Dynamic feedback Stackelberg games with alternating leaders

In all past researches on dynamic Stackelberg games, the leader(s) and the followers are always assumed to be fixed. In practice, the roles of the players in a game may change from time to time. Some player in contract bridge, for example, acts as a leader at some stage but as a follower at the subsequent stage, which motivates the Stackelberg games with unfixed leaders. We aim to analyze the dynamic Stackelberg games with two players under such circumstances and call them dynamic Stackelberg games with alternating leaders. There are two goals in this paper. One goal is to establish models for a new type of games, dynamic Stackelberg games of alternating leaders with two players. The other goal is to extend dynamic programming algorithms to discrete time dynamic Stackelberg games with alternating leaders under feedback information structure.