TY - JOUR
T1 - Interaction sheaves on continuous domains
AU - Abdou, Joseph
AU - Keiding, Hans
N1 - JEL classification: C70; D71
PY - 2009
Y1 - 2009
N2 - We introduce a description of the power structure which is inherent in a strategic 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 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 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 [Abdou, J., Keiding, H., 2003. On necessary and sufficient conditions for solvability of game forms. Mathematical Social Sciences 46, 243-260].
AB - We introduce a description of the power structure which is inherent in a strategic 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 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 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 [Abdou, J., Keiding, H., 2003. On necessary and sufficient conditions for solvability of game forms. Mathematical Social Sciences 46, 243-260].
KW - Faculty of Social Sciences
KW - Nash equilibrium
KW - strong equilibrium
KW - solvability
KW - effectivity
KW - acyclicity
U2 - 10.1016/j.jmateco.2009.05.005
DO - 10.1016/j.jmateco.2009.05.005
M3 - Journal article
SN - 0304-4068
VL - 45
SP - 708
EP - 719
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
IS - 11
ER -