Pricing and Allotment in a Sea-Cargo Supply Chain with Reference Effect: A Dynamic Game Approach

The contract between the carrier and forwarder is a long-term issue, and the repeated contract business makes the forwarder develop a reference point based on the contract prices, and this reference effect, to a large extent, affects the forwarder’s contract purchasing decisions. Based on that, this paper introduces the reference effect in the sea-cargo supply chain and studies a multiple-period contract problem between the carrier and the forwarder. It is found that when the capacity price in the spot market is less than the forwarder’s willingness-to-pay, the forwarder’s contract purchasing decision is not affected by the reference effect, only by the capacity price in the spot market, and the multiple-period contract problem can be simplified into a single-period game. In addition, the carrier’s optimal contract wholesale price approaches the capacity price in the spot market. Although, the forwarder’s contract purchasing decision depends upon the reference effect, it is difficult to derive the closed-form solution. Moreover, because of the risk in the spot market, the carrier tends to sell his/her capacity in the contract market. Finally, we employ the numerical simulation to study the carrier’s contract pricing decisions and the forwarder’s capacity purchasing decisions in two cases.