Collusion, Exclusion, and Inclusion in Random-Order Bargaining

This paper examines three types of contracts in a cooperative game solved by a random-order value (such as Shapley value). An exclusive contract delays the contribution of the excluded player j until the arrival of the excluding player i. It is profitable when j is complementary to other players in the absence of i. An inclusive contract brings the included player j forward to player i's arrival. It is profitable when j is substitutable to other players in the presence of i. Finally, a collusive contract between i and j can be modeled as a proxy agreement under which i always brings j with him. The profit from collusion therefore equals to the sum of profits from exclusion and inclusion. It is positive when i reduces the complementarity between j and the other players.