You can find this paper in (2017) Antitrust Law Journal, 81(2): 537–85. The paper looks at loyalty rebates and the use of price cost tests.
It begins by describing recent European and American case law on the matter, and highlights differences in the judicial approaches on both sides of the Atlantic (i.e. the classic distinction between European formalism and American effects-based tests). The authors then distinguish between economic tests of predation and exclusionary rebates, while noting that both include common economic mechanisms that can involve sacrificing profits.In the last and most important section, they argue that rebates and contracts containing conditions regarding how much buyers purchase from rival suppliers can raise serious anti-competitive concerns. From this point of view, a stricter treatment of exclusive contracts and some loyalty discounts might be justified – which may imply that evidence of above-cost prices may work as a safe harbour for predation, but not for exclusive dealing and loyalty rebates.
Overall, I think we may be seeing the development of a trend: even advocates for strict economic approaches are focusing more and more on elements not directly concerned with price when assessing the legality of business conduct. As is usual in these cases, ditching a bright-line rule for a slightly foggier standard that acknowledges the complexities of assessing rebates and the variety of effects they may have leads to a loss of legal certainty.
Given the variety of rebates and factual scenarios in which they are granted, there seems to be no clear and fast rule on how to identify anticompetitive rebates – which means careful analysis and multiple tools may need to be used in individual cases. This imposes larger costs on agencies and companies (and may enrich lawyers and economic consultants), but may be a cost worth paying: after all, rebates are usually pro-competitive. Furthermore antitrust law has (and should have, to my mind) a bias towards false negatives in this area, which means a rule of reason approach will usually be preferable except in certain exceptional circumstances.