Aggregating the Single Crossing Property
研究了单交叉性质在函数聚合（求和或凸组合）下保持的条件，并应用于目标函数性质、不确定性下最优决策的单调性以及贝叶斯博弈中单调均衡的存在性。
Abstract: The single crossing property plays a crucial role in economic theory, yet there are important instances where the property cannot be directly assumed or easily derived. Difficulties often arise because the property cannot be aggregated: the sum or convex combination of two functions with the single crossing property need not have that property. We introduce a new condition characterizing when the single crossing property is stable under aggregation and also identify sufficient conditions for the preservation of the single crossing property under multidimensional aggregation. We use our results to establish properties of objective functions (convexity, logsupermodularity), the monotonicity of optimal decisions under uncertainty, and the existence of monotone equilibria in Bayesian-games.