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Game-Theoretic Models of Oligopoly: A Review and an Extension


H1 Oligopoly Game Theory: An Introduction --- --- H2 What is Oligopoly? H3 Characteristics of Oligopoly H3 Examples of Oligopoly H2 What is Game Theory? H3 Definition and Assumptions of Game Theory H3 Types of Games H3 Applications of Game Theory H2 How Game Theory Applies to Oligopoly H3 Interdependence and Strategic Behavior H3 The Prisoner's Dilemma H3 Nash Equilibrium and Dominant Strategies H3 Collusion and Cartels H2 Advantages and Disadvantages of Game Theory in Oligopoly Analysis H3 Advantages of Game Theory H3 Disadvantages of Game Theory H2 Conclusion H2 FAQs And here is the article I wrote based on the outline: Oligopoly Game Theory: An Introduction Oligopoly is a market structure where a few large firms dominate the industry and compete with each other by setting prices, advertising, innovating, or entering new markets. Game theory is a branch of mathematics that studies how rational agents make strategic decisions in situations where their actions affect and are affected by the actions of others. In this article, we will explore how game theory can be used to analyze the behavior and outcomes of oligopolistic firms, as well as the advantages and disadvantages of this approach. What is Oligopoly? An oligopoly is a market structure where there are only a few sellers (usually less than 10) who produce similar or differentiated products. The products can be homogeneous (such as steel or oil) or heterogeneous (such as cars or smartphones). The firms in an oligopoly have significant market power, meaning they can influence the price and output of the industry. They also face barriers to entry, such as high fixed costs, economies of scale, patents, or government regulations, that prevent new entrants from competing with them. Characteristics of Oligopoly Some of the main characteristics of oligopoly are: - Interdependence: The firms in an oligopoly are interdependent, meaning their decisions depend on and affect the decisions of other firms in the industry. For example, if one firm lowers its price, it will attract more customers from its rivals, who may respond by lowering their prices as well. This will result in a price war that reduces the profits of all firms. On the other hand, if one firm raises its price, it will lose customers to its rivals, who may take advantage of the opportunity to increase their market share. This will result in a loss of revenue for the firm that raised its price. - Strategic behavior: The firms in an oligopoly engage in strategic behavior, meaning they take into account the possible reactions of their rivals when making their decisions. For example, if one firm decides to invest in research and development (R&D) to create a new product, it will consider how its rivals will react to this move. Will they follow suit and invest in R&D as well? Will they try to imitate or copy the new product? Will they launch a counterattack by increasing their advertising or lowering their prices? The firm will weigh the costs and benefits of its decision based on these scenarios. - Non-price competition: The firms in an oligopoly tend to avoid price competition, because it can lead to a destructive price war that erodes their profits. Instead, they resort to non-price competition, such as advertising, branding, product differentiation, innovation, customer service, or loyalty programs. These strategies aim to increase the demand for their products by making them more attractive or distinctive from their rivals' products. For example, Coca-Cola and Pepsi spend millions of dollars on advertising campaigns to create brand awareness and loyalty among consumers. Examples of Oligopoly Some examples of industries that are characterized by oligopoly are: - Automobile industry: The global automobile industry is dominated by a few large firms, such as Toyota, Volkswagen, General Motors, Ford, Honda, and Hyundai. These firms produce differentiated products that vary in design, quality, features, and performance. They compete with each other by investing in R&D, innovation, marketing, and pricing strategies. - Smartphone industry: The global smartphone industry is dominated by a few large firms, such as Apple, Samsung, Huawei, Xiaomi, and Oppo. These firms produce differentiated products that vary in design, quality, features, and performance. They compete with each other by investing in R&D, innovation, marketing, and pricing strategies. - Airline industry: The global airline industry is dominated by a few large firms, such as American Airlines, Delta Air Lines, United Airlines, Southwest Airlines, and Lufthansa. These firms produce homogeneous products that offer similar services and routes. They compete with each other by offering discounts, frequent flyer programs, in-flight entertainment, and customer service. What is Game Theory? Game theory is a branch of mathematics that studies how rational agents make strategic decisions in situations where their actions affect and are affected by the actions of others. A game is any situation where two or more players (or agents) have conflicting or cooperative interests and can choose from a set of possible actions (or strategies) that determine the outcome of the game. The outcome of the game depends not only on the actions of each player, but also on the actions of the other players. The players are assumed to be rational, meaning they act in their own best interest and try to maximize their payoff (or utility) from the game. Definition and Assumptions of Game Theory A game can be defined by four elements: - Players: The