Dynamic feedback Stackelberg games with non-unique solutions Original Research Article

Stackelberg games, which was originally introduced by Stackelberg, are widely applied in such fields as economics, management, politics and behavioral sciences. Stackelberg games can be modelled as a bi-level optimization problem. There exists an extensive literature about static bi-level optimization problems. However, the studies on dynamic bi-level optimization problems are fairly scarce in spite of the importance in explaining and predicting some phenomena rationally. In this paper, we consider discrete time dynamic Stackelberg games with feedback information. In general, the lower-level strategies are non-unique in practice. For a unique solution, dynamic programming algorithms have been presented with multiple players. We revisit dynamic programming for feedback information dynamic Stackelberg games with non-unique lower-level solution. First, we define some kind of solutions related to the decisions styles. Then, we analyze them, respectively. Moreover, dynamic programming algorithm is successful in solving solve feedback information dynamic Stackelberg games with non-unique lower-level solutions.