Network formation with myopic and farsighted players

Abstract

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

Myopic-farsighted absorbing networks

“…Luo, Mauleon and Vannetelbosch (2021) propose the notion of myopic-farsighted stable set to determine the networks that are stable when some players are myopic while others are farsighted. 7 A set of networks G is a myopic-farsighted stable set if the following two conditions hold.…”

“…Luo, Mauleon and Vannetelbosch (2021) propose the notion of myopic-farsighted stable set. A set of networks is a myopic-farsighted stable set if two conditions hold: (internal stability) for any two networks in the myopic-farsighted stable set there is no myopicfarsighted improving path from one network to the other one; (external stability): for every network outside the myopic-farsighted stable set there is a myopic-farsighted improving path leading to some network in the myopic-farsighted stable set.…”

“…Luo, Mauleon and Vannetelbosch (2021) provide conditions on the utility function that guarantee the existence and uniqueness of a myopic-farsighted stable set.…”

Farsighted Manipulation and Exploitation in Networks

“…Many recent papers study farsightedness in general environments by the use of the farsighted stable set (Ray and Vohra, 2015) and its refinements (Dutta and Vohra, 2017;Bloch and van den Nouweland, 2019), as well as in the context of coalition formation (Mauleon and Vannetelbosch, 2004), network formation (Dutta et al, 2005;Page et al, 2005;Herings et al, 2009), and matching (Klaus et al, 2011). This approach can be extended to the myopic-farsighted stable set to capture the interaction between these two types of players (Herings et al, 2017;Luo et al, 2018). Our paper also studies such interactions.…”

Social Rationalizability with Mediation

“…Alternative notions of farsightedness are suggested by Bloch and van den Nouweland[3], Diamantoudi and Xue[5], Dutta et al[6], Dutta and Vohra[8], Dutta and Vartianen[7], Herings et al[11][12][13][14], Karos and Robles[15], Kimya[16], Luo et al[17], Mauleon and Vannetelbosch[18], Page et al[21], and Page and Wooders[20] among others.…”