系统发育树的夏普利值
定量方法
2009-09-02 v2 计算机科学与博弈论
组合数学
种群与进化
摘要
每个加权树自然对应于一个我们称为“树博弈”的合作博弈；它将每片叶子集映射到这些叶子所跨最小子树的权重之和。在系统发育树语境中，叶子为物种，此赋值捕捉了所考虑物种联盟中存在的多样性。我们考虑树博弈的夏普利值并给出一种生物学解释。我们确定了显示夏普利值对树边权依赖的线性变换M，并计算出M的零空间基。二者均依赖于树的“分裂计数”。最后，我们用四条公理刻画了树博弈上的夏普利值，作为夏普利关于更大类合作博弈原始定理的对应。
引用
@article{arxiv.q-bio/0506034,
title = {The Shapley Value of Phylogenetic Trees},
author = {Claus-Jochen Haake and Akemi Kashiwada and Francis Edward Su},
journal= {arXiv preprint arXiv:q-bio/0506034},
year = {2009}
}
备注
References added, and a section (calculating the Shapley value of a tree game from its subtrees) was removed for length reasons (request of referee) and may appear in another paper. 16 pages; related work at http://www.math.hmc.edu/~su/papers.html. Journal of Mathematical Biology, to appear. The original article is available at http://www.springerlink.com