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首页> 外文期刊>Automatic Control, IEEE Transactions on >An Open-Loop Stackelberg Strategy for the Linear Quadratic Mean-Field Stochastic Differential Game
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An Open-Loop Stackelberg Strategy for the Linear Quadratic Mean-Field Stochastic Differential Game

机译：线性二次平均场随机微分对策的开环Stackelberg策略。

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摘要

This paper is concerned with the open-loop linear–quadratic (LQ) Stackelberg game of the mean-field stochastic systems in finite horizon. By means of two generalized differential Riccati equations, the follower first solves a mean-field stochastic LQ optimal control problem. Then, the leader turns to solve an optimization problem for a linear mean-field forward–backward stochastic differential equation. By introducing new state and costate variables, we present a sufficient condition for the existence and uniqueness of the Stackelberg strategy in terms of the solvability of some Riccati equations and a convexity condition. Furthermore, it is shown that the open-loop Stackelberg equilibrium admits a feedback representation involving the new state and its mean. Finally, two examples are given to show the effectiveness of the proposed results.
机译：本文涉及有限域中均值随机系统的开环线性-二次（LQ）Stackelberg博弈。跟随者通过两个广义的微分Riccati方程，首先解决平均场随机LQ最优控制问题。然后，领导者转向解决线性均值场向前-向后随机微分方程的优化问题。通过引入新的状态变量和代价变量，就某些Riccati方程的可解性和凸性条件而言，我们为Stackelberg策略的存在和唯一性提供了充分条件。此外，还表明，开环的斯塔克尔伯格均衡器接受了涉及新状态及其均值的反馈表示。最后，通过两个例子说明了所提出结果的有效性。

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