网络博弈的加权位置值
Weighted position value for Network games
AI总结：
本文针对网络合作博弈中位置值忽略参与者权重的问题，提出按外生权重比例分配Shapley份额的加权位置值，并给出两个公理化刻画及一个实现该值的竞标机制。
摘要：
在合作框架下的网络博弈中，位置值是一种基于链接的分配规则。它由相关合作博弈的Shapley值得到，在该合作博弈中，网络的链接被视为参与者。每条链接的Shapley值随后在形成这些链接的参与者之间平均分配。其内在假设是，该值对网络中参与者的权重不敏感。例如，根据参与者在网络中的中心程度，或与其他参与者建立链接的能力等，参与者可以被视为具有权重。因此，在此类情形下，将Shapley值在参与者之间平均分配可能是一种过度简化的做法。我们提出位置值的一个广义版本：加权位置值，它按参与者的权重比例分配Shapley份额。这些参与者的权重是外生给定的。我们为我们的值提供了两个公理化刻画。最后，我们构造了一个竞标机制，以证明该机制的任何子博弈完美均衡（SPE）都与加权位置值一致。
英文摘要：
In Network games under cooperative framework, the position value is a link based allocation rule. It is obtained from the Shapley value of an associated cooperative game where the links of the network are considered players. The Shapley value of each of the links is then divided equally among the players who form those links. The inherent assumption is that the value is indifferent to the weights of the players in the network. Depending on how much central a player is in the network, or the ability of making links with other players etc., for example, players can be considered to have weights. Thus, in such situations, dividing the Shapley value equally among the players can be an over-simplistic notion. We propose a generalised version of the position value: the weighted position value that allocates the Shapley shares proportional to the players' weights. These weights of the players are exogenously given. We provide two axiomatic characterizations of our value. Finally, a bidding mechanism is formulated to show that any sub-game perfect equilibrium (SPE) of this mechanism coincides with the weighted position value.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
