David Martimort, Paris School of Economics: "Screening Contracts As A Barrier To Entry"

A seller contracts with a downstream buyer under the threat of upstream entry.
The buyer has private information on his downward sloping demand and on the
efficiency gains of entry. Strategic and screening concerns interact in the design of
nonlinear contracts. We provide a rationale for the use of rebates, discounts and
minimal purchase requirements under various contracting scenarios. With marketshare
contracts, the incumbent designs nonlinear tariffs that depend on whether the
buyer also purchases from the entrant or not. Screening distortions are mitigated
and the incumbent's marginal prices come closer to but remain above marginal cost
when entry occurs. Entry is inefficient, reduced to decrease the buyer's information
rent, but it remains positively correlated with consumption. When restricted to
offer a single nonlinear tarif whether the buyer also purchases from the entrant or
not, the incumbent face a conflict between preventing entry which is now costly and
screening. Entry is no longer positively correlated with consumption and marginal
prices may be lower than marginal cost. The optimal contract shares key features
of an all-unit discount tarif.