Introduction
A duopoly is a kind of oligopoly in which the largest or whole share of the market of a particular item or service is controlled by only two companies. More than a million people may buy competitive products and services from two companies in this market. Because of the fierce rivalry among the companies, monopolistic market dominance is becoming more difficult, if not unattainable, for them to achieve (Shang, Tong, and Wang 2022, p. 258). As a result of the duopolistic structure of the market, pricing and production choices are very strategic. As with oligopolies, a duopoly may influence pricing or production similarly to an oligopolist. Consider the duopolistic rivalry between MasterCard and Visa. The two corporations dominate the payment sector in European and American markets. Roughly 60 per cent of the market is dominated by Visa, while MasterCard has about 30 per cent (Sotiropoulos, Georgoula, and Bilanakos 2019, p. 2). Duopolies like Airbus and Boeing are not exclusive to the aviation industry. Boeing and Airbus dominate the market for commercial aircraft manufacture.
The three duopoly frameworks are the Cournot, Bertrand, and Stackelberg models. As per Cournot Model (Sotiropoulos, Georgoula, and Bilanakos 2019, p. 4), businesses’ competitiveness is determined by their output. Cournot’s theory states that each actor receives a market value for goods or services depending on their availability. In contrast to Cournot’s approach, Bertrand’s model says that the price of goods and services is the crucial driver of rivalry between the two organisations (Shang, Tong, and Wang 2022, p. 259). Following Bertrand’s Model, if customers choose between equivalent merchandise, they will always select the firm that offers the lowest price. To calculate the first-mover advantage, Stackelberg came up with this approach. Like the Cournot Model, this model relies on the same two assumptions but assumes that companies make choices in a different sequence. In the first step, the leader decides on the amount. The final selection is made in the second step, which cannot be changed.
Question #1: Collusion and the Game Theories
This happens when two or more companies make decisions together and operate as if they were one. It is said that collusion occurs when two or more companies agree, either explicitly or implicitly, to restrict their production to get the monopolistic price (Chirat and Guicherd 2022, p. 1935). In an oligopolistic market system, the profitability of enterprises is influenced by both the firm’s actions and those of its rivals.
In-Game theory, strategic dependency is the most crucial idea. This strategic dependency may be explained using the framework of game theory. The use of game theory is critical in assisting the company to consider the potential reactions that its actions may elicit from the competition (Chirat and Guicherd 2022, p. 1937). For instance, in a duopolistic market structure, the game theory may explain why it is difficult for enterprises to collaborate to develop dominant pricing. Cooperation may benefit all companies, but each company has a tremendous incentive to break and undercut its competitors to control a significant piece of the market.
There is a considerable incentive to defect from a collusive agreement if businesses do not feel a sufficient mechanism to punish those who break away. A game theory is known as the “prisoner’s dilemma” has long been used to explain why cooperation between two parties may be difficult even when it is mutually advantageous (Beneke and Mackenrodt 2021, p. 154). In game theory, Nash equilibrium is a fundamental idea. The oligopolistic market structure’s Nash equilibrium is the set of tactics that no one business can outperform by changing its strategies.
Question #2: Comparison of Cournot and Stackelberg Games
Put another way, the price of products and services is set by the total output. Additionally, the downward slope of the need curve indicates that the amount produced by one business affects the pricing of other market participants. The duopolies’ interdependence generates a strategic environment in which the output levels of its rivals impact one firm’s profit maximisation production level (Thomas 2019, p. 161). Industrial economics can always benefit from the conclusions of the Carnot model. Price excess above minimal cost is inversely related to the number of businesses in an asymmetrical oligopoly (Pal 2018, p. 184). With more enterprises competing for market share, prices tend to balance out.
Stackelberg’s model is chronological, while Cournot’s is concurrent (Thomas 2019, p. 161). In Cournot duopolies, the amount sold by the leader business is considerably more than the total sales by the followers. Non-cooperative game, Stackelberg duopoly, is founded on an uneven competition paradigm, also known as Stackelberg rivalry (Pal 2018, p. 184). Stackelberg’s “Market Structure and Equilibrium” in 1934 was groundbreaking in the study of duopolies because it was based on speculation distinct from those of Cournot’s and Bertrand’s duopoly models provided different results.
