Pricing and equilibrium in on-demand ride-pooling markets," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 411-431.
    17. Aussel, Didier & Brotcorne, Luce & Lepaul, Sébastien & von Niederhäusern, Léonard, 2020. "A trilevel model for best response in energy demand-side management," European Journal of Operational Research, Elsevier, vol. 281(2), pages 299-315.
    18. Ding, Xiaoshu & Qi, Qi & Jian, Sisi & Yang, Hai, 2023. "Mechanism design for Mobility-as-a-Service platform considering travelers’ strategic behavior and multidimensional requirements," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 1-30.
    19. Álvarez-SanJaime, Óscar & Cantos-Sanchez, Pedro & Moner-Colonques, Rafael & Sempere-Monerris, Jose J., 2020. "Pricing and infrastructure fees in shaping cooperation in a model of high-speed rail and airline competition," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 22-41.
    20. Luan, Mingye & Waller, S.Travis & Rey, David, 2023. "A non-additive path-based reward credit scheme for traffic congestion management," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    21. Xu, Min & Meng, Qiang & Liu, Zhiyuan, 2018. "Electric vehicle fleet size and trip pricing for one-way carsharing services considering vehicle relocation and personnel assignment," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 60-82.
    22. Li, Sen & Yang, Hai & Poolla, Kameshwar & Varaiya, Pravin, 2021. "Spatial pricing in ride-sourcing markets under a congestion charge," Transportation Research Part B: Methodological, Elsevier, vol. 152(C), pages 18-45.
    23. 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.
    24. Didier Aussel & Anton Svensson, 2020. "A Short State of the Art on Multi-Leader-Follower Games," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 53-76, Springer.
    25. Daron Acemoglu & Asuman Ozdaglar, 2007. "Competition and Efficiency in Congested Markets," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 1-31, February.
    26. Asadabadi, Ali & Miller-Hooks, Elise, 2018. "Co-opetition in enhancing global port network resiliency: A multi-leader, common-follower game theoretic approach," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 281-298.
    27. Zheng, Yu & Zhang, Xiaoning & Liang, Zhe, 2020. "Multimodal subsidy design for network capacity flexibility optimization," Transportation Research Part A: Policy and Practice, Elsevier, vol. 140(C), pages 16-35.
    28. van der Weijde, Adriaan Hendrik & Verhoef, Erik T. & van den Berg, Vincent A.C., 2013. "Competition in multi-modal transport networks: A dynamic approach," Transportation Research Part B: Methodological, Elsevier, vol. 53(C), pages 31-44.
    29. Mohammad Tamannaei & Hamid Zarei & Sajede Aminzadegan, 2021. "A Game-Theoretic Approach to the Freight Transportation Pricing Problem in the Presence of Intermodal Service Providers in a Competitive Market," Networks and Spatial Economics, Springer, vol. 21(1), pages 123-173, March.
    30. Cai, Zeen & Mo, Dong & Tang, Wei & Chen, Yong & Chen, Xiqun (Michael), 2023. "A two-period game-theoretical model for heterogeneous ride-sourcing platforms with asymmetric competition and mixed fleets," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 178(C).
    31. Correa, José & Hoeksma, Ruben & Schröder, Marc, 2019. "Network congestion games are robust to variable demand," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 69-78.
    32. Aimé Kamgaing Kuiteingf & Patrice Marcotte & Gilles Savard, 2017. "Network Pricing of Congestion-Free Networks: The Elastic and Linear Demand Case," Transportation Science, INFORMS, vol. 51(3), pages 791-806, August.
    33. Theodoros P. Pantelidis & Joseph Y. J. Chow & Saeid Rasulkhani, 2019. "A many-to-many assignment game and stable outcome algorithm to evaluate collaborative Mobility-as-a-Service platforms," Papers 1911.04435, arXiv.org, revised Jun 2020.
    34. Yang, Hai & Fung, C.S. & Wong, K.I. & Wong, S.C., 2010. "Nonlinear pricing of taxi services," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(5), pages 337-348, June.
    35. Deng, Yuntian & Shao, Shiping & Mittal, Archak & Twumasi-Boakye, Richard & Fishelson, James & Gupta, Abhishek & Shroff, Ness B., 2022. "Incentive design and profit sharing in multi-modal transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 1-21.
    36. Bellei, Giuseppe & Gentile, Guido & Papola, Natale, 2002. "Network pricing optimization in multi-user and multimodal context with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 36(9), pages 779-798, November.
    37. Zhu, Zheng & Xu, Ailing & He, Qiao-Chu & Yang, Hai, 2021. "Competition between the transportation network company and the government with subsidies to public transit riders," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    38. Harks, Tobias & Schröder, Marc & Vermeulen, Dries, 2019. "Toll caps in privatized road networks," European Journal of Operational Research, Elsevier, vol. 276(3), pages 947-956.
    39. Bin Yu & Liu Zhang & Feng Guan & Zixuan Peng & Baozhen Yao, 2017. "Equity based congestion pricing: considering the constraint of alternative path," Operational Research, Springer, vol. 17(1), pages 313-337, April.
    40. Ke, Jintao & Zhu, Zheng & Yang, Hai & He, Qiaochu, 2021. "Equilibrium analyses and operational designs of a coupled market with substitutive and complementary ride-sourcing services to public transits," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 148(C).
    41. Wu, Di & Yin, Yafeng & Lawphongpanich, Siriphong, 2011. "Pareto-improving congestion pricing on multimodal transportation networks," European Journal of Operational Research, Elsevier, vol. 210(3), pages 660-669, May.
    42. Han, Deren & Lo, Hong K., 2004. "Solving non-additive traffic assignment problems: A descent method for co-coercive variational inequalities," European Journal of Operational Research, Elsevier, vol. 159(3), pages 529-544, December.
    43. Szeto, W.Y. & Wu, Yongzhong & Ho, Sin C., 2011. "An artificial bee colony algorithm for the capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 215(1), pages 126-135, November.
    44. Rasulkhani, Saeid & Chow, Joseph Y.J., 2019. "Route-cost-assignment with joint user and operator behavior as a many-to-one stable matching assignment game," Transportation Research Part B: Methodological, Elsevier, vol. 124(C), pages 60-81.
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