Bertrand Model Research Articles

A Primer on AIDS-Based Models in Antitrust Analysis

The purpose of this paper is to provide an introduction to AIDS-based demand systems (i.e., those based on Deaton and Muellbauer's Almost Ideal Demand System). We discuss derivation of the AIDS model from its microeconomic foundations, clearly state the assumptions underlying AIDS, and provide a primer on how to implement the model in practice. We use a high level of detail to show every step of the AIDS process. We detail the algebra because the original articles by either Deaton and Muellbauer (in 1980) or Hausman et al. (in various papers over several years) skip most of the steps. We discuss using the AIDS model by itself and in two variations of Hausman et al.’s multilevel systems. We briefly discuss some pitfalls common to all demand systems. Finally, at the end of this document, we provide an example of how the elasticities may be used to predict post-merger price changes via a linear approximation to the Bertrand model.

The Dynamics of Bertrand Price Competition with Cost-Reducing Investments

We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to “leapfrog” their rival to attain low-cost leadership – at least temporarily. We show that leapfrogging occurs in equilibrium, resolving the Bertrand investment paradox., i.e. leapfrogging explains why firms have an ex ante incentive to undertake cost-reducing investments even though they realize that simultaneous investments to acquire the state of the art production technology would result in Bertrand price competition in the product market that drives their ex post profits to zero. Our analysis provides a new interpretation of “price wars”. Instead of constituting a punishment for a breakdown of tacit collusion, price wars are fully competitive outcomes that occur when one firm leapfrogs its rival to become the new low cost leader. We show that the equilibrium involves investment preemption only when the firms invest in a deterministically alternating fashion and technological progress is deterministic. We prove that when technological progress is deterministic and firms move in an alternating fashion, the game has a unique Markov perfect equilibrium. When technological progress is stochastic or if firms move simultaneously, equilibria are generally not unique. Unlike the static Bertrand model, the equilibria of the dynamic Bertrand model are generally inefficient. Instead of having too little investment in equilibrium, we show that duopoly investments generally exceed the socially optimum level. Yet, we show that when investment decisions are simultaneous there is a “monopoly” equilibrium when one firm makes all the investments, and this equilibrium is efficient. However, efficient non-monopoly equilibria also exist, demonstrating that it is possible for firms to achieve efficient dynamic coordination in their investments while their customers also benefit from technological progress in the form of lower prices.

Differentiated Bertrand markets: restoring the minimum differentiation principle

I introduce non-perfect substitutability between products into the spatial Bertrand model. I show that if goods are complements, the firms always agglomerate. If goods are substitutes, the firms agglomerate if the transportation costs are not too high.

Chaotic dynamics and chaos control in differentiated Bertrand model with heterogeneous players

PurposeThe purpose of this paper is to investigate the chaotic dynamics behaviours and chaos control of differentiated Bertrand model.Design/methodology/approachThe paper analyzes a nonlinear differentiated Bertrand duopoly game by using the theory of bifurcations of dynamical system, where players have heterogeneous expectations and nonlinear cost function: two types of players are considered – bounded rational and naive expectation. The equilibrium point and local stability of the duopoly game are investigated.FindingsThe paper demonstrates that as some parameters of the game are varied, the stability of Nash equilibrium is lost through period doubling bifurcation. The chaotic features are justified numerically via computing Lyapunov exponents, and sensitive dependence on initial conditions. By using the delay feedback control method, the authors have made the system form chaotic state to stable state.Originality/valueThis paper fulfils an identified need to study the diversity of expectations and how to lead to rich dynamics and complexity.

