Yong Chao

Mixed Bundling in Two-Sided Markets in the Presence of Installed Base Effects

We analyze mixed bundling in two-sided markets where installed base effects are present and find that the pricing structure deviates from traditional bundling as well as the standard two-sided markets literature---we determine prices on both sides fall with bundling. Mixed bundling acts as a price discrimination tool segmenting the market more efficiently. Consequently, as a by-product of this price discrimination, the two sides are better coordinated, and social welfare is enhanced. We show unambiguously that platform participations increase on both sides of the market. After theoretically evaluating the impact mixed bundling has on prices and welfare, we take the model predictions to data from the portable video game console market. We find empirical support for all theoretical predictions. This paper was accepted by J. Miguel Villas-Boas, marketing.

Pay-What-You-Want Pricing: Can It Be Profitable?

Using a game theoretic framework, we show that not only can pay-what-you-want pricing generate positive profits, but it can also be more profitable than charging a fixed price to all consumers. Further, whenever it is more profitable, it is also Pareto-improving. We derive conditions in terms of two cost parameters, namely the marginal cost parameter for the seller, and the social preference parameter of a consumer to incorporate behavioral considerations for paying too little compared to her reference price.

STRATEGIC EFFECTS OF THREE‐PART TARIFFS UNDER OLIGOPOLY

A three-part tariff refers to a pricing scheme consisting of a fixed fee, a free allowance of units up to which the marginal price is zero, and a positive per-unit price for additional demand beyond that allowance. The three-part tariff and its variations are commonly used in both final-goods and intermediate-goods markets. Recently, the offering of three-part tariffs and the like by dominant firms has become a prominent antitrust issue. Existing studies have focused on monopoly models, interpreting the three-part tariff as a price discrimination device. In this paper, I investigate the strategic effects of three-part tariffs in a sequential-move game and offer an equilibrium theory of three-part tariffs in a competitive context. I show that, compared with linear pricing equilibrium and two-part tariff equilibrium, a three-part tariff always strictly increases the dominant firms (the leaders) profit when competing against a rival (the follower) with substitute products, in the absence of usual price discrimination motive. To explore the effects of a three-part tariff on welfare, I further perform comparative statics analysis using general differentiated linear demand system. I show that the competitive effect of a three-part tariff in contrast to linear pricing depends on the degree of substitutability between products: Competition is intensified when two products are more differentiated, yet softened when two products are more substitutable. This is in stark contrast with the competitive scenario posed by a two-part tariff: A two-part tariff always enhances competition and gives the highest total surplus of these three pricing schemes. Moreover, the rival firm always gets hurt in both profit and quantity sale when the dominant firm switches from linear pricing to a two-part tariff, yet it enjoys higher profit when the dominant firm moves from a two-part tariff to the more ornate three-part tariff, despite the fact that its quantity and market share are decreased even further. My findings offer a new perspective on three-part tariffs, a perspective which could help antitrust enforcement agencies distinguish the exclusionary three-part tariff from the procompetitive one.

All-Units Discounts as a Partial Foreclosure Device

All-units discounts (AUD) are pricing schemes that lower a buyer’s marginal price on every unit purchased when the buyer’s purchase exceeds or is equal to a pre-specified threshold. The AUD and related conditional rebates are commonly used in both final-goods and intermediate-goods markets. Although the existing literature has thus far focused on interpreting the AUD as a price discrimination tool, investment incentive program, or rent-shifting instrument, the antitrust concerns on the AUD and related conditional rebates are often their plausible exclusionary effects. In this article, we investigate strategic effects of volume-threshold based AUD used by a dominant firm in the presence of a capacity-constrained rival. We find that the AUD always increase the dominant firm’s profits, sales volume and market share over linear pricing or two-part tariff. At the same time, the AUD adopted by a dominant firm lead to “partial foreclosure�? of an equally or more efficient rival, in the sense that the rival’s profit, sales volume and market share are strictly reduced, as compared to linear pricing. The buyer’s surplus and total surplus could be either lower or higher under AUD, depending on the rival’s capacity level relative to the demand size. The intuition for our findings is that, due to the limited capacity of the rival, the dominant firm, that has a “captive�? portion of the buyer’s demand in the context of a single product, is able to use the AUD to leverage its market power on the “captive�? to “competitive�? portion of the demand, much like the tied-in selling strategy in the context of multiple products. Our analysis applies to other similar settings in which the dominant firm has some “captive�? market when it offers “must-carry�? brands or a wider range of products.

