Collusion-proof cost sharing mechanisms (Draft)

An auction type mechanism elicits the valuations for getting a good (service) from the agents, allocates some goods (service) to some agents and charge money only to the served agents. We characterize the mechanisms that are immune to three alternative types of collusion of the agents. Under full collusion, agents can coordinate misreports and transfer money between them. We show that only the fixed cost mechanisms, that offer units of good to the agents at a fixed price are immune to full collusion. On the other hand, if the utility profile is random and transfers of money between the agents are not available, agents may sign a contract and coordinate misreports ex-ante at every state of the world. We show that only sequential mechanisms are immune to this type of collusion. Finally, if the utility profile is deterministic and transfers of money between the agents are not available, a large class of mechanisms are immune to coordinated misreports of the agents. We characterize this class and show that it contains most of the mechanisms previously discussed in early literature of group strategyproof cost sharing.