Bertrand Competition Research Articles

When the Threat is Stronger than the Execution: Trade and Welfare Under Oligopoly

We compare trade liberalization under Cournot and Bertrand competition in reciprocal markets. In both cases, the critical level of trade costs below which the possibility of trade affects the domestic firm’s behavior is the same; trade liberalization increases trade volume monotonically; and welfare is U-shaped under reasonable conditions. However, welfare is typically greater under Bertrand competition; for higher trade costs the volume of trade is greater under Cournot competition, implying a “van-der-Rohe Region” in parameter space; and, for even higher trade costs, there exists a “Nimzowitsch Region”, where welfare is higher under Bertrand competition even though no trade takes place.

Cournot and Bertrand Competition in a Mixed Oligopoly With a Corrupt Public Firm

We analyze a mixed duopoly where the government runs the public firm partly with the objective of maximizing the profits of the private firm. The incumbent does so to secure funding for its political party. We find that it results in lower (higher) overall output goods are substitutes (complements) compared to the standard mixed oligopoly case. Price charged by the public firm is higher (lower) when goods are substitutes (complements), while price charged by the private firm is always higher compared to the standard case. We find that the social welfare is higher in Bertrand competition only in cases when the weight given to the private firm’s profit is low, else it is higher under Cournot competition. We also find that it is optimal from the social welfare point of view that the public firm place some weight on the profit function of the private firm in the case of Cournot competition and no weight at all in the case of Bertrand competition.

Consumer Search and the Uncertainty Effect

We consider a model of Bertrand competition where consumers are uncertain about the qualities and prices of firms' products. Consumers can inspect all products at zero cost. A share of consumers is expectation-based loss averse. For these consumers, a purchase plan, which involves buying products of varying quality and price with positive probability, creates scale-dependent dis-utility from gain-loss sensations. Even if their degree of loss aversion is modest, they may refrain from inspecting all products and choose an individual default that is first-order stochastically dominated. Firms' strategic behavior can exacerbate the scope for this uncertainty effect', and sellers of inferior products may earn positive profits despite Bertrand competition. We find suggestive evidence for the predicted association between consumer behavior and loss aversion in new survey data.

Horizontal Outsourcing and Price Competition: The Role of Sole Sourcing Commitment

Previous studies on horizontal outsourcing between competing duopolists emphasize cost factors such as economies of scale and/or variable cost advantages in Cournot markets as potential explanations. This paper studies horizontal outsourcing when two competing firms engage in Bertrand competition, and highlights the important role of sole sourcing commitment. We adopt the framework of a duopolistic multi-stage game that comprises of an incumbent and an entrant. The incumbent has the technology know-how to make a key component in-house, and the entrant, who is a rival of the incumbent in the downstream market, can source the component either from the incumbent or from a supplier that does not participate in the end product market. We find that if the entrant commits to sole sourcing, horizontal outsourcing can occur when the incumbent has a component cost advantage or even a small cost disadvantage over the alternative supplier. Specifically, if the component cost gap is small, horizontal outsourcing may soften downstream market competition and benefit both firms at the expense of inducing higher prices for the consumers. If the incumbent has a significant cost advantage, horizontal outsourcing may lead to increased downstream price competition by expanding the total supply of end products. Without sole sourcing commitment, horizontal outsourcing occurs only if the incumbent has a cost advantage, and it always strengthens downstream price competition and benefits the consumers. In contrast, when the firms engage in downstream Cournot competition, sole sourcing commitment has no impact on the adoption of horizontal outsourcing, and the entrant sources from her rival only when the incumbent enjoys a significant component cost advantage. Finally, we also study various model extensions to confirm the robustness of our main results to key model assumptions.

Agency or Wholesale? The Role of Retail Pass-Through

With the rapid growth of e-commerce, agency selling is currently gaining popularity among online retailers (e-tailers). Prior research implicitly abstracts away cross-brand pass-through under traditional wholesale selling (i.e., how the retail price of another brand adjusts to changes in a given brand's wholesale price) and suggests that a shift to agency selling benefits e-tailers but harms suppliers. As an important counterweight to this result, we discover that an e-tailer's choice regarding selling format is critically moderated by retail pass-through behavior. On the one hand, agency selling can improve channel efficiency compared to wholesale selling. On the other hand, the relative intensity of supplier competition between these two selling formats is ambiguous. We show that the existing result applies only for a nonnegative cross-brand pass-through rate (e.g., under linear demands); otherwise (e.g., under multiplicative or exponential demands), the opposite may hold. Interestingly, we find that the conflict over the preference of selling format may not arise, and that all channel members could be better off with wholesale selling. Compared to the case of Bertrand competition, the e-tailer is even more likely to adopt wholesale selling under Cournot competition. Finally, under agency selling with an endogenous commission fee, we advise caution regarding the seemingly innocuous normalization of suppliers' marginal costs. Surprisingly, suppliers may benefit from higher marginal costs. Overall, our findings not only shed light on the theory of agency selling but also provide a plausible explanation for the observation that wholesale selling continues to prevail in online markets.

