Market share contracts, exclusive dealing, and the integer problem

This paper compares exclusive dealing and market share contracts in a model of naked exclusion. We discuss how the contracts work and identify a fundamental trade-off that arises: market share contracts are better at maximizing a seller's benefit from foreclosure (because they allow the seller to obtain any foreclosure level it desires), whereas exclusive-dealing contracts are better at minimizing a seller's cost of foreclosure (because, unlike with market share contracts, the seller does not have to overpay for the units it forecloses). We identify settings in which each can be more profitable and show that welfare can be worse under market share contracts.