A Modified Stackelberg Game for a Duopoly Cruise Market with a Potential New Entrant

This paper develops a modified Stackelberg game model for a duopoly market. Unlike the traditional duopoly where the leader and the follower both exist in the market, the modified model supposes a preexisting leader and a follower that has not yet entered the market. This specific situation has often been found recently in many emerging Asian cruise markets as one of the world-class cruise lines initiates a new local cruise market. In spite of the discontinuity of the follower’s reaction function, the Nash equilibrium is found to exist as a pair of optimal capacities of both lines. A decision making criterion is established for the follower to enter the market regarding the fixed-charge incorporated into the follower’s cost function. The optimal capacities of both lines and the resulting market capacities and market shares are computed. A remarkable property is also found that a new monopoly market could result from a duopoly competition by the modified Stackelberg game.