Bertrand Oligopoly Research Articles

How much you talk matters: cheap talk and collusion in a Bertrand oligopoly game

How much you talk matters: cheap talk and collusion in a Bertrand oligopoly game

Overlapping ownership, pass-through, and product differentiation

Overlapping ownership can lead firms to raise prices, but what determines the magnitude of this effect? I study how the price effect of overlapping ownership depends on demand and cost conditions and the degree of product differentiation in a Bertrand oligopoly. I do so by extending Weyl and Fabinger’s (2013) conduct parameter approach which highlights the importance of pass-through.

Uniform, efficient and independent Ramsey taxes across markets

In a perfectly competitive market and in multi-product monopoly with linear demands and costs, the socially optimal taxes are Ramsey independent taxes (RIT), which are independent of each other, have a simple structure, reduce all products proportionally, and affect consumers and firms in similar ways. Under imperfect competition, while not optimal in general for both social welfare and consumer surplus objectives, RIT nevertheless retain attractive uniform effects in all markets. In asymmetric Cournot and Bertrand oligopolies, the socially and consumer-efficient taxes are surprisingly complex even in simple settings. Postulating a third objective of taxation as the average of social welfare and consumer surplus restores the optimality of RIT. Finally, another important property is that RIT impose equal corresponding marginal costs across all types of markets, as required for economy-wide efficient taxation.

How do antitrust regimes impact on cartel formation and managers’ labor market? An experiment

We explore the impacts of different antitrust regimes on managers’ labor contracts, when shareholders are intent on their managers engaging in price fixing activities. We compare legal regimes that fine firms to regimes that prosecute managers. We build a theoretical model, which we take to the laboratory. We observe contract choices of shareholders for a given legal regime, as well as the probability of managers forming explicit cartels and coordinating on prices in a repeated Bertrand oligopoly, taking contract and legal regime as given. Our results suggest that there is less collusion when the legal regime prosecutes managers. High-powered contracts do not incentivize cartel formation or price coordination effectively, irrespective of legal regime. Nevertheless, high-powered contracts were most frequently chosen by shareholders, often with collusive intents.

Merger effects in asymmetric and differentiated Bertrand oligopolies

This paper advances Motta’s (2004) study of two-firm Bertrand mergers with arbitrary synergies in symmetric linear models to m-firm mergers with cost-savings in asymmetric linear models. It identifies a set of Bertrand mergers that reduce not only consumer surplus but also rival firms’ profits. Such severely anti-competitive mergers are intriguing because they can never happen in both Farrell and Shapiro (1990) and Nocke and Schutz (2018).

How Much You Talk Matters: Cheap Talk and Collusion in a Bertrand Oligopoly Game

This study investigates the impact of cheap talk on price in a repeated Bertrand oligopoly experiment. Each participant plays 20 rounds. Participants are placed in three-person bidding groups where the lowest bid wins. During the first 10 rounds, participants are not allowed to communicate with each other. All three-person groups converged to the zero-profit equilibrium in the first 10 periods. We then play another 10 rounds where participants can text with one another using an instant message system. Some groups were allowed to text before every round, some to text before every other round, some to text every third round, some to text every fourth round, and some to text only every fifth round. When texting is allowed, All groups attempt to collude to raise the price after being allowed to text, but the only groups who can maintain the higher price and converge over time to the joint-profit maximum are the groups who can text before every period. Hence, cheap talk is only effective when subjects can continuously monitor or converse.

Is Voting for a Cartel a Sign of Cooperativeness?

This paper tests the hypothesis that a (partial) reason why cartels—collective but costly and non-binding price agreements—lead to higher prices in a Bertrand oligopoly could be because of a selection effect: decision-makers who are willing to form price agreements are more likely to be less competitive and pick higher prices in general. To test this hypothesis we run an experiment where participants play two consecutive Bertrand pricing games: first a standard version without the opportunity to form agreements; followed by a version where participants can vote whether to have a (costly) non-binding agreement as a group to pick the highest number. We find no statistically significant difference between the numbers picked in the first game by participants who vote for and against an agreement in the second game. We do confirm that having a non-binding agreement to cooperate leads to higher numbers being picked on average. Both participants who voted for and against the agreement increase the number they pick in situations with an agreement. However, this effect is bigger for participants who voted in favour.

