Abstract: The fluctuation of container ocean freight rates is considered crucial to the income of liner shipping companies. Facing increasingly fierce market competition and the changing customer demands, liner shipping companies (carriers) must develop reasonable pricing strategies to attract and retain customers (shippers), ensuring successful cooperation of their container transportation business. This study focuses on the pricing issues of long-term freight rate contracts between the carrier and shipper, aiming to construct an effective game model by deeply analyzing the bargain strategy of both parties under different market conditions. The goal is to find a balance point that maximizes the income of carriers while satisfying the shippers’ needs for their cost control. This paper enriches the application of operations research and management science in theory and provides valuable pricing strategies for carriers in practice, which will have significant theoretical and practical implications.
A game model is built based on the Rubinstein’s alternating offer framework, which simulates the bargain strategy between carriers and shippers in the long-term freight rate contracts. The model specifically considers the bidding policies under the presence of irrational offers and explores the impact of irrational offers on the attitude of both parties in the game under different market situations. Through this model, we are able to gain a deeper understanding of the changes in the shipper’s attitude in freight rate bargains and its impact on the carrier’s bidding strategies under excess or insufficient capacity market conditions.
The results show that in an excess capacity shipping market, shippers usually occupy a dominant position in bargain. In such circumstances, there is an uncertainty in the carrier’s first-stage bidding strategy, while the shipper’s rational bargain directly affects the final outcome of the deal. When the shipper adopts an irrational bargaining strategy, if the carrier fails to recognize this, the offers may decline and the bargain ends,or else the first-stage fails and comes to the second stage. In an insufficient capacity shipping market, the shipper is in a passive position and will accept the offer as long as the carrier’s bid is below their acceptable price.
The empirical analysis further validates the effectiveness of game theory and reveals the final game structure of both parties and factors such as expectation for the future market, discount factors, and bidding strategy. Through the solution of the model, we have obtained the optimal bidding strategies under different shipping market scenarios, providing practical guidance for carriers and shippers in actual bargains. The empirical analysis indicates that by adopting the strategies proposed in this study, carriers can effectively increase contract signing rate, enhance long-term cooperative relationships with shippers, and thereby gain a stable market share in the fiercely competitive market.
Future studies may further focus on more market factors, such as the operational efficiency of liner companies, the bargaining power of shippers, and potential market entrants. In addition, studies can also be extended to other types of transportation such as multimodal transport, and exploring more pricing game methods such as dynamic pricing. These studies will help carriers and shippers better respond to market changes, thereby achieving more scientifically sound and reasonable long-term transportation contracts.

Key words: container liner, transportation, freight rate, game, model

摘要： 运用鲁宾斯坦森轮流出价思想,建立了承运人和托运人关于集装箱班轮公司长期合同运价的博弈模型,模拟承托双方的谈判过程,研究了存在可信欺骗情况下的承托双方出价政策,讨论了在不同航运市场存在虚假报价情况下承托双方在博弈中的地位。分析结果表明:在航运市场运力过剩时,托运人在运价谈判中占主动地位,承运人第一阶段出价存在不确定性,若托运人理性协商,成交结果取决于运价的期望值及贴现率,若托运人非理性压价,而承运人未意识到时,报价走低,谈判结束,否则第一阶段博弈失效,进入第二阶段;当航运市场运力不足时,托运人在运价谈判中据被动地位,只要承运人的出价低于其承受底线值,便会接受报价。通过对模型求解,发现双方最终的博弈结构与航运市场环境、双方对未来市场的预期值、贴现因子以及出价政策有关。最后给出博弈双方在不同航运市场情景下的最优出价策略。

关键词: 集装箱班轮, 运输, 运价, 博弈, 模型