Open-loop and closed-loop models of dynamic oligopoly in the cruise line industry

In this paper, the competition of dynamic oligopoly in the cruise line industry is modeled as an N-person nonzero-sum noncooperative dynamic game where a finite number of cruise lines compete to maximize their profits over a fixed planning horizon. The noncooperative Nash equilibrium capacity investment strategies of cruise lines are theoretically analyzed under the open-loop and closed-loop information structures. The optimality conditions for open-loop and closed-loop Nash equilibrium solutions are derived using a Pontryagin-type maximum principle and given economic interpretations so as to demonstrate the differences between the open-loop and closed-loop Nash equilibrium solutions. The dynamic oligopolistic competition of three cruise lines in a hypothetical setting is numerically analyzed by using the iterative algorithms for open-loop and closed-loop models. Numerical results provide a number of important managerial guidelines for cruise capacity investment decisions. The paper concludes with a discussion on future research directions.