Bertrand Model Research Articles

On Cournot and Bertrand competition in collusive mixed oligopolies

AbstractWe consider a mixed oligopoly of one public and N private firms where goods are horizontally differentiated. In our setting, an interdependent payoff structure characterizes the degree of collusion among private firms. We show that, whereas in the Bertrand model, private firms are willing to collude as much as possible, in the Cournot model, the existence of a public firm reduces the scope of collusion. We also prove that the classic discussion comparing price and quantity competition crucially depends on market collusion. More precisely, price competition unambiguously yields larger profits for private firms only if collusion is high enough. In an infinitely repeated game, we prove that collusion is easier to sustain in a larger oligopoly because, in this case, a larger N helps mitigate the effect of the public firm on private firms’ collusion sustainability. Finally, we also find that collusion is always more easily sustained in the Bertrand case than in the Cournot case.

ВЛИЯНИЕ ОЛИГОПОЛИСТИЧЕСКОЙ КОНКУРЕНЦИИ НА ЭКОНОМИКУ СТРАНЫ

This paper studies the essence and significance of one of the components of imperfect competition – oligopoly. In the course of writing the paper, the main specific features of oligopoly that distinguish it from monopoly and monopolistic competition have been identified. In addition, the main conditions of its emergence were noted, with the allocation of varieties of the category under consideration. An important place in the study was given to the main models of oligopoly, in particular: price leadership model, Bertrand model, cartel model and Cournot model. In addition, a comparative analysis was conducted to identify the positive and negative sides of the existence of oligopoly. Undoubtedly, the topic of our research is very relevant at the current stage of economic development. This is primarily due to the fact that oligopoly acts as one of the most common market structures. After all, almost all technically complex industries belong to oligopoly, in particular such industries as metallurgy, electronics, automobile manufacturing and many others.

Tencents Success in Video Streaming: An Economic Theory-based Analysis

With the rise of internet technology and the popularity of mobile devices, the video industry has become an increasingly important part of the global entertainment landscape. This paper discusses the pricing strategy of Tencent in the video streaming industry. The paper states that Tencent has used the Bertrand Model to set prices equal to marginal costs to attract customers and expand its market share. However, in the case of Tencent Videos subscription price hike, the Cournot Model may be more applicable as the firm assumes that customers will continue to subscribe during the pandemic period. Despite the subscription price increase, the change in the price would be larger than the change in demand, leading to higher profits. The article also discusses the increase in demand for Tencent Video memberships and the factors contributing to it. From a game theory perspective, Tencent and its members can be modeled as playing a classic prisoners dilemma game. Finally, the article discusses the opportunity cost for consumers and the concerns regarding the fairness of the increase in membership fees. This paper also utilizes the SWOT analysis.

Asymmetries in banking conduct: A Cournot - Bertrand model

This paper presents a Cournot – Bertrand model with differentiated loans and deposits. In this context, banks compete in different strategic variables, with bank 1 competing in quantities and bank 2 in interest rates. It is shown that loan and deposit differentiation are necessary conditions for a unique Nash equilibrium. The analysis constitutes a simple framework for the introduction of asymmetries in the behavior of oligopolistic banks, providing possible policy and bank ownership extensions.

Bertrand under Uncertainty: Private and Common Costs*

Does asymmetric information about costs in a homogeneous‐good Bertrand model soften competition? Earlier literature has shown that the answer (perhaps counter‐intuitively) is “no,” while assuming (i) private (i.e., independent) cost draws and (ii) no drastic innovations. I first show, in a fairly general setting, that by relaxing (i) and instead allowing for sufficiently much common (interdependent) cost draws, asymmetric information indeed softens competition. I then study a specification that yields a closed‐form solution and show that relaxing (ii) but not (i) does not alter the result in the earlier literature. While relying on specific functional forms, this specification is quite rich and might be useful in applications. It allows for any (positive) degree of interdependence between the cost draws, for any demand elasticity, and for any number of firms. The closed‐form solution is simple and in pure strategies.

Research on Price War of Payment Platform based on Repeated Game-Taking Alipay and Wechat as Examples

Price war is an inevitable product of the market economy and is an important mean of stimulating market development. The development of the Internet financial market has brought about a new era of universal mobile payments. The price war between the two mobile payment giants - Alipay and WeChat - in this new era is of particular concern. As the battle between the two platforms gradually enters a white-hot stage, how they act to maximize their own interests has become a major focus of the Internet financial market. This paper explores the price war between these two payment platforms from the perspective of repeated games and makes preliminary assumptions based on the Bertrand model. Based on the findings and the context of the times, this paper suggests strategies for the development of both Alipay and WeChat which are aiming to promote the mobile payment platforms towards healthy competition in order to achieve a mutually beneficial and win-win market.