All-units discounts as a partial foreclosure device

All-units discounts (AUD) are pricing schemes that lower a buyer’s marginal price on every unit purchased when the buyer’s purchase exceeds or is equal to a pre-specified threshold. The AUD and related conditional rebates are commonly used in both final-goods and intermediate-goods markets. Although the existing literature has thus far focused on interpreting the AUD as a price discrimination tool, investment incentive program, or rent-shifting instrument, the antitrust concerns on the AUD and related conditional rebates are often their plausible exclusionary effects.In this article, we investigate strategic effects of volume-threshold based AUD used by a dominant firm in the presence of a capacity-constrained rival. We find that the AUD always increase the dominant firm’s profits, sales volume and market share over linear pricing or two-part tariff. At the same time, the AUD adopted by a dominant firm lead to “partial foreclosure” of an equally or more efficient rival, in the sense that the rival’s profit, sales volume and market share are strictly reduced, as compared to linear pricing. The buyer’s surplus and total surplus could be either lower or higher under AUD, depending on the rival’s capacity level relative to the demand size.The intuition for our findings is that, due to the limited capacity of the rival, the dominant firm, that has a “captive” portion of the buyer’s demand in the context of a single product, is able to use the AUD to leverage its market power on the “captive” to “competitive” portion of the demand, much like the tied-in selling strategy in the context of multiple products. Our analysis applies to other similar settings in which the dominant firm has some “captive” market when it offers “must-carry” brands or a wider range of products.

Why Discrete Price Fragments U.S. Stock Exchanges and Disperses Their Fee Structures

We propose a theoretical model to explain two salient features of the U.S. stock exchange industry: (i) sizable dispersion and frequent changes in stock exchange fees; and (ii) the proliferation of stock exchanges offering identical transaction services, highlighting the role of discrete pricing. Exchange operators in the United States compete for order flow by setting “make” fees for limit orders (“makers”) and “take” fees for market orders (“takers”). When traders can quote continuous prices, the manner in which operators divide the total fee between makers and takers is irrelevant because traders can choose prices that perfectly counteract any fee division. If such is the case, order flow consolidates on the exchange with the lowest total fee. The one-cent minimum tick size imposed by the U.S. Securities and Exchange Commission’s Rule 612(c) of Regulation National Market Systems for traders prevents perfect neutralization and eliminates mutually agreeable trades at price levels within a tick. These frictions (i) create both scope and incentive for an operator to establish multiple exchanges that differ in fee structure in order to engage in second-degree price discrimination; and (ii) lead to mixed-strategy equilibria with positive profits for competing operators, rather than to zero-fee, zero-profit Bertrand equilibrium. Policy proposals that require exchanges to charge one side only or to divide the total fee equally between the two sides would lead to zero make and take fees, but the welfare effects of these two proposals are mixed under tick size constraints.

Vertical Probabilistic Selling under Competition: The Role of Consumer Anticipated Regret

This paper studies probabilistic selling with vertically differentiated products when firms compete and consumers anticipate the potential post-purchase regret raised by possibly obtaining the inferior products. Intuitively, anticipated regret hurts the attractiveness of probabilistic selling. However, we find that probabilistic selling can be more profitable, and more likely to arise with anticipated regret than without it. This is due to the i°reverse quality discriminationi± (perceived quality of the random product becomes decreasing in consumer type at the competition margin), which increases the perceived differentiation, and may still maintain sufficient attractiveness of the random product for infra-marginal consumers. Meanwhile, it may hurt the competitor.

The Degree of Distortions under Second-Degree Price Discrimination

Under second-degree price discrimination, both types of consumers get efficient quantities when the net-of-cost valuation functions intersect at least once at some positive quantity and the point of intersection lies between the two peaks. Distortions can be upward or downward.

Pay-What-You-Want Pricing Under Competition: Breaking the Bertrand Trap

This paper investigates the viability of Pay-What-You-Want (PWYW) pricing when firms compete without restrictions of a minimum payment requirement. We show that the equilibrium outcomes are different when underpayers, consumers paying less than marginal cost, are present as opposed to when they are absent. In particular, when PWYW pricing is practiced without restricting the presence of underpayers or any minimum payment requirement, then the only two equilibrium structures are: either both firms use the posted price and earn zero profits, or one firm adopts PWYW pricing and the other uses the posted price. The asymmetric pricing equilibrium leads to a softening of price competition where both firms earn positive profits and the Bertrand Trap is broken.