Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2004-005 (April 21, 2004)

Dynamic Programming Approach to Discrete Time Dynamic Feedback Stackelberg Games with Independent and Dependent Followers
by Pu-yan Nie, Li-hua Chen and Masao Fukushima

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Stackelberg games play extremely important roles in such fields as economics, management, politics and behavioral sciences. Stackelberg game can be modelled as a bilevel optimization problem. There exists extensive literature about static bilevel optimization problems. However, the studies on dynamic bilevel optimization problems are relatively 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. Dynamic programming algorithms are presented for the solution of discrete time dynamic feedback Stackelberg games with multiple players both for independent followers and for dependent followers. When the followers act dependently, the game in this paper is a combination of Stackelberg game and Nash one.