Abstract
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 improving path 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.
Highlights
Many social, economic and political activities are conducted by groups or coalitions of individuals.For example, consumption takes place within households or families; production is carried out by firms which are large coalitions of owners of different factors of production; workers are organized in tradeGames 2010, 1 unions or professional associations; public goods are produced within a complex coalition structure of federal, state, and local jurisdictions; political life is conducted through political parties and interest groups; and individuals belong to networks of formal and informal social clubs.The formation of coalitions has been studied adopting either the cooperative game-theoretic approach or the noncooperative one
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 well off, (ii) if there
We have proposed a concept, the farsightedly stable set of coalition structures, to predict which coalition structures may be formed among farsighted players
Summary
Economic and political activities are conducted by groups or coalitions of individuals.For example, consumption takes place within households or families; production is carried out by firms which are large coalitions of owners of different factors of production; workers are organized in tradeGames 2010, 1 unions or professional associations; public goods are produced within a complex coalition structure of federal, state, and local jurisdictions; political life is conducted through political parties and interest groups; and individuals belong to networks of formal and informal social clubs.The formation of coalitions has been studied adopting either the cooperative game-theoretic approach or the noncooperative one. Economic and political activities are conducted by groups or coalitions of individuals. Games 2010, 1 unions or professional associations; public goods are produced within a complex coalition structure of federal, state, and local jurisdictions; political life is conducted through political parties and interest groups; and individuals belong to networks of formal and informal social clubs. The formation of coalitions has been studied adopting either the cooperative game-theoretic approach or the noncooperative one. The cooperative approach has first proposed myopic notions of stability such as core-stability, β-stability, α-stability, δ-stability or γ-stability (see Hart and Kurz [1]). These concepts assume that deviations cannot be countered by subsequent deviations. Farsightedness of the coalitions means that a coalition considers the possibility that, once it acts, another coalition might react, a third coalition might in turn react, and so on without limit.
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