Inter-Port Competition and Cooperation Under Different Market Environments

Aiming at the competition and cooperation decision-making problem between two ports in the same regional port group, this paper studies four kinds of dynamic game scenarios of two adjacent ports—namely, independent strategy–independent strategy (i.e., DD combinations), independent strategy–integrated strategy (i.e., DT combinations), integrated strategy–independent strategy (i.e., TD combinations), and integrated strategy–integrated strategy (i.e., TT combinations). By introducing port demand models and using the dynamic game method, the paper performs a comparative study of port service pricing, port demand, and port profit in different combinations of competition and cooperation. The results show that taking port profit as payment function, the equilibrium strategy of the leader port is the independent strategy, which is also the dominant strategy, while the independent strategy or integrated strategy of the follower port depends on the degree of service substitution provided by the two competing ports. When the degree of service substitution is low (0 < γ < 0.53), the equilibrium strategies of two competing ports are the DD combinations, but the equilibrium strategies can be improved by Pareto, and further analysis shows that TT combinations are the Pareto equilibrium strategies at this time. By contrast, when the degree of service substitution provided by the two competing ports is high (0.53 ≤γ < 1), the DT combinations are the equilibrium strategies of the two competing ports, which are also the Pareto equilibrium strategies at this time. The research shows that when the degree of service substitution of the two ports is low, to encourage the two ports to carry out differentiated development of service functions, it is conducive to promote the two ports to adopt the integrated cooperation strategies.

A differential game of N persons in which there is Pareto equilibrium of objections and counterobjections and no Nash equilibrium

A linear-quadratic positional differential game of N persons is considered. The solution of a game in the form of Nash equilibrium has become widespread in the theory of noncooperative differential games. However, Nash equilibrium can be internally and externally unstable, which is a negative in its practical use. The consequences of such instability could be avoided by using Pareto maximality in a Nash equilibrium situation. But such a coincidence is rather an exotic phenomenon (at least we are aware of only three cases of such coincidence). For this reason, it is proposed to consider the equilibrium of objections and counterobjections. This article establishes the coefficient criteria under which in a differential positional linear-quadratic game of N persons there is Pareto equilibrium of objections and counterobjections and at the same time no Nash equilibrium situation; an explicit form of the solution of the game is obtained.

To the individual stability of Pareto equilibrium of objections and counterobjections in a coalition differential positional 3-person game without side payments

The notion <<individual stability>> of Pareto equilibrium of objections and counter objections in one differential linear-quadratic 3-person game without side payments is used. The explicit form corresponding equilibrium is found.