A Stackelberg duopoly is a chronological element in the game theory (unlike Cournot’s model, which is simultaneous) (Thomas 2019, p. 165). In this case, the cost and demand functions of the two companies selling the same product are the same. As a result, the leader, which may be more well-known or have more substantial brand equity, is better positioned to choose which amount to sell first. As a result, the follower, which is less well-known, determines its manufacturing volume (Thomas 2019, p. 165). As with every sequential game, we must apply backward induction to determine the Nash equilibrium. That is to say, look at the follower’s choice.
The Stackelberg equilibrium is the ideal state of affairs in a game. It cannot be guaranteed that the leader will create more and gain more money than the follower in this game since the leader has elected not to act according to Cournot’s model (Pal 2018, p. 183). There will be more production and lower prices, but the market leader (the one who moves first) will be effectively off than the follower. This illustrates the relevance of precise market intelligence and the interconnection of each player’s strategies, mainly when a market leader and a follower.
Compared to Cournot’s duopoly model, the macroeconomic efficiency results are identical. Isoprofit curves are not tangential to one another in Nash equilibrium, which means a loss in profit maximisation (Pal 2018, p. 187). However, in the Stackelberg duopoly, the loss is lesser than Cournot’s. In a one-period model, the Stackelberg and Cournot transitions are stable.
Question #3: Role of Regulation and Legislation in Limiting Collusion
Countries across the globe have laws against collusion. Antitrust legislation is designed to make it more difficult for corporations to enter into and carry out a colluding agreement. Companies in industries with solid restrictions may have a more challenging time working together with other organisations (Jones and Pereira 2021, p.103). A primary goal of antitrust law is to break up monopolies and decrease collaboration in the marketplace. Consequently, antitrust laws are designed to reduce the prevalence of illegal corporate actions, such as mergers, monopolies, and conspiracies (Grinikh and Petrosyan 2021, p. 256). Antitrust laws are intended to prohibit cartels and other forms of collaboration. A cartel is a group of market players that work together to increase their earnings and take over the market.
Price-fixing, supply restriction, and bid-rigging are just a few tactics that cartels might use to manipulate the market and increase profits. Bid rigging occurs when multiple parties work together to determine who will win a contract before bidding (Jones and Pereira 2021, p.105). A cartel that participates in bid-rigging is an example of four significant corporations choosing a company that will win a particular agreement in a specific industry. As long as they are assured of future contracts, the cartel’s members agree to the deal (Jones and Pereira 2021, p.105). A well-executed cartel scenario would eliminate all competition by capturing all market share and imposing price controls.
Antitrust and monopoly laws were enacted under the Sherman Act, which prohibits any agreement or conspiracy to thwart commerce, monopolise, or conspire to monopolise. Although the legislation was designed to prevent the transaction from obstructing, it did not contain all trade opposition (Grinikh and Petrosyan 2021, p. 256). It was a crucial provision since numerous moral and professional business acts, such as establishing a partnership might impede the flow of goods and services. Those found guilty of violating the law face a maximum of 10 years in jail.
Unfair competition and misleading activities or practices are prohibited under the Federal Trade Commission Act (Jones and Pereira 2021, p.105). If an activity violates the Sherman Act, it also infringes the Federal Trade Commission Act since the two are intertwined. Following the Act’s passage, a new agency was established: the FTC. Customers who have been abused may seek monetary compensation or other payment types under the Act (Dal Bó and Fréchette 2019, p. 31). The Federal Trade Commission also investigates data gathering concerning commercial enterprises and their management.
