Games with a local permission structure: separation of authority and value generation

The priority value for cooperative games with a priority structure

“…These two models have been extensively studied in the literature (van den Brink, 2017;Algaba et al, 2017, survey some results) and have in common that the associated structure imposes some restriction on the formation of coalitions or on the subset of coalitions to which an allocation rule is sensitive. In van den Brink and Gilles (1996), van den Brink (1997) and van den Brink and Dietz (2014), the so-called conjunctive, disjunctive and local permission values are computed as the Shapley value of a restricted game in which only the "feasible" part of a coalition is productive, where the "feasible" part is the largest subset of the coalition that contains all the hierarchical superiors deemed necessary for the worth generation (these vary depending on the model: conjunctive, disjunctive or local). In the Shapley value for games with precedence constraints studied by Faigle and Kern (1992), the principle of the marginal vectors underlying the classical Shapley value is restricted to those orderings in which each agent must appear after its hierarchical superiors, preventing de facto the formation of some coalitions.…”