THE NATURE OF OUTSOURCING RELATIONSHIPS: EVIDENCE FROM OAP PRICES

I. INTRODUCTION The dramatic growth in international outsourcing has fueled the expansion of international trade and deepened international integration. (1) Developments in outsourcing attract public attention due to concern that improvements in information technologies enable companies to relocate production or assembly activities to lower-cost overseas locations. (2) However, while international outsourcing allows firms to take advantage of factor price differences, Grossman and Helpman (2005) demonstrate that country cost differences are not sufficient by themselves to guarantee outsourcing, as international outsourcing decisions are based on many factors including the costs of search and customization. More generally, new research in international trade recognizes information as a key element in the globalization process. However, informational improvements, such as reduced communication costs or increasingly sophisticated bar code transmission and management tools may not affect all producers uniformly. As Ranch and Trindade (2003) show, product differentiation in consumption or production, when combined with informational uncertainty, produces a degree of natural protection. For this reason, information technology improvements are likely to deliver the greatest increases in global integration for those markets where the matching of differentiated partners is critical to the formation of new international partnerships. Similarly, as noted by Antras (2003) and Bernard et al. (2010), the organization of a firm's global operations depends further on factors including the importance of headquarters investments and the degree of product contractibility. (3) A key goal of this paper is to study whether outsourcing decisions are consistent with outsourcing models that feature search and adaptation costs. To this end, this paper studies U.S. outsourcing conducted under the auspices of the overseas assembly program, or OAP. The OAP program was designed to allow firms to avoid tariffs on U.S.-origin inputs that they utilized in final goods they assembled overseas. Thus, while the OAP does not include all U.S. outsourcing activities--it does not capture U.S. assembly of foreign parts, or overseas contract manufacturing that is based on U.S. designs and specifications--OAP imports provide insight into a wide swath of U.S. outsourcing and represented 8.5% of U.S. import value during the sample period. Since the OAP provides tariff benefits to manufacturers who use U.S. inputs in their overseas production, it is administered by U.S. customs. Consequently, while the OAP provides insights into manufacturing outsourcing decisions, it does not provide information on developments in services outsourcing. Since OAP exempts U.S. inputs from tariffs, the program requires participating firms to provide detailed information on the U.S. and foreign content of their outsourcing imports. Thus, OAP data records facilitate the precise measurement of cost shocks and trade frictions at the country-product level. In particular, heterogeneity in input choices both across countries and products can be exploited to identify cost pass-through and general price responses for outsourcing imports. For example, year-by-year pass-through can be estimated by regressing yearly OAP price changes at the product-country level on product-country cost changes. Plots of the year-by-year coefficients in Figure 1 show that the raw rate of OAP pass-through ranged from 6% to 23%. (4) However, accurate outsourcing pass-through estimation requires a theory-based estimation framework that controls for economic factors that also influence price decisions. This paper adopts Feenstra's (1989) passthrough model, which is modified to account for the cost structure and tariff treatment facing outsourcing firms who produced products for import under the OAP. This framework, which is based on a Bertrand model of competition in internationally differentiated goods, focuses its attention on cost pass-through and on the degree to which producers emulate the price changes of their competitors. …

Bertrand competition with asymmetric costs: Experimental evidence

We provide supporting evidence from the laboratory for the Nash predictions of the homogeneous-good Bertrand model under asymmetric constant unit costs.

Does Cost Uncertainty in the Bertrand Model Soften Competition?

The answer is no. Although naive intuition may suggest the opposite, uncertainty about costs in the homogeneous-good Bertrand model intensifies competition: it lowers price and raises total surplus (but also makes profits go up). For some economic environments, this is implied by Hansen’s (RAND, 1988) analysis of a procurement auction. However, several authors appear to have overlooked Hansen’s results. Moreover, his results are derived under two assumptions that, if relaxed, conceivably could reverse them. The contributions of the present paper are threefold. First, it clarifies the implications of Hansen’s results for the relationship between uncertainty and competition in the Bertrand model. Second, it shows that his results hold also if drastic innovations are possible. Finally, the paper assumes asymmetric cost distributions and shows, using numerical methods, that then uncertainty lowers price and raises total surplus even more than under symmetry. If the asymmetry is large enough, however, industry profits are lower under uncertainty. This is in contrast to the known results and reinforces the notion that uncertainty intensifies competition rather than softens it.

Multidimensional Game of Cournot-Bertrand Model with Incomplete Information and Its Analysis

According to the theory of multidimensional game, the paper studies the two-dimensional game of Cournot-Bertrand model with incomplete information and its equilibrium, when the two companies have some of the old and the new alternative products. It shows that for the new and old products have no substitute, the one-dimensional static game of Cournot and Bertrand model is a special case of the two-dimensional static game model. Also, it comes to the conclusion that the equilibrium of two-dimensional static game is better than that of one-dimensional static game of Cournot and Bertrand model.

The Effect of Mobile Termination Rate Changes on Fixed Markets in Australia

Competitive mobile network owners may have some discretion over the interconnection prices they charge other mobile and fixed network owners for terminating calls on their networks. These interconnection prices are typically regulated. Recent regulatory debates have focused on whether competition will result in suppliers passing through any future reductions in interconnection prices to retail prices and whether there should be any regulated retail price controls to force pass through. In this paper, we calibrate a standard differentiated Bertrand model of competition to the Australian fixed network telephony market for the 2010/11 financial year. We find that the fixed network operators would pass through to retail prices most of the reduction in their marginal cost caused by a reduction in the interconnection price. Further, social welfare would be higher without regulated retail price controls that force interconnection price reductions to be passed through to fixed-to-mobile calls.

