Network formation with myopic and farsighted players

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.