Abstract
Stability of matchings was proved to be a new cooperative equilibrium concept in Sotomayor (Dynamics and equilibrium: essays in honor to D. Gale, 1992). That paper introduces the innovation of treating as multi-dimensional the payoff of a player with a quota greater than one. This is done for the many-to-many matching model with additively separable utilities, for which the stability concept is defined. It is then proved, via linear programming, that the set of stable outcomes is nonempty and it may be strictly bigger than the set of dual solutions and strictly smaller than the core. The present paper defines a general concept of stability and shows that this concept is a natural solution concept, stronger than the core concept, for a much more general coalitional game than a matching game. Instead of mutual agreements inside partnerships, the players are allowed to make collective agreements inside coalitions of any size and to distribute his labor among them. A collective agreement determines the level of labor at which the coalition operates and the division, among its members, of the income generated by the coalition. An allocation specifies a set of collective agreements for each player.
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This paper was motivated from discussions with David Gale (1921–2008) in 1990. The main ideas were developed and elaborated and new ones were incorporated during my stay at Brown University in the fall of 2008. We thank two anonymous referees for their suggestions and helpful comments which contributed to the improvement of this work. This paper was partially supported by CNPq-Brazil.
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Sotomayor, M. Stability property of matchings is a natural solution concept in coalitional market games. Int J Game Theory 39, 237–248 (2010). https://doi.org/10.1007/s00182-009-0206-1
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DOI: https://doi.org/10.1007/s00182-009-0206-1