Analysis of Game Theory on the Price of Supply Chain Based on Bertrand Model

As market competition intensifies, Price competition as the most common and effective way of market competition among operators is quite active. Used game theory, analysis price game and inter-enterprise competition by Bertrand model, and illustrated the importance of product differentiation and build the core competitiveness by case.

Complexity of triopoly price game in Chinese cold rolled steel market

This paper considers a Bertrand model based on nonlinear demand functions which are closer to reality and different from previous studies. We apply the model into Chinese cold rolled steel market and study game process of triopoly. By using the theory of bifurcations of dynamical systems, local stable region of Nash equilibrium point is obtained. Simulations show complex dynamical behaviors of the system. The results illustrate that altering the relevant parameters of system can affect the stability of Nash equilibrium point and cause chaos to occur, and the complex dynamical behaviors will disappear by parameters control method. The results have an important theoretical and practical significance to Chinese cold rolled steel market.

Why Can’t We All Just Get Along: Structural Modeling and Natural Experiments in Merger Analysis

Economists have two basic methodologies: structuralism, in which formal economic models control the analysis, and experimentalism, in which economic theory guides the analysis, but data from experiments determines the policy recommendation. The choice between the two approaches is often quite controversial, although each approach has its own strengths and limitations. Under either approach, the scientific method requires testing and, when choosing between models with comparable empirical support, verification. We describe how these approaches play out in merger analysis; where Cournot and Bertrand models of competition are the standard Structuralist tools. In contrast, Experimentalists generally search for some type of evidence of a relationship between structure and market performance. Which methodology is superior for merger analysis depends first on empirical testing of the relevant theories and then on how closely the facts of the market match the assumptions of the relevant economic theory and how much precision the analysis requires to generate a useful conclusion. We illustrate these tradeoffs with examples from three recently-litigated cases.

Research on Complex Mechanism of Oligarchy Pricing Based on Price Repeated Game Model

Based on domestic and international study, this paper proposes an innovative Bertrand model and discusses its complex dynamics characteristics. Results show that the best choice for oligopoly is to reduce price adjustment speed and the satisfactory game result is to maintain equilibrium price. According to oligopolies’ game strategy, the paper uses parameters adjustment control method to make the chaotic state of price stable at the equilibrium state.

The Cournot–Bertrand model and the degree of product differentiation

We consider a duopoly model with a Cournot-type firm and a Bertrand-type firm. Both survive and the equilibrium is stable when there is sufficient product differentiation. With no differentiation, only the Cournot-type firm survives, and the outcome is perfectly competitive.

Symmetric duopoly and price competition. Case study without residuals.

Price competition is seldom mentioned in the economic literature. Models like Cournot duopoly and Stakleberg duopoly assumed that firms compete through quantity. Bertrand duopoly assumed that firms compete through price simultaneously. This paperwork assumes that firms compete through price sequentially. It made also different assumptions from Bertrand model like finite production capacity, fix costs, constant returns and competition on two markets (market for product and market for raw material).

Price Interventions in Bertrand Oligopoly with Costly Entry

When firms set prices and face entry costs, efficiency in production and in entry are not simultaneously achieved, generating the possibility that regulatory interventions can lead to efficiency enhancements. We show through the Bertrand model that in markets with public entry and regular downward-sloping demand, if firms are symmetric and engage in symmetric behaviour in equilibrium, a low price floor, close to the marginal cost, can induce a Pareto improvement, leaving firms at least indifferent, while enhancing consumers’ surplus. The effect may leave a trace when entry costs are low. The optimal floor-ceiling combination fixes the price, equating the two.

Container terminal concessions: A game theory application to the case of the ports of Pakistan

The objective of this article is to analyse the effect of the type of concession contracts on port user surplus and on profits of terminal operators (or port authorities) with the help of game theory. We have selected three ports in Pakistan to perform this analysis. These ports function as ‘landlords’ and have signed concession contracts with private container terminal operators. However, the features of the contracts at present are different for each terminal. We analyse four cases in this article. The first case is the present situation in which we treat competition between terminals as a Bertrand game in which each terminal non-cooperatively determines charges for container handling and pays fees to port authorities according to the contract. The Bertrand model seems to reproduce, to a satisfactory degree, the market shares and handling fees observed. Furthermore, in the second and third cases, a cost-benefit analysis is conducted by solving the Bertrand model. The results reveal that in the long run it is profitable for the Karachi Port to establish a same fixed fee contract with its private terminals. However, users are better off in a situation where a percentage fee concession contract would be adopted instead. The game theoretic framework is then extended to the analysis of the strategic decision faced by port authorities with respect to the trade-off between unit fees and annual rent in the last case. An optimal concession contract is obtained that is feasible for both parties in the sense that it contains high unit fees (variable cost) and low annual rent (fixed cost).

