The Theory of Sequential Decision Making

该项目旨在重新考虑非合作博弈理论，特别是广泛形式博弈理论，而不简化有限性或离散性假设。通过重写博弈论的数学基础，以证明每一步的特征结果为目标，我们希望扩展博弈论的当前范围，并开辟新的领域，使博弈论的进一步应用。当前的任务是将库恩定理的证明推广到一般的框架，并为随机策略提供一个严格的模型。此外，对于大多数应用程序，下离散条件似乎是自然的，似乎允许一个显着的简化相关的定义，从而提供了一个紧凑的规范定义的博弈论的原语。在下一步中，我们希望探索的偏好关系，可以在游戏中的顺序决策的可能范围。

The project aims at a reconsideration of the theory of non-cooperative games, in particular the theory of extensive form games, without simplifying finiteness or discreteness assumptions. By redoing the mathematical foundations of game theory, with the goal of proving characterization results in each and every step, we hope to extend the current confines of game theory and break new ground that allows for further applications of game theory. Immediate tasks are to extend the proof of Kuhn s theorem to the general framework and to provide a rigorous model for randomized strategies. Further, for most applications, a down-discreteness condition seems natural and appears to allow for a significant simplification of the relevant definitions, thereby providing a compact canonical definition of the primitives of game theory. In the next step we hope to explore the possible range of preference relations that can govern sequential decision-making in games.