Which Networks Permit Stable Allocations? A Theory of Network-Based Comparisons

Theoretical Economics, forthcoming

37 Pages Posted: 10 Jan 2019 Last revised: 20 Dec 2021

See all articles by Chen Cheng

Chen Cheng

Johns Hopkins University - Carey Business School

Yiqing Xing

Johns Hopkins University - Carey Business School

Date Written: November 26, 2021

Abstract

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

Cheng, Chen and Xing, Yiqing, Which Networks Permit Stable Allocations? A Theory of Network-Based Comparisons (November 26, 2021). Theoretical Economics, forthcoming, Available at SSRN: https://ssrn.com/abstract=3307723 or http://dx.doi.org/10.2139/ssrn.3307723

Chen Cheng

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

Yiqing Xing (Contact Author)

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

HOME PAGE: http://yiqingxing.com

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
96
Abstract Views
677
rank
371,790
PlumX Metrics