Network stability under limited foresight

Abstract

We propose a decision-theoretic and cognitive-hierarchy based notion of network stability by examining the decision-making nodes' incentives to change the structure of a network by establishing/dissolving links in between them. While evaluating the desirability of initiating such changes, each node internalizes, to the extent of its limited foresight, the effect of further changes that may be induced thereafter. The nodes may exhibit heterogeneity in their level of foresight, and coalitions of nodes may collectively alter the network structure. We define a limited foresight stable set as our stability concept. The primary characteristic of this set, which always exists and is unique, is that the process of link additions/deletions always leads to networks in this set. This set may vary with both the extent and heterogeneity of the nodes' foresight, and with the possibility of coalitional deviations – so, we present “tight” sufficient conditions under which this set is independent of these considerations.