Kuhn's Equivalence Theorem for Games in Product Form

2021/04/12 by Heymann, Benjamin, de Lara, Michel, Chancelier, Jean-Philippe
#Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2104.05249

Abstract

We propose an alternative to the tree representation of extensive form games. Games in product form represent information with σ-fields over a product set, and do not require an explicit description of the play temporality, as opposed to extensive form games on trees. This representation encompasses games with a continuum of actions, randomness and players, as well as games for which the play order cannot be determined in advance. 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.

Related

• Kuhn's Equivalence Theorem for Games in Intrinsic Form
• Kuhn's Theorem for Games of the Extensive Form with Unawareness
• Specifying a Game-Theoretic Extensive Form as an Abstract 5-ary Relation
• A Category for Extensive-Form Games
• Behavioral Equivalence of Extensive Game Structures