Specifically, the Clayton Act was established to tackle mergers and interlocking boards amongst rivals that the Sherman Act did not cover. Mergers that might lead to a monopoly or significantly reduced competition are prohibited under the Clayton Act (Grinikh and Petrosyan 2021, p. 256). A corporation must also tell the government ahead of time if it intends to combine or acquire substantially more than one company. Consequently, the Clayton Act protects American consumers by preventing acquisition opportunities that would reduce competition and raise costs.
Question #4: The Impact of Treating each of the Three Types of Duopolies
Companies operating in duopolies must consider the influence their operations will impact their competitors and how that rivalry will react as a consequence of those activities. As a consequence of this transition in the way companies operate and how they market their products, the types of services and items that are provided and priced may change (Grinikh and Petrosyan 2021, p. 258). Bertrand Prices in a duopoly tend to decrease to or below the manufacturing cost, therefore eliminating the prospect of turning a profit.
So most duopolistic organisations find it profitable and necessary to agree to form a monopoly, determining the price at which both firms may occupy a market area. Consequently, each company can earn one split of the profit. Because the Sherman Act prohibits cooperation and other antitrust restrictions in the United States, using this strategy may be difficult and even risky (Dal Bó and Fréchette 2019, p. 30). Duopolies perform best when they function and attain competitiveness in production quantity instead of pricing to avoid legal difficulties and enable each enterprise to share profits.
Using his critique of Cournot’s duopoly model, he contributed significantly to oligopolistic and game theory, culminating in informing his paradigm of duopolies, known as the Bertrand Model. In contrast to Cournot, who thought that production volume would still be the determining element in the competition amongst the rival companies, Bertrand believed that price would always be the deciding component in the competition (Skyrms 2022, p. 3). According to Bertrand’s duopoly thesis, buyers would choose the business that provides the lowest price when presented with an option between two similar or comparable items or services. Therefore, both companies would be forced to cut their prices, leading to a loss of profit. The Stackelberg duopoly is one of the most common models of imperfect competition because it is simple and easy to understand (Grinikh and Petrosyan 2021, p. 259). Stackelberg’s 1934 book “Market Structure and Equilibrium” presented a new method of looking at duopolies since it was founded on a different vantage point and yielded conclusions in contrast to those obtained by Cournot and Bertrand’s duopoly simulations in the previous decades.
In this expansion of the original Stackelberg game, the concepts of bounded rationality valuation Stackelberg games and liquid duopoly game frameworks are discussed. The stable points of this model are investigated via the lens of the theory of turbulence in dynamic systems (Skyrms 2022, p. 4). Making comparisons is also accomplished via the Bertrand game of rational behavior. A steady zone, bifurcation diagram, The Largest Lyapunov notation, an unusual fixation, and responsiveness to the initial conditions are valuable tools for illustrating complex dynamic behavior. Both computational fluid diligent investigations show the efficacy of the valuations Stackelberg duopoly game, including limited rationality players to be dependent only on the leader’s dynamic pricing speed (Skyrms 2022, p. 4). The well-known Cournot-Bertrand duopoly game is not similar because of the constraint on reason. Furthermore, the pace of dynamic pricing of the entirely rational leader upsets this model.
Question #5: Explaining the Grim Trigger Strategy
When playing the Iterated Prisoner Dilemma (IPD) on a regular grid, the emergence of Grim Trigger as the dominant approach is probed using three kinds of mimicking rules: the classical imitation rule, which copies the integrated database of the opposition’s moves, and also the multiple realistic selective imitation guidelines that replicate only a subcategory of the opposition’s activities premised on the collected data from previous games played (Skyrms 2022, p. 2). This pattern is repeated across all replication rules. This pattern is followed by developing the Grim Trigger groupings initially in the game until these clumps of Grim Triggers consolidate into more significant patches in the regular grid.
The grim-trigger approach, developed by Friedman, is often used in valuation analysis, primarily because of its practicality, to demonstrate that collusion may be perpetuated via a subgame stable harmony (as opposed to a perfect equilibrium) (Dal Bó and Fréchette 2019, p. 29). Using essential circumstances, it is feasible to enhance the grim-trigger approach while still keeping subgame brilliance and, in certain situations, even adding mild renegotiation evidence-based best to the strategy (Skyrms 2022, p. 3). Essentially, after a deviation, the dishonest, instead of remaining in the Nash equilibrium, indefinitely selects an auto penalty that communicates, in a highly forceful fashion, that they could not diverge again if cooperation were restored to the situation.
