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Aggregating the Single Crossing Property
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AI
DOI：10.3982/ECTA9869.png)
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摘要
En 中文
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.
Keyword:
Monotone comparative statics
single crossing property
Bayesian games
monotone strategies
logsupermodularity
signed-ratio monotonicity
