Optimal Pricing of a Duopoly Platform with Two-Sided Congestion Effect (original) (raw)

Optimal pricing of a two-sided monopoly platform with a one-sided congestion effect

International Review of Economics, 2010

This paper studies the optimal pricing of a two-sided monopoly platform when one side is affected by congestion. We show that the divide-and-conquer pricing strategy (or skewed pricing) depends not only on the relative magnitude of the sides’ price elasticities of demand but it also depends on the marginal congestion cost that an agent imposes on the others. Compared with the no-congestion case, this pricing strategy gives rise to some interesting features that violate the results of Rochet and Tirole (J Eur Econ Assoc 1:990–1029 in 2003, Rand J Econ 37:645–667 in 2006). In the case of equal price elasticities of demand, the no-congested side is charged the highest price. On the other hand, in the case of different price elasticities, the platform congestion pricing depends on a certain threshold of the marginal congestion cost. We show, under some conditions, that the divide-and-conquer pricing strategy is reversed. In the social context, the Rochet and Tirole’s (J Eur Econ Assoc 1:990–1029 in 2003) cost allocation condition is modified by the congestion cost. We show that the congestion does not only affect the buyers’ contribution to the sellers’ surplus, but it also affects the sellers’ contribution to the buyers’.

Price symmetry in a duopoly with congestion

2000

We show that in a duopoly operating in a congested market, with a general congestion function and an arbitrary distribution of consumer disutility for congestion, there cannot exist an asymmetric Nash equilibrium. We also show that whenever an equilibrium does exist it is unique. Closed form expressions for the symmetric equilibrium prices and profits are provided. JEL Classification Numbers: C72, D43.

Optimal capacity sharing of a two-sided monopoly platform: the case of a trade fair

We study in this paper the optimal capacity sharing of a private two-sided monopoly platform when positive indirect externalities and within-sides congestion simultaneously matter. Our paper concerns a trade fair that enables exhibitors and visitors to interact. In the short run equilibrium, we show that an increase in a side's willing-ness to pay in order to avoid congestion cannot only decrease its price but it also contributes at increasing the other's. Moreover, we show that the divide-and-conquer pricing strategy can be reversed insofar as the needed-more side can be no longer subsidized. In addition, we show, under certain conditions, that a side's price reaches whether a price-bottom or a price-ceiling while taking into considertion a change in the sides'one another valuations. In the long run equilibrium, we verify that the Cost Recovery Condition holds. Moreover, some in-teresting results that go in the same line with the two-sided market literature appear. ...

sided congestion effect

This paper studies the optimal pricing of a two-sided monopoly platform when one side is affected by congestion. We show that the "divide and conquer" strategy (or skewed pricing) depends not only on the relative magnitude of the sides' price elasticities of demand but it also depends on the marginal cost of congestion that an agent imposes on the others. Compared with the no congestion case, this pricing strategy gives rise to some interesting features that violate the results of Tirole (2003, 2006). In the case of equal price elasticities of demand, the no-congested side is charged the higher price. On the other hand, in the case of different price elasticities, the platform congestion pricing depends on a certain threshold of the marginal cost of congestion. We show, under some conditions, that the "divide and conquer" strategy is reversed.

Congestion pricing of inputs in vertically related markets

Research Papers in Economics, 2005

This paper conducts a welfare analysis of a two-part tariff that is applied to the congestion pricing of inputs supplied by a natural monopolist with increasing returns to scale to competitive firms that require an input in a fixed proportion to output. Congestion pricing of inputs is optimal for both the welfare-maximizing regulator and the profit-maximizing monopolist if it is applied in the form of a uniform price for the input. However, a two-part tariff for the congestion pricing of inputs is optimal if competition in the downstream market is imperfect or if there is demand uncertainty in the market.

Competition, bargaining power and pricing in two-sided markets

We develop a model of two-sided markets that illustrates the role of bargaining power between the two sides of the market. We are interested in the profit maximizing usage fees set by identical duopolistic platforms which engage in homogeneous, Bertrand-type competition. We find that for a sufficiently low marginal cost duopolistic two-sided competition reduces to a “grab-the-dollar” game with two asymmetric (pure) Nash equilibria. These equilibria are characterized by highly skewed prices, in which the side with all the bargaining power pays a minimum price. The other side of the market is used for cross-subsidization and is charged a high price. Compared to the monopoly outcome, competition lowers the total price charged to both sides, although the seller's equilibrium price may exceed the monopoly price. Both platforms enjoy excess profits.Key Words: platform competition, bargaining power, asymmetric equilibria, skewed pricing

Feasibility of predatory pricing in a capacity-constrained duopoly

Ricerche Economiche, 1993

Predatory pricing is feasibleonly if the minimax profit of the prey is strictly smaller than the expected profit in the corresponding Bertrand-Nash equilibrium. We completely characterize the conditions for feasibility of predatory pricing in Kreps and Scheinkman's model of capacity-constrained duopoly. The predator must have a capacity larger than that of the prey, and also larger than the Cournot capacity. Surprisingly, predatory pricing may be infeasible not only if the prey is too large but also if it is too small.

Second-Degree Price Discrimination by a Two-Sided Monopoly Platform

American Economic Journal: Microeconomics

We study second-degree price discrimination by a two-sided monopoly platform. The incentive constraints of the agents on the value creation side may be in conflict with internalizing externalities on the value capture side, which may render pooling optimal. Even without such conflict between the two sides, pooling may be optimal due to type-dependent Spence effects when the preferences of the marginal agents diverge from those of the average agents on the value capture side. We perform a welfare analysis of price discrimination and show that prohibiting price discrimination improves welfare when there is a strong conflict between the two sides. (JEL D42, D62, D82, L12, L82)

Monopoly pricing with network externalities

International Journal of Industrial Organization, 1999

How should a monopolist price a durable good or a new technology that is subject to network externalities? In particular, should the monopolist set a low ''introductory price'' to attract a ''critical mass'' of adopters? In this paper, we provide intuition as to when and why introductory pricing might occur in the presence of network externalities. Incomplete information about demand or asymmetric information about costs is necessary for introductory pricing to occur in equilibrium when consumers are small.

Congestion pricing, Bertrand oligopoly, and forward contracts for bandwidth

2007

We develop a pricing game modelling a monopoly and an oligopoly of Internet Service Providers selling bandwidth on two complementary segments of a multi-provider communication network. We consider pricing behavior when the oligopolists have previously sold part of their capacity by means of forward contracts, assuming all prices are set simultaneously. We find the equilibria in pure strategies where they exist. Where they do not exist, we find an equilibrium allowing the oligopolists to use mixed strategies. This requires solving an extension of the Bertrand-Edgeworth game with symmetric capacities and asymmetric contracting levels. Although providers have an incentive to sell forward contracts to insure against demand uncertainty, contracting also commits them to lower prices in general. We find that any equilibrium with contracting levels is asymmetric with a unique provider choosing the lowest level of contracting. By refraining from signing too many contracts, this provider guarantees a high general downstream price level at a private cost. An increase in the lowest contracting level results in negative marginal externalities on all other oligopolists. On the other hand, an increase in any other contracting level causes positive marginal externalities.