Ordoliberal theory and gas market in Germany within the framework of international energy cooperation

German economic policy is a special model of a coordinated market economy, which is based on the tradition of ordoliberalism. This theoretical concept is at the core of the regulation of most economic processes in Germany, and its energy markets are no exception. The article analyses the present state of German gas industry, its transformation in connection with the introduction of the Third Energy Package, the liberalization and development of gas projects. The authors compare the main results of the reforms and the stipulations of the ordoliberal theory. The conclusion is that the German government generally upholds this concept, although sometimes the consequences are of negative nature, manifested in rising prices, added complexity of international natural gas trade, especially with the largest supplier – the Russian Federation. Using the Bertrand competition model, the article justifies the conditions under which the export of liquefied natural gas is beneficial for the Russian Federation.

Antidumping protection and welfare in a differentiated duopoly

This paper employs a two-country Cournot model to investigate the protection and welfare effects of an antidumping (AD) duty and a price-undertaking policy under different dumping measures (i.e., injury margin and dumping margin) in a differentiated duopoly. We show that the welfare levels of the host country and the world as a whole are lower under a price-undertaking policy than an AD-duty policy. However, the former is superior to the AD-duty policy in terms of protection. These results are robust even if the firms engage in Bertrand competition.

Network externalities and process R&D: A Cournot–Bertrand comparison

This paper examines the implication of the nature of competition in a market with network externalities on strategic investment in process R&D by firms. It shows that network externalities have a larger positive effect on process R&D under Bertrand competition than that under Cournot competition. If network externalities are sufficiently strong, regardless of the degree of product differentiation, Bertrand firms have a stronger incentive for process R&D than Cournot firms. Further, Bertrand R&D can be higher than Cournot R&D even in the presence of weak network externalities. These results hold true regardless of whether networks are incompatible or imperfectly compatible.

BORDER ADJUSTMENTS SUPPLEMENTING A CAP AND TRADE SYSTEM TO COMBAT CLIMATE CHANGE

In the post-Paris Agreement era, the number of carbon pricing initiatives in order to combat climate change grows continuously. However, carbon prices vary substantially among countries which yields negative drawbacks in terms of carbon leakage and loss of competitiveness for firms producing in countries with more stringent regulations. Border adjustments (BAs) could help tackle these negative drawbacks through harmonizing carbon prices across countries. We model a two-stage game where Country A can choose whether to implement BAs in the first stage. In the second stage, producers from both countries compete over prices in Bertrand competition or over quantities in Cournot competition. Most analyses on BAs so far focus on carbon pricing in the form of carbon taxes. However, we observe that many governments achieve their mitigation targets by implementing a cap and trade system with some kind of free allocation of emission allowances. From the current global carbon pricing situation, we identify two conditions for the compliance with the WTO’s national treatment principle that have not been dealt with in detail in previous models: (i) the application of BAs in the form of a cap and trade system and (ii) accounting for free allocation of emission allowances. Our results show that irrespective of the competition type, BAs supplementing a cap and trade system with free allocation improve welfare if the competitive pressure is high.

Translucent players: Explaining cooperative behavior in social dilemmas

In the past few decades, numerous experiments have shown that humans do not always behave so as to maximize their material payoff. Cooperative behavior when noncooperation is a dominant strategy (with respect to the material payoffs) is particularly puzzling. Here we propose a novel approach to explain cooperation, assuming what Halpern and Pass call translucent players. Typically, players are assumed to be opaque, in the sense that a deviation by one player in a normal-form game does not affect the strategies used by other players. However, a player may believe that if he switches from one strategy to another, the fact that he chooses to switch may be visible to the other players. For example, if he chooses to defect in Prisoner’s Dilemma, the other player may sense his guilt. We show that by assuming translucent players, we can recover many of the regularities observed in human behavior in well-studied games such as Prisoner’s Dilemma, Traveler’s Dilemma, Bertrand Competition, and the Public Goods game. The approach can also be extended to take into account a player’s concerns that his social group (or God) may observe his actions. This extension helps explain prosocial behavior in situations in which previous models of social behavior fail to make correct predictions (e.g. conflict situations and situations where there is a trade-off between equity and efficiency).

