Discrete time dynamic multi-leader–follower games with stage-depending leaders under feedback information

Abstract

Discrete time dynamic Stackelberg games with alternating leaders are recently brought forward by and dynamic programming algorithms are extended to discrete time dynamic Stackelberg games of two players with alternating leaders under feedback information structure. In many practical problems, there are multiple leaders and multiple followers. Moreover, the positions of leaders and followers may change at some stages. We aim to extend the results of discrete time dynamic Stackelberg games with alternating leaders to multi-leader–follower games and to obtain a new type of game, dynamic multi-leader–follower game with stage-depending leaders. To simplify the problem, all players in the model are divided into two groups. At each stage, players in one group act as leaders and the players in other group are followers. In the subsequent stage, the positions may go to the contrary. Actually, whether the players in some group act as leaders or not at some stage, depends on the information at the previous stage(s). Furthermore, dynamic programming algorithms are extended to dynamic multi-leader–follower game with stage-depending leaders under feedback information structure in this paper.