Allocation Rules for Networks Inspired by Cooperative Game-Theory

This survey presents theories of how players should allocate the value generated by their cooperation when their opportunities to cooperate are limited by or determined by a communication network. We present allocation rules, on one hand, for communication games, that is cooperative games enriched by a communication structure and on the other hand, for network games, in which the networks themselves are the building blocks that generate value. We focus mainly on allocation rules that in some sense generalize the Shapley value to settings with restricted communication but also present some other important allocation rules. To better understand the properties of various allocation rules, we present and compare the axiomatic properties that characterize each of them. Finally we present some areas of application of this theory: evaluating voters? power as a function of their place in an ideological landscape, estimating an individual?s centrality and influence in a network, deriving rankings of the contenders in a competition based on their past performance, and finally the problem of sharing a common natural ressource, the so called river-sharing problem.