Frequency competition among airlines on coordinated airports network

Frequency competition is critical for a full-service airline in gaining market share, and adopting a proper strategy can improve an airline’s profits. This study proposes a new equilibrium programming model with flow balance to address frequency competition on airports network with time slot constraints. We first show that a pure-strategy Nash equilibrium may not always exist, and thus forming a pure strategy profile in frequency competition among airlines may naturally lead to deviation from current frequency. Therefore, we formulate the problem as a programming model with a mixed-strategy Nash equilibrium. To avoid shocks from dramatic frequency changes across the network, airlines tend to fine-tune frequencies on select segments during each adjustment. We propose a procedure to generate a computationally tractable amount of representative strategies from a finite set of feasible strategies to demonstrate mixed-strategy Nash equilibrium. We conduct an empirical analysis using an example in which industry profitability increased by as much as 7.89%. We then extend the model to formulate frequency competition among metal-neutral alliances. The results show that forming metal-neutral alliances can improve total industry profits by 10.59%. In particular, a sensitivity analysis with real data on the tolerance of flow imbalance demonstrates that deducting the potential costs due to the relaxation of flow balance between congested airports may earn additional total industry profits in a frequency competition.