Kuhn's equivalence theorem for games in product form

• 成果类型: Article
• 署名作者: Heymann, Benjamin; De Lara, Michel; Chancelier, Jean -Philippe
• 署名单位: Institut Polytechnique de Paris; Ecole des Ponts ParisTech
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2022.06.006
• 发表日期: 2022
• 页码: 220-240
• 关键词: Games with information; Kuhn?s equivalence theorem; Perfect recall; Witsenhausen intrinsic model

摘要

We propose an alternative to the tree representation of extensive form games. Games in product form represent information with sigma-fields over a product set, and do not require an explicit description of the play temporal ordering, as opposed to extensive form games on trees. This representation encompasses games with continuum of actions and imperfect information. We adapt and prove Kuhn's theorem - regarding equivalence between mixed and behavioral strategies under perfect recall - for games in product form with continuous action sets.