Collusion, Exclusion, and Inclusion in Random-Order Bargaining

This paper examines the profitability of three types of integration in a cooperative game solved by a random-order value ("e.g." the Shapley value). Collusion between players i and j is a contract merging their resources in the hands of one of them, say <formula i. This contract can be represented as a combination of exclusion, which lets i exclude j's resource but not use it himself, and inclusion, which lets i use j's resource but not exclude j from it. This representation yields a third-difference condition on the characteristic function that determines the profitability of collusion, generalizing existing results for specific games. Namely, collusion is profitable [unprofitable] when the complementarity of the colluding players is reduced [increased] by other players. Copyright The Review of Economic Studies Limited, 2003.