Game-theoretical models for competition analysis in a new emerging liner container shipping market

•Investigated the competitive behaviors between two liner container shipping carriers.•Formulated the game-theoretical models with discrete pure strategy set and non-differential payoff function.•Analyzed the combinational optimization of freight rate and ship capacity setting.•Defined a ε-approximate Nash equilibrium and proposed a numerical solution algorithm.•Examined the impacts of deterrence objective on deterrence effect and optimal shipping deployment.

This paper develops three game-theoretical models to analyze shipping competition between two carriers in a new emerging liner container shipping market. The behavior of each carrier is characterized by an optimization model with the objective to maximize his payoff by setting optimal freight rate and shipping deployment (a combination of service frequency and ship capacity setting). The market share for each carrier is determined by the Logit-based discrete choice model. Three competitive game strategic interactions are further investigated, namely, Nash game, Stackelberg game and deterrence by taking account of the economies of scale of the ship capacity settings. Three corresponding competition models with discrete pure strategy are formulated as the variables in shipment deployment are indivisible and the pricing adjustment is step-wise in practice. A ɛ -approximate equilibrium and related numerical solution algorithm are proposed to analyze the effect of Nash equilibrium. Finally, the developed models are numerically evaluated by a case study. The case study shows that, with increasing container demand in the market, expanding ship capacity setting is preferable due to its low marginal cost. Furthermore, Stackelberg equilibrium is a prevailing strategy in most market situations since it makes players attain more benefits from the accommodating market. Moreover, the deterrence effects largely depend on the deterrence objective. An aggressive deterrence strategy may make potential monopolist suffer large benefit loss and an easing strategy has little deterrence effect.