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  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.