Wasserstein空间上的一个微分对策。部分监控在弱可达性问题中的应用
A differential game on Wasserstein space. Application to weak approachability with partial monitoring
摘要：
研究一些离散时间动力学的连续时间对应物现在是一种标准的和富有成效的技术，因为一些性质在两种设置中都成立。在对策论中，这通常通过考虑欧几里得空间上的微分对策来实现。这允许推断属性上的重复游戏的值的收敛，以处理各种概念的可接近性等，在本文中，我们介绍了一个具体的，但相当抽象的微分对策定义的Wasserstein空间的概率分布，我们证明了它的价值的存在。回到离散时间动力学，我们得出的结果弱可接近部分监测：我们证明，任何一组满足适当的兼容性条件是弱可接近或弱可排除。我们还得到了具有非预期策略的微分对策的值与那些用一种新的策略概念定义的微分对策的值相同，这种新的策略概念非常适合于与重复对策联系起来。
英文摘要：
Studying continuous time counterpart of some discrete time dynamics is now a standard and fruitful technique, as some properties hold in both setups. In game theory, this is usually done by considering differential games on Euclidean spaces. This allows to infer properties on the convergence of values of a repeated game, to deal with the various concepts of approachability, etc. In this paper, we introduce a specific but quite abstract differential game defined on the Wasserstein space of probability distributions and we prove the existence of its value. Going back to the discrete time dynamics, we derive results on weak approachability with partial monitoring: we prove that any set satisfying a suitable compatibility condition is either weakly approachable or weakly excludable. We also obtain that the value for differential games with nonanticipative strategies is the same that those defined with a new concept of strategies very suitable to make links with repeated games.
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