Platform Operations under Dual-Channel Catering Supply Chain

In the modern catering business model, restaurants usually use established platforms to promote their food and use two channels to sell their food: online and offline sales. We construct demand functions for online and offline, considering promotion and substitution relationships by a revised Bertrand model. We first consider three classic models: the decentralized decision model, the equilibrium decision model, and the centralized decision model. In the decentralized decision model, the platform decides both the promotional effort and the online discount; in the equilibrium decision model, the platform decides the online discount, while the food service provider decides the promotional effort. In the centralized decision model, the takeaway platform and the food service provider have maximized the overall profit as the decisive goal. We find that the online discount decreases in price when the impact factor of the online promotion is high but increases in price when the impact factor of the online promotion is low. Then, we analyze and compare the results under three models. We find that when the substitution factor is low enough, or the impactor factor of online promotion is low enough, the global optimal platform discount is higher than the equilibrium platform discount and the decentralized online discount; otherwise, the results are the opposite. In addition, the global optimal promotional effort is always higher than the optimal promotional effort in the decentralized model. When the substitution factor is low enough, or the impactor factor of online promotion is low enough, the global optimal promotional effort is higher than the equilibrium optimal promotional effort; otherwise, the result is the opposite.

Theory and Practical Application Based on Game Theory

Game theory refers to the method in which one of the interacting parties obtains the decision-making information of the other party and uses it to influence the other party in turn. Therefore, game theory is also called "game theory". Game theory can be divided into cooperative game and non-cooperative game. In recent decades, the theory of game theory has developed rapidly with the establishment of John Nash and has been applied to many fields such as medical, engineering, military, and business. In this paper, the author starts from the basic definition of game theory and analyze the prisoner's dilemma, concordance fallacy, median voter theorem, Gounod model, Bertrand model, iterative deletion of dominated strategy, etc. through specific cases. The research results show that game theory has been widely used in the economy. For bilateral games, the results of Nash equilibrium are unstable. The research in this paper broadens the theory of game theory and has important practical significance for the application research of game theory.

Analysis of E-commerce Platforms’ Price War: Based on Game Theory Model

Based on the fact that T-mall and JD.com, two major e-commerce platforms, reduce prices significantly every year in the shopping festival, but still can obtain high profits, this paper explains the causes and profit mechanism from the perspective of game theory. Meanwhile, this article builds a Bertrand model to analyze the profit mechanism of the two firms. The Nash equilibrium is (Discount, Discount) until they drop their prices to 0, which is obviously against the reality that both companies can gain high profits during the shopping festival, and consumers can also buy goods at lower prices. Therefore, there is a possibility of a collusion between the two firms. Finally, this paper introduces trigger strategy, the conclusion is that the two companies can make profits in the long run as long as they cooperate with each other. In addition, from the perspective of consumers, e-commerce platforms and the government, this paper also gives a reasonable decision-making strategy in the shopping festival. This research not only provides promotion programs for e-commerce platforms, but also helps consumers understand the profit mechanism of e-commerce platforms. At the same time, the government can also get inspiration from it, such as setting a minimum price to avoid the disruption of market order by vicious competition.

Research on Tesla's Pricing Strategy in China Based on Bertrand Game and SWOT Analysis

With the advent of the post-subsidy era, new energy vehicles are the future development direction of China’s automobile industry, the Chinese government has established a number of New-Energy Vehicle (NEV) market stimulus programs. As a foreign car company in China, The price approach employed by Tesla in the Chinese market has turned into an important concern. This article analyzes the future pricing development strategy of the NEV industry represented by Tesla in China, and then analyzes the development trend of electric vehicle companies under different pricing. Using the method of combining SWOT and Bertrand model, a strategic analysis is carried out from two different perspectives, this article focusing on using the SWOT analysis method to conduct a strategic analysis of the overall environment of Tesla's NEV industry with various literatures as the model background, and proposes the future Continue technological innovation, improve production efficiency, reduce production costs and other related development suggestions.

