Interaction Sheaves on Continuous Domains

We introduce a description of the power structure which is inherent in a strate- gic game form using the concept of an interaction sheaf. The latter assigns to each open set of outcomes a set of interaction arrays, specifying the changes that coalitions can make if outcome belongs to this open set. The interaction sheaf generalizes the notion of effectivity functions which has been widely used in im- plementation theory, taking into consideration that changes in outcome may be sustained not only by single coalitions but possibly by several coalitions, depend- ing on the underlying strategy choices. Also, it allows us to consider game forms with not necessarily finite sets of outcomes, generalizing the results on solvability of game forms obtained in the finite case in Abdou and Keiding (2003).