Regular Papers

International Journal of Control, Automation, and Systems 2023; 21(9): 2904-2915

https://doi.org/10.1007/s12555-022-0534-5

© The International Journal of Control, Automation, and Systems

Stackelberg Strategy of Two-player Stochastic Difference Game With Time Delay

Jingmei Liu, Wei Wang*, Juanjuan Xu, and Huanshui Zhang

Shandong University

Abstract

In this paper, we study the open-loop Stackelberg strategy of the stochastic Stackelberg game with time delay. The main contribution is to give the explicit Stackelberg strategy in terms of Riccati equations. The key to solving the problem is the explicit solvability of the forward and backward stochastic difference equations (FBSDEs). Moreover, the optimal costs are indicated by using the initial value of the state.

Keywords Difference game, maximum principle, Stackelberg strategy, stochastic, time delay.

Article

Regular Papers

International Journal of Control, Automation, and Systems 2023; 21(9): 2904-2915

Published online September 1, 2023 https://doi.org/10.1007/s12555-022-0534-5

Copyright © The International Journal of Control, Automation, and Systems.

Stackelberg Strategy of Two-player Stochastic Difference Game With Time Delay

Jingmei Liu, Wei Wang*, Juanjuan Xu, and Huanshui Zhang

Shandong University

Abstract

In this paper, we study the open-loop Stackelberg strategy of the stochastic Stackelberg game with time delay. The main contribution is to give the explicit Stackelberg strategy in terms of Riccati equations. The key to solving the problem is the explicit solvability of the forward and backward stochastic difference equations (FBSDEs). Moreover, the optimal costs are indicated by using the initial value of the state.

Keywords: Difference game, maximum principle, Stackelberg strategy, stochastic, time delay.

IJCAS
July 2024

Vol. 22, No. 7, pp. 2055~2340

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