99 Cent: Price Points in E-Commerce

This paper attempts to shed light on the pricing behaviour of firms or sellers in market places with price competition. In particular, it aims at testing the mechanism that lies at the heart of one of the most famous models in economics, namely the Bertrand model of competition. This model suggests that firms' profits will be zero as soon as there are at least two sellers in the market. The model is built on the idea that consumers will go to the cheapest shop, even if the differences in prices are infinitesimal. As a result, firms are tempted to undercut their opponents' price by a small amount and they do so over and over until they end up charging the cost at which they produce their products. However, the underlying assumption is at odds with the observation that consumers typically do not care very much about a single cent and the predicted outcome clearly goes against the fact that many prices end in 99c. If sellers really charged the price at which they buy or produce a good or a service, we should observe all possible price endings. Basu (2006) argues that the prevalence of 99 cent prices in shops can be explained by consumers who disregard the rightmost digits of the price. This bounded rational behaviour leads to an Bertrand equilibrium with positive mark-ups allowing firms to make at least small profits. We use data from an Austrian price comparison site, which bears the advantage that in such an environment other factors than price both can be observed online and play a minor role. Price comparison sites are therefore highly suited for our test. We find results highly compatible with Basu's theory. We can show that price points - in particular prices ending in 9 - are more frequent than other endings and have significant impact on consumer demand. This shows that the mechanism that was postulated by Bertrand is not in place. Consumers do not necessarily choose the cheapest price and they even less do so when the Euro digits of the price are the same (i.e. when the difference is small). Moreover, the nine-ending prices are sticky: neither the price-setter itself wants to change them nor the rivals do underbid these prices, if they represent the cheapest price on the market. This might either show that shops seem to believe that it is no use to only slightly undercut a rival's price if this doesn't trigger a change in the Euro, or it is an indication that there might be some sort of silent agreement to not undercut a price ending in 9. Our findings shed new light on the behaviour of consumers and firms, and propose that theoretical investigations on competitive behaviour should consider discrete state spaces, i.e. markets where the smallest plausible price change is by a Euro or at least by a full Cent.

Demand forecast information sharing in the competitive online and traditional retailers

An important strategic issue for retailing business managers to study is the information strategy. In this paper, we develop a profit-maximization model to investigate the benefits of demand forecast information sharing for the competitive online and traditional retailers with the consideration of the compatibility of the product with online marketing. Both retailers use a Bertrand model to compete. We analyze and compare two scenarios: (1) when forecast information is not shared between the online and traditional retailers; (2) when forecast information is shared between the online and traditional retailers. Our results show that both the online and traditional retailers will be better off from information sharing. Especially when the channel forecast is less accurate, the product is more compatible with online marketing, and the market is more volatile, both retailers will profit more. Based on our results, optimal strategies are derived and probable paths of future research are identified.

Optimal Auction Design and Equilibrium Selection in Sponsored Search Auctions

In analyses of sponsored search auctions for online advertising, it is customary to model the dynamic game of incomplete information by considering a static game of complete infor mation. This approach is used in Benjamin Edelman, Michael Ostrovsky and Michael Schwarz (2007) (EOS), Hal R. Varian (2007), and the subsequent literature. Modeling complex interactions in uncertain environments as games of complete information has a long history. For example, the Bertrand model of oligopolistic competition posits that companies know their competitors' costs based on their experience from prior interactions. The use of a static game of complete infor mation often offers important benefits. For one, it is tractable?avoiding complex multi period information sets in a dynamic game. Furthermore, a suitably chosen static game can capture important characteristics of the under lying dynamic game. When a game is repeated over an extended period, there is good reason to think participants will learn many characteris tics of their counterparts?supporting the use of a complete information model. Yet the use of a static game of complete information is also unsatisfying. There is no clear way to identify which (if any) equilibria of the static game of complete information are a relevant approximation of the equilibria of the dynamic game of incomplete information.