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Envelopes and Geometrical Covers of Side-Payment Games and Their Market Representations

Institut de Recherches Mathematiques Avancees, Universite Louis Pasteur, F-67084 Strasbourg Cedex, France
Center for Operations Research and Econometrics, B-1348 Louvain-La-Neuve, Belgium
Universite des Sciences Sociales de Toulouse and GREQE, Ecole Hautes Etudes en Sciences Sociales, ERA CNRS 983, Universite D'Aix-Marseille, Hospice de la Vielle Charite, F-13001 Marseille, France

This paper deals with issues concerning the core as a solution concept for games in coalitional form as well as the use of these games in representing economies of a certain formal type. Side-payment games are imbedded in the more general class of no-side-payment games. It is shown that to a given side-payment game having an empty core one may associate two different no-side-payment games with the same (nonempty) core: the "envelope" and the "geometrical cover." The discrepancy is explained in terms of market games.

Key Words: side-payment games; core; market games