The purpose of this paper is to study 2-person zero-sum stochasticdifferential games, in which one player is a major one and the other player isa group of $N$ minor agents which are collectively playing, statisticallyidentical and have the same cost-functional. The game is studied in a weakformulation; this means in particular, we can study it as a game of the type"feedback control against feedback control". The payoff/cost functional isdefined through a controlled backward stochastic differential equation, forwhich driving coefficient is assumed to satisfy strict concavity-convexity withrespect to the control parameters. This ensures the existence of saddle pointfeedback controls for the game with $N$ minor agents. We study the limitbehavior of these saddle point controls and of the associated Hamiltonian, andwe characterize the limit of the saddle point controls as the unique saddlepoint control of the limit mean-field stochastic differential game.
展开▼
机译：本文的目的是研究两人零和随机差分博弈，其中一个参与者是主要参与者，另一个参与者是一组N $次要代理，它们共同参与，具有统计意义并且具有相同的成本函数。以弱公式研究游戏。这尤其意味着，我们可以将其作为“反馈控制与反馈控制”类型的游戏进行研究。通过控制后向随机微分方程定义收益/成本函数，假设驱动系数关于控制参数满足严格的凹凸关系。这可以确保存在带有$ N $个未成年人代理的游戏的鞍形点反馈控件。我们研究了这些鞍点控制和相关哈密顿量的极限行为，并且将鞍点控制的极限表征为极限均值场随机微分博弈的唯一鞍点控制。
展开▼
