Dynamic Price Competition Research Articles

Switching Costs and Dynamic Price Competition in Network Industries

Motivated by policy makers' recent interest in reducing switching costs in various network industries to increase competition, this paper investigates how switching costs affect market outcome in such industries. The results show that the effects of switching costs on market concentration and prices critically depend on two factors: the strength of network effects and the quality of the outside good. For example, switching costs lower prices if network effects are modest and the outside good is attractive, but raise prices otherwise. Therefore, policy makers need to carefully evaluate those two factors in order to make informed decisions.

Dynamic Price Competition with Network Effects

I consider a dynamic model of competition between two proprietary networks. Consumers die and are replaced with a constant hazard rate. Firms compete for new consumers to join their network by offering network entry prices (which may be below cost). New consumers have a privately known preference for each network. Upon joining a network, in each period consumers enjoy a benefit which is increasing in network size during that period. Firms receive revenues from new consumers as well as from consumers already belonging to their network. Using a combination of analytical and numerical methods, I discuss various properties of the equilibrium. I show that very small or very large networks tend to price higher than networks of intermediate size. I also show that, around symmetric states, the gap between the large and the small network tends to widen (increasing dominance) whereas the opposite is true (reversion to the mean) around very asymmetric states.

Dynamic price competition with discrete customer choices

Abstract For many years, dynamic pricing has proven to be an effective tool to increase revenue in the airline and other service industries. Most studies, however, focused on monopolistic models and ignored the fact that nowadays consumers can easily compare prices on the Internet. In this paper, we develop a game-theoretic model to describe real-time dynamic price competition between firms that sell substitutable products. By assuming the real-time inventory levels of all firms are public information, we show the existence of Nash equilibrium. We then discuss how a firm can adapt if it knows only the initial – but not the real-time – inventory levels of its competitors. We compare a firm’s expected revenue under different information structures through numerical experiments.

Do Switching Costs Make Markets Less Competitive?

The conventional wisdom in economic theory holds that switching costs make markets less competitive. This article challenges this claim. The authors formulate an empirically realistic model of dynamic price competition that allows for differentiated products and imperfect lock-in. They calibrate this model with data from frequently purchased packaged goods markets. These data are ideal in the sense that they have the necessary variation to identify switching costs separately from consumer heterogeneity. Equally important, consumers exhibit inertia in their brand choices, a form of psychological switching cost. This makes the results applicable to the broad range of products that are distinctly identified (i.e., branded) rather than just to products for which there is a product adoption cost or explicit switching fee. In the simulations, prices are as much as 18% lower with than without switching costs. More important, equilibrium prices do not increase even in the presence of switching costs that are of the same order of magnitude as product price.

Dynamic Pricing of Perishable Assets Under Competition

We study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets. Each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon. Customers sequentially arrive at the market, make a purchase choice, and then leave immediately with some likelihood of no purchase. The purchase likelihood depends on the time of purchase, product attributes, and current prices. The demand structure includes time-variant linear and multinomial logit demand models as special cases. Assuming deterministic customer arrival rates, we show that any equilibrium strategy has a simple structure, involving a finite set of shadow prices measuring capacity externalities that firms exert on each other: equilibrium prices can be solved from a one-shot price competition game under the current-time demand structure, taking into account capacity externalities through the time-invariant shadow prices. The former reflects the transient demand side at every moment, and the latter captures the aggregate supply constraints over the sales horizon. This simple structure sheds light on dynamic revenue management problems under competition, which helps capture the essence of the problems under demand uncertainty. We show that the equilibrium solutions from the deterministic game provide precommitted and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart, when demand and supply are sufficiently large. This paper was accepted by Yossi Aviv, operations management.

Dynamic Pricing of Perishable Assets under Competition

We study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets. Each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon. Customers sequentially arrive at the market, make a purchase choice and then leave immediately with some likelihood of no-purchase. The purchase likelihood depends on the time of purchase, the product attributes and the current prices. The demand structure includes time-variant linear and MultiNomial Logit demand models as special cases. Assuming deterministic customer arrival rates, we show that any equilibrium strategy has a simple structure, involving a finite set of shadow prices measuring capacity externalities that firms exert on each other: equilibrium prices can be resolved from a one-shot price competition game under the current-time demand structure, taking into account capacity externalities through the time-invariant shadow prices. The former reflects the transient demand side at every moment and the latter captures the aggregate supply constraint over the sales horizon. This simple structure sheds light on dynamic revenue management problems under competition, which helps capture the essence of the problems under demand uncertainty. We show that the equilibrium solutions from the deterministic game provide pre-committed and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart, when demand and supply are sufficiently large.

Dynamic Price Competition with Network Effects

I consider a dynamic model of competition between two proprietary networks. Consumers die and are replaced with a constant hazard rate. Firms compete for new consumers to join their network by offering network entry prices (which may be below cost). New consumers have a privately known preference for each network. Upon joining a network, in each period consumers enjoy a benefit which is increasing in network size during that period. Firms receive revenues from new consumers as well as from consumers already belonging to their network.Using a combination of analytical and numerical methods, I discuss various properties of the equilibrium. I show that very small or very large networks tend to price higher than networks of intermediate size. I also show that, around symmetric states, the gap between the large and the small network tends to widen (increasing dominance) whereas the opposite is true (reversion to the mean) around very asymmetric states.

Do Switching Costs Make Markets Less Competitive?