Nash equilibria of the pay-as-bid auction with K-Lipschitz supply functions

We model a system of n asymmetric firms selling a homogeneous good in a common market through a pay-as-bid auction. Every producer chooses as its strategy a supply function returning the quantity S(p) that it is willing to sell at a minimum unit price p. The market clears at the price at which the aggregate demand intersects the total supply and firms are paid the bid prices. We study a game theoretic model of competition among such firms and focus on its equilibria (Supply function equilibrium). The game we consider is a generalization of both models where firms can either set a fixed quantity (Cournot model) or set a fixed price (Bertrand model). Our main result is to prove existence and provide a characterization of (pure strategy) Nash equilibria in the space of K-Lipschitz supply functions.

To Be or Not to Be? Strategic Analysis of Carbon Tax Guiding Manufacturers to Choose Low-Carbon Technology

This paper analyzes the environmental tax’s effect on manufacturers’ choice of low-carbon technology in competitive supply chains. The existing studies only consider a single oligopoly enterprise and ignore the competition between supply chains. Few papers study the manufacturer’s technology choice under the carbon tax policy in the competitive supply chains, especially investigating the factors influencing the technology choice, including the market volume, and technology carbon emission reduction efficiency because different industry sectors have their distinctive carbon emissions reduction efficiencies and facing the different market volume. The study adopts a game theoretical approach, including the three-level supply chain consisting of the regulator, the manufacturers, and the retailers. A high carbon tax does not always help firms choose low-carbon technology. However, the monotonous effect of the carbon tax on manufacturer technology selection is no longer valid if the market volume and the carbon-reducing efficiency are considered. When the market volume is large, the regulator can set a high carbon tax to induce the manufacturers to choose low-carbon technology. We identify cases where the manufacturers are caught in a prisoner’s dilemma. When the market volume is small, and the carbon-reducing efficiency is high, the competitive manufacturers adopt the common technology. However, if the regulator increases the carbon tax, the manufacturers acquire the differential technology strategic choice, which is the Pareto optimal. We also extend the base model to the imperfect substitutable Cournot model and the Bertrand model to check the robustness and find our main results still hold in these extensions.

Bertrand competition in vertically related markets

ABSTRACT We build a successive Bertrand model with a homogenous good. We show that increasing the production efficiency of an industry can reduce firms’ profits. We also show that this result holds in the successive Cournot model. Hence, an industrial policy aimed at improving production efficiency may be undesirable for firms.

Partial privatization with endogenous choice of strategic variable

AbstractThis paper analyzes the optimal privatization policy when firms endogenously choose their strategic variable. The level of privatization is shown to determine: (i) the choice of strategic variable, whereby an asymmetric equilibrium could emerge (either Cournot–Bertrand or Bertrand–Cournot); (ii) the stability of equilibrium when the partially privatized firm and the private firm choose quantity and price respectively as the strategic variable; and (iii) the level of welfare, whereby Cournot–Cournot and Bertrand–Cournot games could lead to a greater welfare than the Bertrand–Bertrand model.

Streaming Stimulates the Live Concert Industry: Evidence from YouTube

The removal of Warner Music content from YouTube in the first three quarters of 2009 constitutes a plausible natural experiment to investigate the impact of streaming on live concert sales. This Warner-YouTube blackout had statistically and economically negative effects on Warner artists relative to non-Warner artists. Specifically, relative revenues and prices were lower and relative attendance was not higher. These effects were stronger among artists who recently had a song in the Billboard Hot 100 and among those who were more frequently searched on YouTube just prior to the blackout. These findings suggest that the diffusion of streaming has stimulated the demand for live concerts. The evidence is also consistent with a differentiated Bertrand model of ticket pricing in which prices are strategic complements and prices and streaming penetration gives rise to increasing differences in the artist profit function. This suggests that concerts and streaming are complements in demand for a given artist, and that concerts by different artists are substitutes. More broadly, the paper is an example of how the results from the monotone comparative statics literature can be adapted for use with difference-in-differences estimation.

Applications of Game Theory in Microeconomics

Game theory has been used as a potent analytical tool by numerous areas since its inception. It has been more popular in microeconomic analysis in recent years. It is not an exaggeration to claim that it completely rewrites microeconomics. The major ideas of game theory are summarized in this paper, as well as their application in microeconomics. This study examines the three elements and key types of game theory in its fundamental material. The Nash equilibrium and other equilibria expanded by Nash equilibrium are then reviewed in game theory equilibrium. Then, the Cournot model, Stackelberg model, and Bertrand model are discussed in game theory and market analysis. Finally, in the section on game theory and auction, it explained that, within the context of the game, English auctions and second-price sealed-bid auctions should use comparable strategies, however Dutch auctions and first-price sealed-bid auctions should conceal their own valuations.

