Leader-follower games in marketing: a differential game approach

In normal differential game models, players are assumed to make decisions simultaneously. Thus, a competitor does not know the decision policies of others as he decides on his own strategy or control. However, in reality, it is not unusual for competitors to make decisions at different times. Thus, the roles of competitors are not always the same. Some competitors have priority in making decisions of policy over others. Those who make decisions first are called leaders, the others are called followers. This type of game is called Leader-Follower (L-F) or Stackelberg game. The solution of such a game is no longer in terms of Nash equilibrium. In this paper, we consider an L-F differential game to model competition in the final stage of a product life cycle in a non-symmetric market environment, derive and solve the optimality conditions in terms of a new definition of solution.