Farsightedly stable networks

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.

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