The stability of a dynamic duopoly Cournot–Bertrand game model

The paper is devoted to exploring the complex dynamics of a Cournot–Bertrand model, where one agent chooses quantity and the other chooses price. A nonlinear discrete system is built to illustrate the game model with bounded rationality. Theoretically, the local and global stability of equilibrium are investigated. The simulation reveals that Flip and Neimark–Sacker​ bifurcation phenomena occur when the adjustment speed of one firm increases through different boundary curves. Therefore three different chaotic attractors are presented. The standard Logistic mapping is applied to analyze the dynamics of the system on invariant axes. The critical curves classify the number of preimage of the quantity or price. Besides, simulations give more intuitive results: the cycle attractor, chaotic attractor and the basin of attraction with “holes” are given.

Price response of the high fructose corn syrup industry in the United States: a Bertrand model application

ABSTRACT This paper uses a Bertrand duopoly model application and derives a high fructose corn syrup (HFCS) price reaction function that shows the response of the price of HFCS to changes in the price of sugar. It conducts cointegration analysis and assesses the performance of the HFCS price reaction model by estimating a Dynamic Ordinary Least-Squares model. It finds that the prices of HFCS-55, sugar, and corn are cointegrated over the period 1981:1 to 2017:12. The estimated long-run relationship shows that a one percent increase in the price of sugar increases the price of HFCS-55 by 0.19 percent. Additionally, the price of corn has a positive effect on the price of HFCS-55. The model and the results offer important insights for antitrust litigation.

Review of monopoly models and implications for antitrust

In February 2021, the Ministry of Commerce Anti-monopoly Bureau of the People’s Republic of China released the Antitrust Guidelines for the Platform Economy Industry. This announcement signaled more governmental supervision and governance with Internet-related business. In practice, tech giants have been suffering administrative penalties one after another. This study presents a review and analysis of the research literature on the monopoly quantitative models, outlining the components and concluding the implications for anti-monopoly. This paper delineates three main research topics relating to the monopoly models within the literature: the oligopoly, monopolistic competition, and Internet platform monopoly. The Cournot model, Bertrand model, Stackelberg model, and Innovational model represent the oligopoly studies when a small group of large sellers dominates the market. We then discuss the monopolistic competition models as the Krugman model, D-S Model, and Lancaster Model. We pay particular attention to the platform economy to reflect the new era of monopoly with Marshall’s Dilemma. After the summary and comparison of the literature research trajectory, our analysis culminates in implications for antitrust: why Internet corporations and government meet this monopoly predicament, who are involved by monopoly policy, how consumers and market got impacted, and what countermeasures could be taken to improve the antitrust. This study contributes to overview the development of monopoly models and critically analyze based on the current antitrust situation and trend of platform economy integration. We should scrutinize the feasibility to adopt engrain view of monopoly mechanisms as benefit loss on the information technology economy. Therefore, this research raises the novel question and synergistic effects of monopoly.

Bertrand competition under asymmetric conditions

Abstract Analyzing price competition through game theory is one of the most important frameworks of oligopoly theory, especially in industrial organizations. Numerous studies have been conducted in this direction, as companies are forced to adjust their sustainable pricing policy to operate in the long term. Thus, the players make a regular adjustment of the pricing strategy. Of all the models developed based on Bertrand’s reference model (1883), the most analyzed were those in which informational symmetry predominated. Since informational symmetry presents only a theoretical framework, economists have turned their attention to information asymmetry. This type of information best describes a complex economic game, as it creates an information gap between players and generates opportunities in the decision-making process. Thus, asymmetric information is the main parameter of the decision-making process that determines decision makers to resort to different decision strategies than those assumed by the analytical model. Any asymmetric Bertrand model predicts competitive and efficient market outcomes, a direct relationship between a firm’s conduct, market structure and finally market performance. This paper undertakes an analysis of the Bertrand model in the case of demand and asymmetric costs. We determine the Bertrand-Nash equilibrium under the scenario in which close, but not perfect substitutes exist for the differentiated product with hypothetical data. Then we highlight what happens with profits when we consider that discrete cross marginal demand gradually increases. For more research, there are numerous studies based on sequential games, Bayesian games and signaling games both in discrete time and in continuous time.