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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Single crossing condition ： ウィキペディア英語版 Single crossing condition In economics, the single-crossing condition or single-crossing property refers to how the probability distribution of outcomes changes as a function of an input and a parameter. Cumulative distribution functions ''F'' and ''G'' satisfy the single-crossing condition if there exists a ''y'' such that $\backslash forall\; x,\; x\; \backslash ge\; y\; \backslash implies\; F(x)\; \backslash ge\; G(y)$ and $\backslash forall\; x,\; x\; \backslash le\; y\; \backslash implies\; F(x)\; \backslash le\; G(y)$; that is, function $h(x)\; =\; F(x)-G(y)$ crosses the x-axis at most once, in which case it does so from below. This property can be extended to two or more variables. Given x and t, for all x'>x, t'>t, $F(x\text{'},t)\; \backslash ge\; F(x,t)\; \backslash implies\; F(x\text{'},t\text{'})\; \backslash ge\; F(x,t\text{'})$ and $F(x\text{'},t)\; >\; F(x,t)\; \backslash implies\; F(x\text{'},t\text{'})\; >\; F(x,t\text{'})$. This condition could be interpreted as saying that for x'>x, the function g(t)=F(x',t)-F(x,t) crosses the horizontal axis at most once, and from below. The condition is not symmetric in the variables (i.e., we cannot switch x and t in the definition; the necessary inequality in the first argument is weak, while the inequality in the second argument is strict). The single-crossing condition was posited in Samuel Karlin's 1968 monograph 'Total Positivity'. It was later used by Peter Diamond, Joseph Stiglitz, and Susan Athey, 〔Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," ''Econometrica'', Econometric Society, vol. 69(4), pages 861-89, July.〕 in studying the economics of uncertainty, The single-crossing condition is also used in applications where there are a few agents or types of agents that have preferences over an ordered set. Such situations appear often in information economics, contract theory, social choice and political economics, among other fields. ==See also== * Brouwer fixed-point theorem 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Single crossing condition」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.