Inclusive Collusion Neutrality on Networks

In the context of cooperative games with transferable utility, an inclusive collusion grants each colluding player access to resources of all colluding players and therefore transforms a given game. Inclusive collusion neutrality requires that no group of players can change their total payoff with an inclusive collusion. Assuming that collusion formation is governed by a network defined over players, we show that if the network is cyclic, no solution satisfies inclusive collusion neutrality, efficiency, and the null-player property. Tree (acyclic) networks allow us to escape the impossibility: affine combinations of the hierarchical solutions satisfy the three axioms. Further, we establish that the latter family of solutions are characterized by the three axioms and linearity.

JEL Classification Numbers: C71

Key Words: inclusive collusion neutrality, hierarchical solution, network

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