Stable Allocations with Network-Based Comparisons

Abstract

Economic agents often care about their relative well-being: they compare themselves with their neighbors in a social network. In this case, what net- work structures permit stable allocations? We construct a model in which an agent’s utility depends on the ranking of their allocation among those of their network neighbors. An allocation is α-stable if it is not revoked under α-majority voting. We find a sufficient and necessary condition for a network to permit any α-stable allocation: the network has an independent set whose size is at least 1−α of the population size. We provide several comparative statics results for Erdos–Renyi random networks: as networks become more connected, more populated, or more homophilous, they are less permissive; i.e., they permit stable allocations for a smaller set of α. We generalize this model to allow for arbitrary sets of blocking coalitions and provide a sufficient and necessary condition for permissive networks in this case. We also show that our characterization of permissive networks are robust to several variations of the preferences. Other extensions of the model concern directed networks and comparisons made to non-neighbors.