The method proposes cooperation, to begin with, and for as long as the others collaborate. If any of us deviates from the strategy, it recommends moving to each equilibrium approach and continuously playing it indefinitely. Its most significant disadvantage is that any divergence, even a simple error, prohibits future collaboration indefinitely (Dal Bó and Fréchette 2019, p. 33). Furthermore, if one person cheats, all participants’ consequences are the same. This tactical profile is thus not vulnerable to renegotiation as a result of this. Using the forgiving-trigger approach, a solution to these shortcomings while maintaining subgame perfection and improving the method’s weak renegotiation proof can be realised.
For example, in the Prisoners’ Dilemma, the discounting factor is critical in deciding whether or not trigger methods can maintain cooperation over time. Grim-strategy penalties grow exceedingly painful when the asset’s value approaches a recognised value because they entail an endless stream of actual cost losses in the long run. Indite punishments may be employed to maintain various potential outcomes (Grinikh and Petrosyan 2021, p. 259). In this way, the folk argument for indefinitely repeated games may be explained mathematically. For a player, choose any stage-game payment between the one that corresponds to Nash equilibrium and the maximum one that exists anywhere in the given array.
The gloomy trigger approach is hardly the only approach used to elicit cooperative conduct in prisoners’ dilemma games that are played repeatedly. The common characteristic of cooperation-inducing methods is that they penalise the other player for engaging in cheating behavior. For example, if a player believes that their competitor would ultimately be responsible if the player violates the recurrent prisoners’ dilemma, the player will freely comply. Although cheating is the most popular strategy in a one-shot game, the possibility of eventual reprisal and a consequent decline in profit further than the initial period offers an impetus for a player to preserve reciprocal altruism.
References
Beneke, F. and Mackenrodt, M.O., 2021. Remedies for algorithmic tacit collusion. Journal of Antitrust Enforcement, 9(1), pp.152-176.
Chirat, A. and Guicherd, T., 2022. Oligopoly, mutual dependence and tacit collusion: the emergence of industrial organisation and the reappraisal of American capitalism at Harvard (1933–1952). The European Journal of the History of Economic Thought, 29(1), pp.112-145.
Dal Bó, P. and Fréchette, G.R., 2019. Strategy choice in the infinitely repeated Prisoner’s Dilemma. American Economic Review, 109(11), pp.3929-52.
Grinikh, A.L. and Petrosyan, L.A., 2021. An effective punishment for an n-person prisoner’s dilemma on a network. Труды Института математики и механики УрО РАН, 27(3), pp.256-262.
Jones, A. and Pereira Neto, C.M.D.S., 2021. Combatting corruption and collusion in public procurement: Lessons from Operation Car Wash. University of Toronto Law Journal, 71(supplement 1), pp.103-150.
Pal, M., 2018. Third-party political participation and anti‐collusion rules. Canadian Public Administration, 61(2), pp.284-303.
Shang, W., Tong, S. and Wang, Y., 2022. Duopolistic positioning and pricing competition with variety‐seeking and strategic consumers. Naval Research Logistics (NRL), 69(2), pp.257-270.
Skyrms, B., 2022. The Social Contract, the Game of Life and the Shadow of the Future. Homo Oeconomicus, pp.1-9.
Sotiropoulos, D.N., Georgoula, I. and Bilanakos, C., 2019, July. Optimal Duopolistic Competition Strategies in Social Networks. In 2019 10th International Conference on Information, Intelligence, Systems and Applications (IISA) (pp. 1-7). IEEE.
Thomas, S., 2019. Harmful Signals: Cartel Prohibition and Oligopoly Theory in the Age of Machine Learning. Journal of Competition Law & Economics, 15(2-3), pp.159-203.
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