Mixed effectivity and the essence of stability

Effectivity functions (EFs) are models of coalitional power. An EF is said to be stable when its core is nonempty irrespective of player preferences. When the outcome space is composed of lotteries, each player's indifference map will be a family of parallel hyperplanes. By explicitly recognizing this fact, we are able to attain much sharper stability results than found using traditional infinite EF theory. Frequently the inherent nature of cooperative problems imposes further restrictions on the domain of admissible preferences. Results are further refined by incorporating these restrictions into concepts relating to stability. A number of applications are also presented, including a study of pure exchange in the EF framework.The author is very grateful to two anonymous referees whose suggestions greatly improved the quality of this paper. Errors or shortcomings are the sole responsibility of the author.