This article analyses contractual situations between many principals and many agents. The agents have private information, and the principals take actions. Principals have the ability to contract not only on the reports of the agents but also on the contracts offered by other principals. Contracts are required to be representable in a formal language. The main result of the article is a characterization of the allocations that can be implemented as equilibria in our contracting game. We then restrict attention to exclusive-contracting environments, in which the agent may select the contract of at most one principal. In this setting, our characterization result implies that principals can collude to implement the monopolist outcome. Finally, in general, equilibrium contracts turn out to be incomplete. That is, a contract will restrict the action space of a principal but will not necessarily determine a single action.
