Mean Field Stackelberg Games: Aggregation of Delayed Instructions

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Mean Field Stackelberg Games: Aggregation of Delayed Instructions

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Title: Mean Field Stackelberg Games: Aggregation of Delayed Instructions
Author(s):
Bensoussan, Alain;
Chau, M. H. M.;
Yam, S. C. P.
Item Type: article
Keywords: Stackelberg equilibrium
Backward stochastic dynamics
Riccati equation
Abstract: In this paper, we consider an N-player interacting strategic game in the presence of a (endogenous) dominating player, who gives direct influence on individual agents, through its impact on their control in the sense of Stackelberg game, and then on the whole community. Each individual agent is subject to a delay effect on collecting information, specifically at a delay time, from the dominating player. The size of his delay is completely known by the agent, while to others, including the dominating player, his delay plays as a hidden random variable coming from a common fixed distribution. By invoking a noncanonical fixed point property, we show that for a general class of finite N-player games, each of them converges to the mean field counterpart which may possess an optimal solution that can serve as an epsilon-Nash equilibrium for the corresponding finite N-player game. Second, we provide, with explicit solutions, a comprehensive study on the corresponding linear quadratic mean field games of small agents with delay from a dominating player. Given the information flow obtained from both the dominating player and the whole community via the mean field term, the filtration to which the control of the representative agent adapted is non-Brownian. Therefore, we propose to utilize backward stochastic dynamics (instead of the common approach through backward stochastic differential equations) for the construction of adjoint process for the resolution of his optimal control. A simple sufficient condition for the unique existence of mean field equilibrium is provided by tackling a class of nonsymmetric Riccati equations. Finally, via a study of a class of forward-backward stochastic functional differential equations, the optimal control of the dominating player is granted given the unique existence of the mentioned mean field equilibrium for small players.
ISSN: 0363-0129
Persistent Link: http://dx.doi.org/10.1137/140993399
http://hdl.handle.net/10735.1/4909
Bibliographic Citation: Bensoussan, A., M. H. M. Chau, and S. C. P. Yam. 2015. "Mean Field Stackelberg Games: Aggregation of Delayed Instructions." Siam Journal on Control and Optimization 53(4), doi: 10.1137/140993399 2237-2266.
Terms of Use: ©2015 Society for Industrial and Applied Mathematics
Sponsors: Hong Kong RGC GRF 500113, Hong Kong RGC GRF 404012, Hong Kong RGC GRF 14301015 and the National Science Foundation under grant DMS 1303775.

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