We study situations where agents can form or sever links in a network: what agents can do exactly is described by effectivity functions. A power index assigns to such an effectivity function a number for each agent, measuring the opportunities of that agent. We characterize a class of power indices by four axioms: the Transfer Property, the Dummy Property, Symmetry, and Network Neutrality. As a corollary, we obtain power indices for the case where effectivity functions are induced by preferences of agents about the other agents. Applications include one-to-one, one-to-many, and many-to-many matching markets, as well as roommate problems.

中文翻译：

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网络的功率指数，以及匹配市场的应用

我们研究代理可以在网络中形成或切断链接的情况：代理可以做什么是由有效性函数描述的。权力指数为每个代理人的这种有效性函数分配一个数字，衡量该代理人的机会。我们通过四个公理来描述一类权力指数：转移属性、虚拟属性、对称性和网络中性。作为推论，我们获得了效率函数是由代理人对其他代理人的偏好引起的情况的权力指数。应用包括一对一、一对多和多对多匹配市场，以及室友问题。