Strategic vertical contracting with endogenous number of downstream divisions

We characterize vertical contracts in oligopolistic markets where each upstream firm may contract with multiple downstream firms (divisions). If the number of divisions is chosen before the terms of fee-and-royalty contracts, each upstream firm minimizes the number of its downstream firms. When the contracts are chosen sequentially, it is the leader that minimizes the number of divisions. Lastly, if the contracts are chosen before the number of divisions, or if the contracts involve either only fees or only royalties, then upstream firms do not have an incentive to minimize the number of their respective divisions.