Coalition-proof stable networks

Abstract

We propose the notion of coalition-proof stability for predicting the networks that could emerge when group deviations are allowed. A network is coalition-proof stable if there exists no coalition which has a credible group deviation. A coalition is said to have a credible group deviation if there is a profitable group deviation to some network and there is no subcoalition of the deviating players which has a subsequent credible group deviation. Coalition-proof stability is a coarsening of strong stability. We emphasize the importance of coalition-proof stability by considering four models where a strongly stable network fails to exist while a coalition-proof stable network does exist. We provide an easy to verify condition for the existence of a coalition-proof stable network while a strongly stable network may not exist. There is no relationship between the set of coalition-proof stable networks and the set of networks induced by a coalition-proof Nash equilibrium of Myerson’s linking game.

Local farsightedness in network formation

“…13 Dutta and Mutuswami (1997), Jackson and van den Nouweland (2005) extend the notion of pairwise stability to group deviations, while Luo et al (2022) propose the notion of coalition-proof stability for predicting the networks that could emerge when group deviations are allowed. A network g is strongly stable if for any S N g , ′ ⊆…”