Stable Allocations with Network-Based Comparisons

Economic agents often care about their relative well-being: they compare with their neighbors in a social network. In this case, which network structures permit stable allocations? We construct a model in which agents’ payoffs depend on the ranking of their allocations among the payoffs of their network neighbors’. An allocation is α-stable if it is not revoked under α-majority voting; that is, there exists no alternative allocation such that a fraction of at least α of the population have their rankings strictly improved under the alternative. We find a sufficient and necessary condition for a network to permit any α-stable allocation: the network has an independent set of size at least (1 - α) of the population. We say a network is more permissive if it permits stable allocations for a larger set of α’s. With this simple necessary and sufficient condition, we provide several comparative statics results for Erdős–Renyi random networks: as networks become more connected, more populated (with a fixed link probability), or more homophilous, they are less permissive. We generalize this model to allow for arbitrary sets of blocking coalitions and provide a sufficient and necessary condition for permissiveness in this case. Other extensions of the model concern (1) agents’ preferences based on both relative and absolute terms, (2) directed networks, and (3) comparisons made to non-neighbors.