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.

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 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.

A set of coalition structures P is farsightedly stable (i) if all possible deviations from any coalition structure p belonging to P to a coalition structure outside P are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improvingpath from any coalition structure outside the set leading to some coalition structure in the set, and (iii) if there is no proper subset of P satisfying the first two conditions. A non-empty farsightedly stable set always exists. We provide a characterization of unique farsightedly stable sets of coalition structures and we study the relationship between farsighted stability and other concepts such as the largest consistent set and the von Neumann-Morgenstern farsightedly stable set. Finally, we illustrate our results by means of coalition formation games with positive spillovers

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

We develop a model of strategic networks in order to analyze how trade unions will affect the stability of R&D networks through which knowledge is transmitted in an oligopolistic industry. Whenever firms settle wages, the partially connected network is likely to emerge in the long run if and only if knowledge spillovers are large enough. However, when unions settle wages, the complete network is the unique stable network. In other words, the stronger the union bargaining power is, the more symmetric stable R&D networks will be. In terms of network efficiency, the partially connected network (when firms settle wages) does not Pareto dominate the complete network (when unions settle wages) and vice versa. JEL classification: C70, L13, L20, J50, D85Réseaux de connaissance entre des firmes syndiquées. Nous développons un modèle de réseaux stratégiques afin d'analyser comment les syndicats vont affecter la stabilité des réseaux R&D par lesquels les connaissances sont transmises dans une industrie oligopolistique. Lorsque les firmes fixent les salaires, le réseau partiellement connectéémergeà long-terme si et seulement si les externalités de connaissance sont très grandes. Cependant, lorsque les syndicats fixent les salaires, le réseau complet est l'unique réseau stable. En d'autres mots, plus les syndicats sont puissants, plus les réseaux de R&D stables sont symétriques. En ce qui concerne l'efficacité des réseaux, le réseau partiellement connecté (lorsque les firmes fixent les salaires) ne domine pas au sens de Pareto le réseau complet (lorsque les syndicats fixent les salaires) et vice versa.

We develop a model of wage determination with private information, in which the union has the option to delegate the wage bargaining to either surplus-maximizing delegates or to wage-maximizing delegates (such as senior union members). We show that the wage outcome in case of surplus-maximizing delegates is not necessarily smaller than the wage outcome in case of wage-maximizing delegates, even when the wage bargaining with private information is close to one with complete information. However, if it is commonly known that the union is stronger than the firm and the demand is sufficiently elastic, then delegating to wage-maximizing delegates definitely increases the wage at equilibrium. The maximum delay in reaching an agreement is greater whenever the union chooses wage-maximizing delegates instead of surplus-maximizing delegates and remains finite even when the period length shrinks to zero. JEL classification: C70, C71, C72, C78De´le´gation syndicale strate´gique et activite´de gre`ve. Nous e´tudions comment l'option pour les syndicats de de´le´guer la ne´gociation salariale va influencer le salaire ne´gocie´et les incitations a`faire la gre`ve. Nous de´veloppons un mode`le de ne´gociation salariale avec information incomple`te dans lequel le syndicat a l'option de de´le´guer la ne´gociation a`un de´le´gue´qui maximise le surplus ou a`un de´le´gue´qui maximise le salaire. Nous montrons que le salaire ne´gocie´par un de´le´gue´qui maximise le surplus n'est pas ne´cessairement infe´rieur au salaire ne´gocie´par un de´le´gue´qui maximise le salaire. Cependant, si le Ana Mauleon and Vincent Vannetelbosch are Chercheurs Qualifie´s at the Fonds National de la Recherche Scientifigue, Belgium. We wish to thank two anonymous referees for valuable comments. The research of Ana Mauleon has been made possible by a fellowship of the Fonds Europe´en du De´veloppement Economique Re´gional (FEDER). Financial support from the Belgian French Community's program Action de Recherches Concerte´e 99/04-235 and from the research project BEC 2003-02084 (Spanish government) is gratefully acknowledged. syndicat est plus fort que la firme et la demande est e´lastique, alors le fait de de´le´guer la ne´gociation a`un de´le´gue´qui maximise le salaire va augmenter le salaire d'e´quilibre. Finalement, nous montrons que de plus longues gre`ves sont observe´es lorsque le syndicat de´le`gue la ne´gociation a`un de´le´gue´qui maximise uniquement le salaire.

We reconsider the Goyal and Moraga-González (Rand Journal of Economics, Vol. 32 (2001), pp. 686-707) model of strategic networks in order to analyse how government policies (e.g. subsidies) will affect the stability and efficiency of networks of R&D collaboration among three firms located in different countries. A conflict between stability and efficiency is likely to occur. When governments cannot subsidize R&D, this conflict will occur if public spillovers are not very small. However, when governments can subsidize R&D, the likelihood of a conflict is considerably reduced. Indeed, a conflict will arise only if public spillovers are very small or quite large. Copyright � 2007 The Authors; Journal compilation � 2007 Blackwell Publishing Ltd and The University of Manchester.