微弱单调比较制表师 (Weak Monotone Comparative Statics)

We develop a theory of monotone comparative statics based on weak set order -- in short, weak monotone comparative statics -- and identify the enabling conditions in the context of individual choices, Pareto optimal choices% for a coalition of agents, Nash equilibria of games, and matching theory. Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of the choice environments and underlying preferences of agents. We apply the theory to establish existence and monotone comparative statics of Nash equilibria in games with strategic complementarities and of stable many-to-one matchings in two-sided matching problems, allowing for general preferences that accommodate indifferences and incompleteness.

翻译：我们开发了基于弱定顺序的单质比较静态理论(简言之,弱单质比较静态),并确定了个人选择、Pareto最佳选择率(Pareto 最佳选择 % ) 、代理人联盟、 Nash 游戏平衡和匹配理论背景下的有利条件。与以强定秩序为基础的现有理论相比,弱单质比较静态的条件比较弱,有时在选择环境和代理人基本偏好的结构方面相当脆弱。我们运用这一理论在具有战略互补性的游戏中建立Nash 平衡的存在和单质比较静态,并在双面匹配问题中建立稳定的多对一匹配,允许满足冷漠和不完全的一般偏好。