We study behavior-based pricing (BBP) in a vertically differentiated model. Vertical differentiation is innately asymmetric because all customers prefer the higher-quality product when prices are equal. This asymmetry causes BBP to have different properties than symmetric horizontally differentiated models. We highlight two dimensions that affect the analysis: the role of quality-adjusted cost differences between the firms and the role of consumer discounting relative to firm discounting. In the second period, consistent with the prior literature, we find that there are conditions based on market shares and quality-adjusted costs under which either the low-quality firm or the high-quality firm—but not both—will reward its current customers with lower prices than it charges to new customers. We then consider whether these conditions can arise in a two-period equilibrium. We find that if consumers sufficiently discount the future periods, then firms at enough of a competitive disadvantage will reward their customers: i.e., the low-quality firm will reward its current customers if the quality-adjusted cost differential between the two firms is small, while the high-quality firm will reward its current customers if this cost differential is large. Conversely, we find that if consumers do not discount the future very much, then the firm at a competitive disadvantage (i.e., a low-quality firm competing against a low-cost high-quality firm, or a high-quality firm that has very high costs) can earn greater profits with BBP than without BBP, although there are cases where both firms may benefit from BBP. This paper was accepted by J. Miguel Villas-Boas, marketing.

This paper demonstrates that increased product differentiation will make it more difficult to sustain collusion when it is costly to coordinate or maintain collusion. This result holds for a wide range of models, including all those commonly used to model competition between differentiated products. This contrasts with the previous theoretical literature, which shows that, in the absence of these costs, greater differentiation can help foster collusion under some common models of product differentiation but is consistent with the empirical literature, which suggests that collusion tends to occur most among homogeneous firms.game theory, product differentiation, competition, collusion

I examine collusive bidder behavior in auctions with negative externalities and show that the optimal bidding scheme exhibits only partial rigidity. Because of externalities, a cartel not only has incentive to maximize gains from trade but also to minimize the probability of sales. I identify the tension between the two incentives and show that the more rigid the bidding scheme, the higher the possibility of sales. As the extent of externalities increases, the cartel finds it more important to keep a low probability of sales than to minimize payment to the seller. This results in a partially-rigid optimal collusive bidding scheme.

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