Strategic environmental policy and international market share rivalry under differentiated Bertrand oligopoly

Abstract We analyse strategic environmental policies under international Bertrand oligopoly when firms in different industries, located in different countries, produce differentiated products. Under cooperation, emission prices always exceed the joint marginal damage from pollution. Under non-cooperation, internationally nontradable and tradable emission permit prices are always higher than the domestic marginal damage from emissions (the Pigovian tax); emission taxes can also exceed the Pigovian tax. The non-cooperative emission prices under all instruments can exceed the joint pollution damage. Internationally tradable permits generate outcomes closest to cooperation — they result in the lowest pollution and the highest welfare among all instruments under non-cooperation. Pollution is the highest and welfare the lowest with taxes. Our results provide support for allowing international trade in emission permits even when governments choose their permit levels non-cooperatively.

Collusive Incentives in Markets with Differentiated Products

This paper proposes a generalized framework for the analysis of collusion in Bertrand oligopoly markets with possibly differentiated products and asymmetric cost structures. We first study how product differentiation interacts with the intensity of collusion (i.e., the cartel’s proximity to the industry profit frontier) among symmetric firms, determining both pricing in the deviation phase from the collusive path and the penal codes available to firms. We then clarify under what conditions collusion is sustained. The second part introduces the relation between product differentiation and cost asymmetry, focusing on the case of collusion at the profit frontier. Two alternative forms in the firms’ cost structure are proposed. Whether such a cost asymmetry ultimately facilitates, or hampers, or even excludes the possibility of collusion at different levels of product differentiation depends, first, on the form of cost asymmetry between firms (homogeneous vs. heterogeneous input) and, second, on the penal code used by firms as a function of the demand variation.

The Effect of COVID-19 on Amazon Mturk

This paper examines the effect of COVID-19 on experiments run using Amazon Mturk. We run a Bertrand Oligopoly experiment with conversation before and after the pandemic outbreak. The outcome shows that after COVID-19, more participants do not fully engage in the experiment and “cherry-pick” the participation fee. There is a 36.51% decrease in the number of participants who actually participate in conversations and a 31.71% decrease in the number of groups discussing pricing behavior.

On the existence and stability of equilibria in N-firm Cournot–Bertrand oligopolies

This paper takes a novel approach to studying the existence and stability of Nash equilibria in N-firm Cournot–Bertrand oligopolies. First, we show that such games can be monotonically embedded into a game of strategic heterogeneity, so that each firm best responds to the choices of all other firms in a monotonic way. We then show that this monotonicity can be exploited to derive conditions which guarantee the existence of a unique, dominance solvable Nash equilibrium which is stable under all adaptive dynamics. These conditions constitute a strict improvement over existing results in the literature. Finally, we examine the effect on these conditions resulting from additional firms entering the market.

Multimarket Contact and Mutual Forbearance in Audit Markets

In this paper we argue that audit firms rationally consider the potential reactions of their rivals when deciding how fiercely to compete in a given market. Based on prior literature in the field of industrial organization (Bernheim and Whinston [1990]), we hypothesize that competing with the same audit firms across different industries within a geographical region (which we label “multi-industry contact”) leads to less (price) competition overall, which suggests mutual forbearance among rivals. As we characterize the audit market as a differentiated Bertrand oligopoly, pricing is a main strategic choice variable for audit firms. We predict and test whether the extent of multi-industry contact is positively associated with audit fees including several tight fixed effects specifications to rule out potential confounds. Based on a sample of 19,641 observations from 2004-2012, we find that the extent of multi-industry contact between audit firms is positively associated with audit fees controlling for inter-year, inter-industry, inter-geographical area, inter-client and inter-market segment heterogeneities. This evidence is consistent with mutual forbearance between audit firms. In supplementary tests, we find that the likelihood of client switching is negatively associated with multi-industry contact.

On the coalitional stability of monopoly power in differentiated Bertrand and Cournot oligopolies

In this article, we revisit the classic comparison between Bertrand and Cournot competition in the presence of a cartel of firms that faces outsiders acting individually. This competition setting enables to deal with both non-cooperative and cooperative oligopoly games. We concentrate on industries consisting of symmetrically differentiated products where firms operate at a constant and identical marginal cost. First, while the standard Bertrand–Cournot rankings still hold for Nash equilibrium prices, we show that the results may be altered for Nash equilibrium quantities and profits. Second, we define cooperative Bertrand and Cournot oligopoly games with transferable utility on the basis of their non-cooperative foundation. We establish that the core of a cooperative Cournot oligopoly game is strictly included in the core of a cooperative Bertrand oligopoly game when the number of firms is lower or equal to 25. Moreover, we focus on the aggregate-monotonic core, a subset of the core, that has the advantage to select point solutions satisfying both core selection and aggregate monotonicity properties. We succeed in comparing the aggregate-monotonic cores between Bertrand and Cournot competition regardless of the number of firms. Finally, we study a class of three-firm oligopolies with asymmetric costs in which the core inclusion property mentioned above still holds. We also provide numerical examples to illustrate the difficulty to generalize this result to an arbitrary number of firms because of negative equilibrium quantities.

