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

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 AMS 1980 subject classification: Primary: 90D12 IAOR 1973 subject classification: Main: Games OR/MS Index 1978 subject classification: Primary: 234 Games/group decisions/cooperative Reprinted from Mathematics of Operations Research, 11(1), 19–29, February 1986. Institut de Recherches Mathématiques Avancées, Université Louis Pasteur Center for Operations Research and Econometrics, Louvain-la-Neuve Université des Sciences Sociales de Toulouse and GREQE.