臺灣博碩士論文加值系統

摘要: 從 Hsiao [5], 我們把 Shapley 值的系數待為一個條件機率. 這
條件機率的隨機性是在聯盟上, 和傳統的機率解釋是不同的. 這一篇
論文的主要結果是: (1)我們設隨機在聯盟上, 且計算在對稱 Shapley 值
n 個人的合作對局中聯盟形成的機 率. (2)再者, 我們計算在重量
Shapley 值 n 個人的合作對局中聯盟形成的機率. (3)最後, 我們觀察上
面的機率分配, 發現一些組合的等式.

Abstract. Following Hsiao [5], we treat the coefficient of the
Shapley value as a conditional probability. The randomness of
the conditional probability on the coalition which is different
from the traditional probabilistic interpretation. The main
result of this paper are : (1) We assume the randomness is on
the coalition, and calculate the probabilitythat a coalition is
formed in cooperative n-person game for the symmetric
Shapleyvalue. (2) Furthermore, we can calculate the probability
that a coalition has formedin cooperative n-person game for the
weighted Shapley value. (3) Finally, we find some combinatorial
equality by obserbing the aboveprobability distributions.