Interaction Sheaves on Continuous Domains
We introduce a description of the power structure which is inherent in a strategic gameform 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 implementation theory, taking into consideration that changes in outcome may be sustained not only by single coalitions but possibly by several coalitions, depending on the underlying strategy choices. Also, it allows us to consider gameforms with not necessarily finite sets of outcomes, generalizing the results on solvability of game forms obtained in the finite case in Abdou and Keiding [Abdou, J., Keiding, H., 2003. On necessary and sufficient conditions for solvability of game forms. Mathematical Social Sciences 46, 243-260].
|Date of creation:||Dec 2009|
|Publication status:||Published in Journal of Mathematical Economics, Elsevier, 2009, 45 (11), pp.708-719. <10.1016/j.jmateco.2009.05.005>|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00633578|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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- Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
- Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 67-80.
- Abdou, Joseph & Keiding, Hans, 2003. "On necessary and sufficient conditions for solvability of game forms," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 243-260, December.
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