交通运输系统工程与信息

交通运输系统工程与信息 ›› 2026, Vol. 26 ›› Issue (3): 144-155.DOI: 10.16097/j.cnki.1009-6744.2026.03.014

• 综合交通运输体系 • 上一篇    下一篇

基于微分博弈的冷链公铁联运温控协同与补贴优化

李平a ，李海军*a,b ，代存杰a,b ，县勇a,b ，黄岩a,b   

  1. 兰州交通大学，a.交通运输学院；b.高原铁路运输智慧管控铁路行业重点实验室，兰州730070
  • 收稿日期:2026-03-03 修回日期:2026-03-29 接受日期:2026-03-31 出版日期:2026-06-25 发布日期:2026-06-23
  • 作者简介:李平（1997— ），男，甘肃天祝人，博士生。
  • 基金资助:
    国家自然科学基金(52462045, 5256120136)。

Temperature Control Coordination and Subsidy Optimization in Cold Chain Road-Rail Intermodal Transport: A Differential Game Approach

LI Pinga, LI Haijun*a,b, DAI Cunjiea,b, XIAN Yonga,b, HUANG Yana,b   

  1. a. School of Traffic and Transportation; b. Key Laboratory of Railway Industry on Plateau Railway Transportation Intelligent Management and Control, Lanzhou Jiaotong University, Lanzhou 730070, China
  • Received:2026-03-03 Revised:2026-03-29 Accepted:2026-03-31 Online:2026-06-25 Published:2026-06-23
  • Supported by:
    National Natural Science Foundation of China (52462045, 5256120136)。

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摘要： 针对冷链公铁联运产地集散环节温控协同失灵问题，本文构建公路承运人、铁路承运人与政府的三方微分博弈模型。引入协同增益系数表征公铁温控投入的协同效应，并从温度交接、信息协同和学习溢出三渠道推导其理论表达式，证明协同增益系数为正与战略互补性的等价关系，从博弈论角度阐明协同失灵的形成机制。求解分散决策、领导-跟随与合作3种情形的均衡解析解，推导均衡存在边界条件，比较投资补贴与运营补贴的边际效率。主要结论为：三渠道贡献占比分别为33.4%、43.3%和23.3%，信息协同贡献最大，且有40%以上提升空间；分散决策下，公路与铁路温控投入仅达合作最优的30.8%和37.3%，效率损失达72.9%；在小协同效应( β→0)与对称参数假设下，无约束最优补贴强度约90%，受均衡存在性与系统稳定性约束，可行补贴区间为25%~30%，该区间内投资补贴边际效率约为运营补贴的1.73倍（对称极限条件下，理论上界为2）；存在“激励-稳定”权衡，补贴比例从0增至30%时，投入提升65.3%，但均衡存在边界从0.62降至0.43。上述结论对参数变动具有稳健性，可为冷链公铁联运协同机制设计与补贴政策优化提供理论依据。

关键词: 综合交通运输, 协同增益分解, 微分博弈, 公铁联运, 政府补贴优化, 战略互补性

Abstract: This paper addresses the problem of temperature control coordination failure at origin-distribution nodes in cold chain road-rail intermodal transport by constructing a three-party differential game model for road carriers, railway carriers, and the government. A synergy gain coefficient is introduced to characterize the cross-modal spillover effects of temperature control investments, and its theoretical expression is derived from three channels: temperature handover, information synergy, and learning spillover. This paper establishes the equivalence between the positive synergy gain coefficient and strategic complementarity, thereby reveals the game-theoretic root of coordination failure. Analytical equilibrium solutions are obtained for decentralized, leader-follower, and cooperative scenarios. The equilibrium existence boundary is derived, and the marginal efficiencies of investment and operational subsidies are compared. Results show that: (1) the three channels contribute 33.4%, 43.3%, and 23.3% of the total synergy gain, respectively, with a greatest improvement potential of over 40% in the information synergy exhibiting; (2) under the decentralized decision-making, the investments of road and railway temperature control reach only 30.8% and 37.3% of the cooperative optimum, respectively, resulting in an efficiency loss of 72.9%; (3) under the small-synergy ( β→0 ) and symmetric-parameter assumptions, the unconstrained optimal subsidy rate is approximately 90%, yet equilibrium existence and system stability constraints compress the feasible range to 25%~30%; within this range, the marginal efficiency of investment subsidies is approximately 1.73 times that of operational subsidies (theoretical upper bound under symmetry is 2); and (4) an "incentive-stability" trade-off exists: increasing the subsidy rate from 0 to 30% raises total investment by 65.3%, yet the equilibrium existence threshold decreases from 0.62 to 0.43. These conclusions are robust to parameter variations, providing a theoretical basis for coordination mechanism design and subsidy policy optimization.

Key words: integrated transportation, synergy gain decomposition, differential game, road-rail intermodal transport, government subsidy optimization, strategic complementarity

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