A set of networks G is pairwise farsightedly stable (i) if all possible farsighted pairwise deviations from any network g ∈ G to a network outside G are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying conditions (i) and (ii). A non-empty pairwise farsightedly stable set always exists. We provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsighted stability yields a Pareto dominant network, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest pairwise consistent set and the von Neumann-Morgenstern pairwise farsightedly stable set.

We adopt the largest consistent set defined by Chwe (1994; J. Econ. Theory 63: 299-325) to predict which coalition structures are possibly stable when players are farsighted. We also introduce a refinement, the largest cautious consistent set, based on the assumption that players are cautious. For games with positive spillovers, many coalition structures may belong to the largest consistent set. The grand coalition, which is the efficient coalition structure, always belongs to the largest consistent set and is the unique one to belong to the largest cautious consistent set.

We introduce the concept of a horizon-K farsighted set to study the influence of the degree of farsightedness on network stability. The concept generalizes existing concepts where all players are either fully myopic or fully farsighted. A set of networks G K is a horizon-K farsighted set if three conditions are satisfied. First, external deviations should be horizon-K deterred. Second, from any network outside of G K there is a sequence of farsighted improving paths of length smaller than or equal to K leading to some network in G K . Third, there is no proper subset of G K satisfying the first two conditions. We show that a horizon-K farsighted set always exists and that the horizon-1 farsighted set G 1 is always unique. For generic allocation rules, the set G 1 always contains a horizon-K farsighted set for any K . We provide easy to verify conditions for a set of networks to be a horizon-K farsighted set, and we consider the efficiency of networks in horizon-K farsighted sets. We discuss the effects of players with different horizons in an example of criminal networks.

Pairwise stability Jackson and Wolinsky [1996] is the standard stability concept in network formation. It assumes myopic behavior of the agents in the sense that they do not forecast how others might react to their actions. Assuming that agents are perfectly farsighted, related stability concepts have been proposed.We design a simple network formation experiment to test these extreme theories, but find evidence against both of them: the subjects are consistent with an intermediate rule of behavior, which we interpret as a form of limited farsightedness. On aggregate, the selection among multiple pairwise stable networks (and the performance of farsighted stability) crucially depends on the level of farsightedness needed to sustain them, and not on efficiency or cooperative considerations. Individual behavior analysis corroborates this interpretation, and suggests, in general, a low level of farsightedness (around two steps) on the part of the agents.JEL classification: D85, C91, C92