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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 Utility functions on indivisible goods ： ウィキペディア英語版 Utility functions on indivisible goods Some branches of economics and game theory deal with indivisible goods – discrete items that can be traded only as a whole. For example, in combinatorial auctions there is a finite set of items, and every agent can buy a subset of the items, but an item cannot be divided between two or more agents. It is usually assumed that every agent assigns subjective utility to every subset of the items. This can be represented by one of two ways: * An ordinal utility preference relation, usually marked by $\backslash succ$. The fact that an agent prefers a set $A$ to a set $B$ is written $A\; \backslash succ\; B$. If the agent only weakly prefers $A$ (i.e. either prefers $A$ or is indifferent between $A$ and $B$) then this is written $A\; \backslash succeq\; B$. * A cardinal utility function, usually marked by $u$. The utility an agent gets from a set $A$ is written $u(A)$. Cardinal utility functions are often normalized such that $u(\backslash emptyset)=0$, where $\backslash emptyset$ is the empty set. A cardinal utility function implies a preference relation: $u(A)>u(B)$ implies $A\; \backslash succ\; B$ and $u(A)\backslash geq\; u(B)$ implies $A\; \backslash succeq\; B$. Utility functions can have several properties. == Monotonicity == Monotonicity means that an agent always (weakly) prefers to have extra items. Formally: * For a preference relation: $A\backslash supseteq\; B$ implies $A\; \backslash succeq\; B$. * For a utility function: $A\backslash supseteq\; B$ implies $u(A)\; \backslash geq\; B$ (i.e. ''u'' is a monotone function). Monotonicity is equivalent to the free disposal assumption: if an agent may always discard unwanted items, then extra items can never decrease the utility. 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「Utility functions on indivisible goods」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.