The conventional wisdom in economic theory holds that switching costs make markets less competitive. This paper challenges this claim. We find that steady-state equilibrium prices may fall as switching costs are introduced into a simple model of dynamic price competition that allows for differentiated products and imperfect lock-in. To assess whether this finding is of empirical relevance, we consider a more general model with heterogeneous consumers. We calibrate this model with data from a frequently purchased packaged goods market where consumers exhibit inertia in their brand choices, a behavior consistent with switching costs. We estimate the level of switching costs from the brand choice behavior in this data. At switching costs of the order of magnitude found in our data, prices are lower than without switching costs.

Information and Drug Prices: Evidence from the Medicare Discount Drug Card Program

In early 2004, the U.S. Government initiated the Medicare Discount Drug Card Program, which created a market for drug cards that allowed their subscribers to obtain discounts on their prescription drug purchases. Pharmacy-level prices for several drugs were posted on the program website weekly from May 29, 2004 to December 31, 2005, as the largest undertaking in the history of government-sponsored information release aimed at promoting competition by facilitating access to prices. A large sample of pharmacy-level drug price data collected from the Medicare website for several weeks indicate that the program generated significant dispersion in prices across drug cards that persisted over time. Moreover, the time-path of prices was non-monotonic: the prices declined initially and rose later as the program matured. In contrast, contemporaneous control prices unrelated to the program that were collected from on-line drug retailers rose steadily over time, indicating that the program prices evolved in a way different from the general evolution of prices outside the program. In view of the institutional aspects of the program which prevented consumers from changing their card choices at will, the evolution of prices can be reconciled with models of dynamic price competition with consumer switching costs as in Klemperer (1987a,b). The estimates of savings under the program are also provided.

Dynamic price competition

We consider the model of price competition for a single buyer among many sellers in a dynamic environment. The surplus from each trade is allowed to depend on the path of previous purchases, and as a result, the model captures phenomena such as learning by doing and habit formation in consumption. We characterize Markovian equilibria for finite and infinite horizon versions of the model and show that the stationary infinite horizon version of the model possesses an efficient equilibrium where all the sellers receive an equilibrium payoff equal to their marginal contribution to the social welfare.

Dynamic Price Competition with Consumption Externalities

The dynamic price competition in a horizontally differentiated duopoly when consumers value previous market shares is analyzed. The conditions for the existence of stable Markov-Perfect Equilibrium...

Dynamic Price Competition with Price Adjustment Costs and Product Differentiation

We study a discrete time dynamic game of price competition with spatially differentiated products and price adjustment costs. We characterise the Markov perfect and the open-loop equilibrium of our game. We find that in the steady state Markov perfect equilibrium, given the presence of adjustment costs, equilibrium prices are always higher than prices at the repeated static Nash solution, even though, adjustment costs are not paid in steady state.This is due to intertemporal strategic complementarity in the strategies of the firms and from the fact that the cost of adjusting prices adds credibility to high price equilibrium strategies. On the other hand, the stationary open-loop equilibrium coincides always with the static solution. Furthermore, in contrast to continuous time games, we show that the stationary Markov perfect equilibrium converges to the static Nash equilibrium when adjustment costs tend to zero. Moreover, we obtain the same convergence result when adjustment costs tend to infinity.

Tacit collusion and international commodity taxation

The paper employs a model of dynamic price competition to study how international commodity taxation affects the stability of collusive agreements when producers in an international duopoly agree not to export into each other’s home market. We consider both the choice of international tax principle and the harmonization of tax rates and differentiate between a setting where production costs differ between countries, and a setting where exogenous tax rate differentials are the only asymmetry. The conclusions derived from this model differ strongly from those obtained under the assumption of competitive product markets.

Tacit Collusion Under Destination- and Origin-Based Commodity Taxation

The paper employs a standard model of dynamic price competition to study how international principles of value-added taxation affect the stability of collusive agreements when producers in an international duopoly agree not to export into each others's home market and tax rates differ across countries. In this framework, tacit collusion may be more likely to break up under either the destination or the origin principle, depending on the relation between costs of production and market size. A robust result is that tax rate harmonization increases the likelihood of tacit collusion under both tax principles considered.

Commitment and price competition in a dynamic differentiated-product duopoly

This paper characterizes linear Markov-perfect equilibrium in a duopolistic environment where firms engage in dynamic price competition. Firms have constant (but potentially different) marginal costs and produce differentiated products. We show that, for the case of linear demand, dynamically stable Markov-perfect equilibrium prices are strictly higher than one-shot Nash equilibrium prices, but lower than fully collusive (monopoly) prices. We provide closed-form solutions for the Markov-perfect equilibrium prices which, in principle, can be estimated given data on firm demand and costs. Our results suggest that static two-stage models of price commitment are on reasonably solid ground in that they might be viewed as a “reduced form” for more complicated dynamic models.

Dynamic Retail Price and Investment Competition

We develop a model of retail competition in which retailers select prices and investments in cost reduction. An equilibrium is constructed in which several identical firms enter and then engage in a phase of vigorous price competition. This phase is concluded with a shakeout, as a low-price, low-cost firm comes to dominate the market. A central feature of the equilibrium is that low prices are complementary with large investments in cost reduction. Even though the dominant firm's price rises through time, and initially may be below marginal cost, we argue that an interpretation of predatory pricing may be inappropriate.

Dynamic Price Competition, Briefly Sunk Costs, and Entry Deterrence

This article examines how the threat of entry constrains pricing behavior in a natural monopoly with briefly sunk costs. In the model of dynamic price competition explored here, costs are too briefly sunk to confer any strategic advantage to incumbency. Despite the lack of advantage to incumbency, the threat of entry exerts little discipline on prices. In the presence of a slight cost asymmetry, monopoly for the lower-cost firm is the unique equilibrium, regardless of which firm is initially the incumbent.