Comments on: Games with a permission structure - A survey on generalizations and applications

Robert P. Gilles
2017 TOP - An Official Journal of the Spanish Society of Statistics and Operations Research  
Van den Brink's excellent survey brings together many established insights of how the exercise of hierarchical authority a ects the allocation of generated wealth among cooperative participants in the hierarchy. In particular, the survey considers the e ects of three di erent institutional rules through which authority is exercised. Under the conjunctive permission rule, every player has to obtain permission from all her superiors to participate in value-generating processes. is implies that
more » ... litions are only formable if they contain all (direct and indirect) superiors of its members. e disjunctive permission rule imposes that players obtain permission from at least one superior, limiting the authority that these superiors can exercise. Finally, under the local permission rule, the scope of authority is reduced further in that players only have to obtain permission from their direct superiors to participate in such value-generating processes. In this la er environment, authority is exercised directly only rather than directly and indirectly as is the case under the conjunctive and disjunctive permission rules. ese permission rules can be represented as imposing certain restrictions on coalition formation, particularly captured through an antimatroid-de ned as a collection of formable coalitions in the player set N that is closed under taking nite unions and satis es accessibility. 1 In particular, under the conjunctive permission rule, the antimatroid is additionally closed under nite intersections. Similarly, the disjunctive permission rule imposes certain other additional properties on the antimatroid of formable coalitions. In the axiomatic theories considered in this survey, the permission rules are not considered from the viewpoint of facilitating cooperation, but rather from the viewpoint that these rules restrict
doi:10.1007/s11750-017-0442-7 fatcat:ghvnxcfah5cddoez5bzadymucu