Effects of risk-aversion on competing shipping lines’ pricing strategies with uncertain demands

Abstract

Container shipping is facing severe overcapacity, fierce price-based competition and high demand uncertainty. It is natural that some shipping lines may adopt a risk-aversion attitude in their pricing strategies. This paper considers the pricing strategies of two competing ocean carriers facing uncertain demand. The first carrier is risk-neutral with sufficient capacity, whereas the second carrier is risk-averse with limited capacity. The conditional value at risk (CVaR) is used to measure the risk-averse attitude of the second carrier. A Nash game model is formulated to model the pricing decisions and the equilibrium solution is obtained. We find that the pricing solution takes two forms, which can be determined by a threshold value of carrier 2’s capacity. Under uniformly distributed demand, we show that as the second carrier becomes more risk-averse, both carriers’ optimal prices are decreasing, and the threshold value that determines the pricing strategy is also decreasing. We also analyze the impact of price sensitivity and competition intensity parameters on two carriers’ price decisions under more specific conditions. A necessary and sufficient condition is established to determine whether two carriers’ optimal prices would be positively or negatively affected by the competition intensity parameter. A range of numerical experiments are provided to illustrate the analytical results and explore their validity in more general cases. Moreover, it is shown that the main analytical results in this paper can carry over to the cases when both carriers are risk-averse.