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 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.

翻译：我们建议了一种替代树形游戏的替代方式。 产品形式的游戏代表着以$\gma$-field-fields在一组产品上的信息,不需要明确说明游戏的时间性,而不是树上广泛的游戏形式。 它包含一系列动作、随机性和玩家的游戏,以及无法事先确定游戏顺序的游戏。 我们调整并证明Kuhn在以连续动作组合的游戏中,在完美回扣形式上,对混合策略和行为策略的理论等同性。