Stable Allocations with Network-Based Comparisons

37 Pages Posted: 10 Jan 2019 Last revised: 24 Oct 2019

See all articles by Chen Cheng

Chen Cheng

Johns Hopkins University - Carey Business School

Yiqing Xing

Johns Hopkins University - Carey Business School

Date Written: October 22, 2019

Abstract

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–Rényi 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.

Keywords: network, social ranking, relative comparison, voting, independent set, stability, group stability, random networks, homophily

JEL Classification: D85, C71, D91

Suggested Citation

Cheng, Chen and Xing, Yiqing, Stable Allocations with Network-Based Comparisons (October 22, 2019). 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

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