Which Networks Permit Stable Allocations? A Theory of Network-Based Comparisons
Theoretical Economics, forthcoming
37 Pages Posted: 10 Jan 2019 Last revised: 3 Oct 2022
Date Written: November 26, 2021
Economic agents care about their relative well-being, and the comparisons are usually local: they compare themselves with their neighbors in a social network. In this case, a network shapes agents’ preferences and which allocations are satisfying. We construct a model in which an agent’s payoff depends on the ranking of their resource allocation among those of their net- work neighbors. We say that an allocation is α-stable if no blocking coalition whose size is an α fraction of the population can strictly improve their payoffs. We find a sufficient and necessary condition for a network to permit an α-stable allocation: the network has an independent set whose size is at least 1 − α of the network population. The characterization of permissive networks holds not only for our baseline ranking preference but also for a range of preferences under which the sets of stable allocations are expanded. We also provide a sufficient condition for an allocation to be stable. Extensions of the model concern directed networks and the case where agents have limited enforcement power.
Keywords: Network, social ranking, relative comparison, independent set, stable allocations
JEL Classification: D85, D91, D72, C71
Suggested Citation: Suggested Citation