Competitive Intelligence and Disclosure of Cost Information in Duopoly

This paper considers a duopoly in which one firm doesn’t know its rival’s realized cost but can invest in competitive intelligence (CI) to gather information before competition. The incentive to invest in CI and the net benefit from CI investment are higher under Bertrand competition than under Cournot competition. Ex ante, both the firm that is being spied upon and the industry benefit (suffer) from a rival’s CI investment under Cournot (Bertrand) competition while consumer surplus suffers under both types of competition. Overall, CI investment increases (reduces) social welfare when firms compete a la Cournot (Bertrand). Ex post disclosure of cost information that is acquired may either increase or decrease the incentive to invest in CI but does not affect the qualitative results with respect to profit and welfare analyses.

Product line optimisation based on semiparametric choice model

Consumer choice behaviour is important in the product line optimisation problem. The extant literature on product line optimisation is mostly based on traditional consumer choice models, such as the multinomial logit and multinomial probit models. These models either assume that the utility errors are independent from irrelevant alternatives (IIA) or are limited by complex calculation processes or pre-given, specific distributions of measuring errors. The marginal moment model (MMM), which is classified as a semiparametric choice model, does not require specific distributions of errors; thus, it can overcome the IIA shortcoming. This study focuses on the concavity of the profit functions of a product line optimisation model based on MMM. We prove that the profit function based on MMM is concave in market share under a monopoly or oligopoly. Numerical experiments show that the choice probabilities obtained from the MMM, multinomial logit, and multinomial probit models are similar although they are obtained under different assumptions. Experimental results under monopolistic, Cournot, and Bertrand competition based on MMM are compared. Some interesting managerial insights are summarised based on the sensitivity analysis of the various model parameters.

Bertrand versus Cournot competition in a downstream mixed oligopoly with foreign ownership

AbstractFocusing on foreign ownership in the private firm, we examine the Cournot‐Bertrand comparison in a mixed oligopolistic market with vertical market structure. We have found that if public and private firms were charged with uniform price for their inputs, then Cournot‐Bertrand ranking in market outcomes confirms those obtained by Ghosh and Mitra (2010). This implies that under uniform pricing in the upstream sector, the vertical market structure does not have substantial influences on Cournot‐Bertrand ranking. However, if discriminatory pricing is adopted, firm's profits, output, and social welfare are often reversed to those obtained from uniform pricing in the upstream sector. Given the closeness of products, if the share of foreign ownership is sufficiently low, social welfare in Cournot competition can exceed that of Bertrand competition, contrasting with the standard welfare ranking that Bertrand welfare is strictly higher than Cournot. This implies that Cournot competition can be more socially desirable than Bertrand in mixed oligopoly with vertical market structure if discriminatory pricing scheme is adopted by foreign upstream monopolists.

Reasoning About ‘When’ Instead of ‘What’: Collusive Equilibria with Stochastic Timing in Repeated Oligopoly

Abstract We analyze a continuous time game of Bertrand competition with private monitoring that includes asynchronous signals and asynchronous actions. Unlike existing models where firms observe a signal that is imperfectly correlated with demand parameters and firms’ prices, we assume firms observe demand and prices perfectly but at times governed by independent Poisson processes. The signals only reveal information at the instant they are observed and do not contain information about past actions or states of demand. This implies that any firm’s price change will go undetected for some time or may never be detected. Firms are also allowed to engage in costless but unverifiable cheap talk. The model focuses on the strategic considerations that arise when firms reason about then timing of the signals rather than the content. We show that standard Nash reversion arguments can enforce collusion and truthful communication when signals are asynchronous and signals only reveal information about the current state of the world and do not reveal information about past states or actions. Through comparative statics, we disentangle how parameters that govern the timing of events and signals interact to either facilitate or preclude collusion. Finally, we extend the model to show that firms may collude not only to avoid Nash reversion but to prevent opposing firms from believing demand has dropped and thus lowering their price.

Information quality choice and information disclosure in oligopoly

In this paper, we provide a framework to analyze the information disclosure and information quality choice in the oligopoly in which one firm has the opportunity to choose her information quality flexibly and then decide her information disclosure rule after she has observed her information.We find that in the Cournot (Bertrand)competition, when the goods are substitutes (complements) and the degree of substitution (complement) is small enough, the firm will choose the maximal information quality. However, if the degree of substitution (complement) is large enough, the information quality is some intermediate value. On the other hand, in the Cournot (Bertrand) competition, when the goods are complements (substitutes), the maximal information quality will be chosen. We also find that the Fully Revealing case in which the probability of information disclosure is one will occur in (i) the Cournot competition with sufficiently small degree of substitution; (ii) the Cournot competition when goods are complements; (iii) the Bertrand competition when goods are substitutes; (iv) the Bertrand competition with sufficiently small degree of complements. Moreover, we show that the No Revealing case in which the probability of information disclosure is zero will never show up.

