Stable Allocations with Network-Based Comparisons
23 Pages Posted: 10 Jan 2019
Date Written: December 27, 2018
We consider a model in which each agent cares about her network-based (local) ranking, i.e. the ranking of her allocation among her neighbors’ in a network. An allocation is 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 then characterize the size of the largest independent set for Erdős-Rényi random networks, which reflects how permissive a network is. For large enough population, the level of permissibility solely depends on the expected degree. We provide several comparative statics results: more connected networks, more populated networks (with a fixed link probability), or more homophilous networks are less permissive. We generalize our model to arbitrary blocking coalitions and provide a sufficient and necessary condition for this case. Other extensions of the model include: (1) directed networks and (2) comparisons made only 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: Suggested Citation