Price symmetry in a duopoly with congestion (original) (raw)
Related papers
Optimal Pricing of a Duopoly Platform with Two-Sided Congestion Effect
Journal of Research in Industrial Organization, 2011
We study, in this paper, the impact of two-sided congestion effect on the pricing policy of a twosided duopoly platform. Relative to Armstrong (2006), we show that, with congestion effect, (i) competition for submarket share is softened, (ii) the divide-and-conquer pricing strategy is modified insofar as it depends upon the differential of the marginal congestion costs and (iii) each platform charges any agent of one side a price that covers not only the marginal congestion cost that he imposes on agents of his own side having joined its platform, as the traditional principle of the textbook congestion pricing, but also it covers the marginal congestion cost that he indirectly imposes on the of-his-type agents having chosen to join the rival platform. This issue matters despite there is no technical link between the two platforms.
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’.
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.
Dynamic Equilibrium at a Congestible Facility Under Market Power
SSRN Electronic Journal, 2015
Various contributions to the recent literature on congestion pricing have demonstrated that when services at a congestible facility are provided by operators with market power, the case in point often being a few airlines jointly using a congested airport, optimal congestion pricing rules deviate from the familiar Pigouvian rule that tolls be equal to the marginal external costs. The reason is that an operator with market power has an incentive to internalize the congestion effects that its customers and vehicles impose upon one-another, so that Pigouvian tolling would lead to overpricing of congestion. More recent contributions to this literature, however, have brought to the fore that when congestion at the facility takes on the form of dynamic bottleneck congestion à la Vickrey (1969), where trip scheduling is the key behavioural margin, there may exist no Nash equilibrium in arrival schedules for oligopolistic operators also under rather plausible assumptions on parameters. This paper investigates whether in such cases, an equilibrium does exist for another congestion technology, namely the Henderson-Chu dynamic model of flow congestion. We find that a stable and unique equilibrium exists also in cases where it fails to exist under bottleneck congestion (notably when the value of schedule late exceeds the value of travel delays). Our results suggest that self-internalization with only two firms leads to a considerable efficiency gain compared to the atomistic equilibrium (83% or more of the gain from first-best pricing in our numerical exercises). * Financial support from ERC (AdG Grant #246969 OPTION) is gratefully acknowledged. We are also grateful to Robin Lindsey for helpful suggestions.
Nash equilibria in singleton congestion games : Symmetric case
2010
This paper provides a simple formula describing all Nash equilibria in singleton congestion games, reducing the complexity of computing all these equilibria and giving a simple and short proof (without invoking the FIP or the potential function).
On the inefficiency of equilibria in congestion games
2005
We present a short geometric proof of the price of anarchy and price of stability results that have recently been established in a series of papers on selfish routing. This novel proof also facilitates two types of new results: On the one hand, we give pseudoapproximation results that depend on the class of allowable cost functions. On the other hand, we offer improved bounds on the inefficiency of Nash equilibria for situations in which the equilibrium travel times are within reasonable limits of the free-flow travel times, a scenario that captures empirical observations in vehicular traffic networks. Our results actually hold in the more general context of congestion games, which provide the framework in which we describe this work.
A formula for Nash equilibria in monotone singleton congestion games
2011
This paper provides a simple formula describing all Nash equilibria in symmetric monotone singleton congestion games. Our approach also yields a new and short proof establishing the existence of a Nash equilibrium in this kind of congestion games without invoking the potential function or the nite improvement property.
2006
We consider congestion pricing as a mechanism for sharing bandwidth in communication networks, and model the interaction among the users as a game. We propose a decentralized algorithm for the users that is based on the history of the price process, where user response to congestion prices is analogous to “fictitious play” in game theory, and show that this results in convergence to the unique Wardrop equilibrium. We further show that the Wardrop equilibrium coincides with the welfare maximizing capacity allo-
Symmetry in Network Congestion Games: Pure Equilibria and Anarchy Cost
2005
We study computational and coordination efficiency issues of Nash equilibria in symmetric network congestion games. We first propose a simple and natural greedy method that computes a pure Nash equilibrium with respect to traffic congestion in a network. In this algorithm each user plays only once and allocates her traffic to a path selected via a shortest path computation. We then show that this algorithm works for series-parallel networks when users are identical or when users are of varying demands but have the same best response strategy for any initial network traffic. We also give constructions where the algorithm fails if either the above condition is violated (even for series-parallel networks) or the network is not series-parallel (even for identical users). Thus, we essentially indicate the limits of the applicability of this greedy approach. We also study the price of anarchy for the objective of maximum latency. We prove that for any network of m uniformly related links and for identical users, the price of anarchy is \({\it \Theta}({\frac{{\rm log} m}{{\rm log log} m}}\) ).
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. ...