Pay-What-You-Want in Competition

Abstract This paper presents an analysis of Pay-What-You-Want (PWYW) in competition which explains its entry and limited spread in the market. Sellers choose their pricing schemes sequentially while consumers share their surplus. The profitability and popularity of PWYW depend not only on consumers’ preferences, but also on market structure, product characteristics and sellers’ strategies. While there is no PWYW equilibrium, given a sufficiently high level of surplus-sharing and product differentiation, PWYW is chosen by later entrants to avoid Bertrand competition. The equilibrium results and their market characteristics are consistent with empirical examples of PWYW.

Endogenous Horizontal Product Differentiation in a Mixed Duopoly

This paper studies endogenous horizontal product differentiation in a mixed duopoly. In the basic model in which firms have symmetric costs, we find that (i) product differentiation arises provided differentiation costs are sufficiently low; (ii) under Cournot competition, the welfare maximizing public firm always obtains more incentive for product differentiation, and the products are more differentiated in the mixed duopoly than in the private duopoly; and (iii) under Bertrand competition, the private firm invests in product differentiation when differentiation costs are at moderate levels while the public firm does so when differentiation costs are sufficiently low. The products may be more or less differentiated in the mixed duopoly depending on the differentiation costs. Two extensions of the basic model are also examined: one with a foreign private firm and the other with asymmetric costs.

Optimal Export Policy With Upstream Price Competition

We present a third‐market model with a vertical trading structure, in which upstream input suppliers engage in homogeneous price competition. We show that, under downstream Bertrand competition, a non‐monotonic export policy may result. Specifically, the optimal policy of the exporting country can turn into a tax–subsidy–tax as the degree of product substitutability rises. We also confirm the conventional result for which the optimal policy is an export subsidy (tax) if there is Cournot (Bertrand) competition downstream, provided that the number of domestic suppliers is at an intermediate level. We further discuss bilateral policy interventions when both exporting countries offer a subsidy/tax to their domestic downstream firms. We show that a non‐monotonic export policy (tax–subsidy–tax) can arise even in this extended setting.

Managerial Delegation of Competing Vertical Chains with Vertical Externality

We examine that the bilateral supplier affects the incentive contracts that owners of retailers offer their managers, assuming that the manufacturer sets the input price after observing the terms of the incentive contracts offered to management in the downstream market. Thus, we compare the two models: (1) decentralized bargaining between manufacturers and retailers including two-part tariff contract (2) linear input pricing without bargaining. Contrast to previous studies, we find that in equilibrium, the owners of retailers offer delegation contracts to managers for output restriction regardless of competition modes when offering linear input pricing, which implies that owners do not face a prisoners' dilemma situation and Pareto superior profit is obtained for retailer. Thus, managerial delegation of retailer is not socially desirable due to the output restriction. Furthermore, decentralized bargaining allows to equalize all the equilibrium outcomes in the different delegation structure under both Bertrand and Cournot competition and leads no delegation for the endogenous delegation problem.

About a dilemma in the telecommunications sector: Virtual operators or low-cost operators?

A virtual operator is fragile when it is in competition with other virtual operators. This is explained by the “Bertrand paradox”: when firms sell products not differentiated (or not enough differentiated) a price war has terrible consequences (the profits tend to zero). But it is worse if there is a price war between the operators with a network. It occurred in France during the period 2012 – 2018. The entrant Free triggered a price war. The reaction of the incumbents was to create low-cost operators which were their branches. The only virtual operator with a large size, Virgin Mobile, was “bought and closed down” by the incumbent SFR. It suffered too much because of the incumbents decreasing their prices and the low-cost operators, both. It lost many customers. One proposes a model to explain why the “buy and close down” of Virgin Mobile was profitable (and chosen) in these conditions. The method used is Bertrand competition. Also, the “buy and close down” which is profitable is a criterium for products which are not enough differentiated. A few examples are given. The aims of the paper are two: - To study how works a price war in telecommunications. - More generally, the possibility of profitable “buy and close down” allows to propose a criterium for saturated markets. Even, the criterium could be used to build software (to test if a market is saturated or not). The rival models which are presented in the literature are commented