We adopt the notion of myopic-farsighted stable set to study the stability of networks when myopic and farsighted individuals decide with whom they want to form a link, according to some utility function that weighs the costs and benefits of each connection. A myopic-farsighted stable set is the set of networks satisfying internal and external stability with respect to the notion of myopic-farsighted improving path. We first provide conditions on the utility function that guarantee the existence of a myopic-farsighted stable set and we show that, when the population becomes mixed, the myopic-farsighted stable set refines the set of pairwise stable networks by eliminating some Pareto-dominated networks. In the end, when all players are farsighted, the myopic-farsighted stable set only consists of all strongly efficient networks. We next show that, in the case of a distance-based utility function, a tension between stability and efficiency is likely to arise when the population is homogeneous (either all myopic or all farsighted). But, once the population is mixed, the tension vanishes if there are enough farsighted individuals. In the case of a degree-based utility function, myopic and farsighted individuals may end up segregated with myopic individuals being overconnected and farsighted ones getting the socially optimal payoff. Keywords Networks • Stable sets • Myopic and farsighted players • Egalitarian utility • Positive convex externalities • Distance-based utility • Degree-based utility JEL Classification A14 • C70 • D20

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.

We adopt the notion of myopic-farsighted stable set to study the stability of networks when myopic and farsighted individuals decide with whom they want to form a link, according to some utility function that weighs the costs and benefits of each connection. A myopic-farsighted stable set is the set of networks satisfying internal and external stability with respect to the notion of myopic-farsighted improving path. We first provide conditions on the utility function that guarantee the existence of a myopic-farsighted stable set and we show that, when the population becomes mixed, the myopic-farsighted stable set refines the set of pairwise stable networks by eliminating some Pareto-dominated networks. In the end, when all players are farsighted, the myopic-farsighted stable set only consists of all strongly efficient networks. We next show that, in the case of a distance-based utility function, a tension between stability and efficiency is likely to arise when the population is homogeneous (either all myopic or all farsighted). But, once the population is mixed, the tension vanishes if there are enough farsighted individuals. In the case of a degree-based utility function, myopic and farsighted individuals may end up segregated with myopic individuals being overconnected and farsighted ones getting the socially optimal payoff. KeywordsNetworks • Stable sets • Myopic and farsighted players • Egalitarian utility • Positive convex externalities • Distance-based utility • Degree-based utility JEL Classification A14 • C70 • D20