Convexity of Bertrand oligopoly TU-games with differentiated products

We consider Bertrand oligopoly TU-games with differentiated products. We assume that the demand system is Shubik’s and that firms operate at a constant and identical marginal and average cost. Our main results state that Bertrand oligopoly TU-games in $$\alpha $$, $$\beta $$ and $$\gamma $$-characteristic function form satisfy the convexity property, meaning that there exist strong incentives for large-scale cooperation between firms on prices.

Evolution of a Collusive Price in a Networked Market

This paper studies evolution of firms’ behavior in a networked Bertrand oligopoly market, in which firms who are located on vertices of a network compete in price with their neighbors. This network model is also applied to a market with multi-dimensionally differentiated products. In a non-networked market, it is known that the Bertrand–Nash equilibrium pricing is evolutionarily stable. We show, however, that in our large networked market, the Bertrand–Nash equilibrium price is not stable but a collusive price is evolutionarily stable under weak selection. As the magnitude of transportation cost increases, firms charge a more collusive price in the long run. The results suggest that collusive pricing prevails in a large market if and only if it is networked.

The Core in Bertrand Oligopoly TU-Games with Transferable Technologies

Abstract In this article we study Bertrand oligopoly TU-games with transferable technologies under the α and β-approaches. We first prove that the core of any game can be partially characterized by associating a Bertrand oligopoly TU-game derived from the most efficient technology. Such a game turns to be an efficient convex cover of the original one. This result implies that the core is non-empty and contains a subset of payoff vectors with a symmetric geometric structure easy to compute. We also deduce from this result that the equal division solution is a core selector satisfying the coalitional monotonicity property on this set of games. Moreover, although the convexity property does not always hold even for standard Bertrand oligopolies, we show that it is satisfied when the difference between the marginal cost of the most efficient firm and the one of the least efficient firm is not too large.

Price Competition with Cheap Talk (Proposal)

This study investigates the impact of cheap talk on price in a repeated Bertrand oligopoly experiment. Participants are placed in three-person bidding groups where the lowest bid wins. During the first 10 rounds, participants are not allowed to communicate with each other. All three-person groups show decreasing market prices in the first 10 rounds. We then play another 20 rounds where participants can text with one another using an instant message system. Some groups were allowed to text before every round, some to text before every other round, some to text every third round, some to text every fourth round, and some to text only every fifth round. When texting is allowed, All groups attempt to collude to raise the price after being allowed to text. Whether they are successful depends on the combination of how often they can text and whether all three participants actually text.

The impact of the number of sellers on quantal response equilibrium predictions in Bertrand oligopolies

AbstractThis paper studies how increasing the number of sellers in a Bertrand oligopoly with homogenous goods affects the equilibrium price level predicted by logistic quantal response equilibrium (LQRE) and power‐function QRE (PQRE). We show that increasing the number of sellers reduces the average posted price in a PQRE, but can increase the average posted price in an LQRE. Our results indicate that the comparative‐static predictions of QRE (McKelvey & Palfrey, 1995, Games Econ Behav, 10, 6–38) are not necessarily robust to changes of the quantal response function.

A Merger Paradox: Proposal Right and Price Discrimination

This article studies merger incentives in a two-sided Bertrand oligopoly market. Either buyers or sellers receive a proposal right with a probability proportional to their relative bargaining powers. Each buyer or seller, if chosen, offers a payment schedule, or contract, to every opponent. We show that if there is a separable efficient allocation, the post-merger contracts exhibit a higher level of price discrimination than the pre-merger contracts. Thus, the horizontal merger to monopoly is harmful if their bargaining power is weak enough, i.e. the merger of buyers (sellers) decreases their joint profit if buyers (sellers) are responders with a high probability. The proposal right in vertical bargaining determines the horizontal merger incentive through price discrimination. We further show that this merger paradox is likely to emerge when goods are substitutes.

Multilateral limit pricing in price-setting games

In this paper, we characterize the set of pure strategy undominated equilibria in differentiated Bertrand oligopolies with linear demand and constant unit costs when firms may prefer not to produce. When all firms are active, there is a unique equilibrium. However, there is a continuum of non-equivalent Bertrand equilibria on a wide range of parameter values when the number of firms (n) is more than two and n⁎∈[2,n−1] firms are active. In each such equilibrium, the firms that are relatively more cost or quality efficient limit their prices to induce the exit of their rival(s). When n≥3, this game does not need to satisfy supermodularity, the single-crossing property, or log-supermodularity. Moreover, the best responses might have negative slopes. Our main results extend to a Stackelberg entry game where some established incumbents first set their prices, and then a potential entrant sets its price.