| On the Semivalues and the Least Square Values Average Per Capita Formulas and Relationships |
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| 作者姓名： | Irinel DRAGAN |
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| 作者单位： | University of Texas, Mathematics, Arlington, Texas, 76019-0408, USA |
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| 摘 要： |
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| 关 键 词： | 最小平方值 Banzhaf值得 半值 特征函数 |
| 收稿时间： | 2004-02-20 |
| 修稿时间： | 2004-02-202005-09-14 |
On the Semivalues and the Least Square Values Average Per Capita Formulas and Relationships |
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| Irinel DRAGAN.On the Semivalues and the Least Square Values Average Per Capita Formulas and Relationships[J].Acta Mathematica Sinica,2006,22(5):1539-1548. |
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| Authors: | Irinel Dragan |
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| Institution: | (1) University of Texas, Mathematics, Arlington, Texas, 76019-0408, USA |
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| Abstract: | In this paper, it is shown that both the Semivalues and the Least Square Values of cooperative transferable utilities games can be expressed in terms of n^2 averages of values of the characteristic function of the game, by means of what we call the Average per capita formulas. Moreover, like the case of the Shapley value earlier considered, the terms of the formulas can be computed in parallel, and an algorithm is derived. From these results, it follows that each of the two values mentioned above are Shapley values of games easily obtained from the given game, and this fact gives another computational opportunity, as soon as the computation of the Shapley value is efficiently done. |
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| Keywords: | Shapley value Semivalues Least Square Values Average per capita formulas Banzhaf value |
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