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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 Linear production game ： ウィキペディア英語版 Linear production game ''Linear Production Game'' (''LP Game'') is a N-person game in which the value of a coalition can be obtained by solving a Linear Programming problem. It is widely used in the context of resource allocation and payoff distribution. Mathematically, there are ''m'' types of resources and ''n'' products can be produced out of them. Product ''j'' requires $a^j\_k$ amount of the ''kth'' resource. The products can be sold at a given market price $\backslash vec$ while the resources themselves can not. Each of the ''N'' players is given a vector $\backslash vec=(b^i\_1,...,b^i\_m)$ of resources. The value of a coalition ''S'' is the maximum profit it can achieve with all the resources possessed by its members. It can be obtained by solving a corresponding Linear Programming problem $P(S)$ as follows. b^i_j \quad \forall j=1,2,...,m |} == The core of the LP game == Every LP game ''v'' is a totally balanced game. So every subgame of ''v'' has a non-empty core. One imputation can be computed by solving the dual problem of $P(N)$. Let $\backslash alpha$ be the optimal dual solution of $P(N)$. The payoff to player'' i'' is $x^i=\backslash sum\_^m\backslash alpha\_k\; b^i\_k$. It can be proved by the duality theorems that $\backslash vec$ is in the core of ''v''. An important interpretation of the imputation $\backslash vec$ is that under the current market, the value of each resource ''j'' is exactly $\backslash alpha\_j$, although it is not valued in themselves. So the payoff one player i should receive is the total value of the resources he possesses. However, not all the imputations in the core can be obtained from the optimal dual solutions. There are a lot of discussions on this problem. One of the mostly widely used method is to consider the r-fold replication of the original problem. It can be shown that if an imputation ''u'' is in the core of the r-fold replicated game for all r, then ''u'' can be obtained from the optimal dual solution. 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「Linear production game」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.