The sequential equilibrium is a standard solution concept for extensive-form games with imperfect information that includes an explicit representation of the players' beliefs. An assessment consisting of a strategy and a belief is a sequential equilibrium if it satisfies the properties of sequential rationality and consistency. Our main result is that both properties together can be written as a single finite system of polynomial equations and inequalities. The solutions to this system are exactly the sequential equilibria of the game. We construct this system explicitly and describe an implementation that solves it using cylindrical algebraic decomposition. To write consistency as a finite system of equations, we need to compute the extreme directions of a set of polyhedral cones. We propose a modified version of the double description method, optimized for this specific purpose. To the best of our knowledge, our implementation is the first to symbolically solve general finite imperfect information games for sequential equilibria.

翻译：序贯均衡是不完美信息扩展型博弈的标准解概念，它明确刻画了参与者的信念。由策略与信念构成的评估若满足序贯理性与一致性条件，则构成序贯均衡。我们的主要结论是：这两种性质可联合表示为单个有限的多项式方程与不等式系统，该系统的解恰为博弈的序贯均衡。我们显式构造了该系统，并描述了利用柱形代数分解法求解的实现方案。为将一致性表示为有限方程组，需计算多面体锥集的所有极方向。我们提出了一种针对此特定目标优化的双描述法改进版本。据我们所知，本文实现是首个对一般有限不完美信息博弈的序贯均衡进行符号求解的方案。