The theory of Monotone Comparative Statics (MCS) has traditionally required a lattice structure, excluding certain multidimensional environments such as mixed-strategy games where this property fails. We show that this structure is not essential. We introduce a weaker notion, the pseudo-lattice property, and preserve the theory's core results by generalizing the MCS theorems for individual choice and Tarski's fixed-point theorem. Our framework expands comparative statics to pseudo quasi-supermodular games. Crucially, it enables the first MCS analysis of mixed-strategy Nash equilibria and trembling-hand perfect equilibria.

翻译：单调比较静态理论传统上要求格结构，这排除了某些多维环境（例如混合策略博弈），因为在这些环境中格性质不成立。我们证明这种结构并非必需。我们引入了一个更弱的概念——伪格性质，并通过推广个体选择的MCS定理和塔斯基不动点定理，保留了该理论的核心结果。我们的框架将比较静态分析扩展至伪拟超模博弈。关键的是，它首次实现了对混合策略纳什均衡与颤抖手精炼均衡的MCS分析。