Abstract
In this letter, infinite horizon Stackelberg games with a large follower population for stochastic linear parameter-varying (LPV) systems is studied. Players are assumed to have their own local dynamics and they are coupled with each other through a mean field term in the cost functionals. It is assumed that followers adopt Nash equilibrium strategies and can only access their own local state information. First, the conditions for the existence of a centralized Stackelberg strategy set and its solutions are obtained by using the cross-coupled matrix inequalities (CCMIs) and cross-coupled matrix equations (CCMEs), respectively. Then, the conditions for the existence of a decentralized Stackelberg strategy set are obtained by using the reduced-order CCMIs and CCMEs respectively. It is proved that, when the follower population size is sufficiently large, the centralized Stackelberg strategy set approximates to the decentralized strategy set and the approximation is evaluated by using the weakly-coupled stochastic systems theory. Finally, a simple example is computed to demonstrate the validity and usefulness of the proposed approach.
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