Games with a local permission structure: separation of authority and value generation
The paper concerns games with a local permission structure, where each player needs permission from its predecessors to generate worth, but not to give permission to its own successors. After the introduction in Section 1, where the authors cite the related literature and state the focus of the paper, Section 2 presents the preliminaries on cooperative TU-games, games with a permission structure, peer group games, and digraph games. In Section 3 it is shown that peer group games are a special class of weighted digraph games (Proposition 3.1). More precisely, for every peer group situation, the associated peer group game coincides with the digraph game on the transitive closure of the peer group tree. It is also shown (Example 3.2) that not every weighted digraph game is a peer group game. Proposition 3.4 lists a series of results in the digraph game associated to a weighted digraph, in particular, on the relation between the bargaining set and the core, the kernel and the pre-kernel, the core and the selectope, on the positions of the nucleolus and the Shapley value in the core, and on the relation between the core and the Weber set. Section 4 deals with locally restricted games and presents a number of new results. It is shown (Proposition 4.1) that the digraph game associated to a transitive digraph equals the conjunctive restricted game of the corresponding additive game on that digraph as permission structure. The authors generalize (weighted) digraph games and games with a permission structure and focus on locally restricted games, where each player needs permission only from its direct predecessors to cooperate. The notions of active set and authorizing set are defined and some properties of these sets are stated (Propositions 4.6 and 4.8). Besides proving some other results, it is also argued that the locally restricted approach to games with a permission structure generalizes the conjunctive approach and digraph games. In Section 5 the local (conjunctive) permission value is defined and considered. The authors provide two axiomatic characterizations of the local permission value (Theorems 5.3 and 5.4). They also show that while the conjunctive permission value satisfies veto monotonicity (Proposition 5.5), the local permission value does not satisfy veto monotonicity (Example 5.6). The authors conclude in Section 6 with a short discussion on an alternative approach to games with a local permission structure. While the conjunctive approach is applied in the paper, one could apply the disjunctive approach, where it is assumed that a player that has a predecessor needs permission of at least one of its predecessors to cooperate with other players.
scientific article; zbMATH DE number 6305089
scientific article