players are the agents who participate in the game and make strategic decisions. They can be individuals, firms, countries, or any other entities that have interests and preferences. A game can have two or more players. - Strategies: The strategies are the possible actions that each player can choose from in the game. They can be discrete (such as choosing a price or a quantity) or continuous (such as choosing a level of investment or advertising). A strategy can be pure (such as choosing one action with certainty) or mixed (such as choosing one action with some probability). - Payoffs: The payoffs are the outcomes or rewards that each player receives from the game based on the strategies chosen by all players. They can be monetary (such as profits or losses) or non-monetary (such as utility or satisfaction). A payoff can be positive (such as a gain) or negative (such as a loss). - Information: The information is the knowledge that each player has about the game and the other players. It can be complete (such as knowing all the elements of the game) or incomplete (such as not knowing some elements of the game). It can also be perfect (such as knowing all the actions and payoffs of the other players) or imperfect (such as not knowing some actions and payoffs of the other players). Some of the main assumptions of game theory are: - Rationality: The players are rational, meaning they act in their own best interest and try to maximize their payoff from the game. They also have consistent preferences and beliefs about the game and the other players. - Common knowledge: The players have common knowledge of the game and its elements, meaning they know what they know, they know what the other players know, they know what the other players know that they know, and so on. - Equilibrium: The players reach an equilibrium in the game, meaning they choose strategies that are optimal for them given the strategies chosen by the other players. No player has an incentive to deviate from his or her strategy unilaterally. Types of Games There are many types of games that can be classified based on different criteria, such as: - Number of players: A game can have two players (such as a duopoly) or more than two players (such as an oligopoly). A two-player game can be further divided into a zero-sum game (where one player's gain is another player's loss) or a non-zero-sum game (where both players can gain or lose). - Number of stages: A game can have one stage (where each player chooses his or her strategy once and for all) or multiple stages (where each player chooses his or her strategy sequentially or repeatedly). A one-stage game can be further divided into a simultaneous-move game (where each player chooses his or her strategy without observing the other player's choice) or a sequential-move game (where one player chooses his or her strategy after observing the other player's choice). A multiple-stage game can be further divided into a finite-horizon game (where there is a fixed number of stages) or an infinite-horizon game (where there is no fixed number of stages). - Information structure: A game can have complete information (where each player knows all the elements of the game) or incomplete information (where some elements of the game are unknown to some players). A game can also have perfect information (where each player knows all the actions and payoffs of the other players) or imperfect information (where some actions and payoffs of the other players are unknown to some players). Applications of Game Theory Game theory has many applications in various fields of study, such as: - Economics: Game theory is widely used in economics to study the behavior and outcomes of markets, firms, consumers, regulators, and policymakers. It can help explain how firms compete or cooperate with each other in different market structures, such as monopoly, oligopoly, monopolistic competition, or perfect competition. It can also help analyze how consumers make choices under uncertainty, risk, or bounded rationality. Moreover, it can help design optimal mechanisms or incentives for achieving social welfare, efficiency, or fairness in various contexts, such as auctions, bargaining, voting, public goods provision, or taxation. - Biology: Game theory is widely used in biology to study the evolution and adaptation of organisms, species, populations, or genes. It can help explain how natural selection shapes the traits and behaviors of living beings in response to environmental pressures, such as predation, competition, cooperation, or mating. It can also help model the dynamics and stability of ecological systems, such as food webs, symbiosis, mutualism, or parasitism. Furthermore, it can help understand the emergence and maintenance of social phenomena, such as altruism, kin selection, reciprocity, or group selection. - Psychology: Game theory is widely used in psychology to study the cognitive and emotional processes of human decision making and social interaction. It can help explain how people form beliefs, preferences, expectations, or intentions based on their own and others' information and actions. It can also help predict how people behave strategically or rationally in various situations involving conflict, cooperation, communication, trust, or deception. Additionally, it can help explore how people learn from experience or feedback and how they update their beliefs or strategies over time. - Political science: Game theory is widely used in political science to study the behavior and outcomes of political actors, institutions, systems, or policies. It can help explain how political leaders or parties compete or cooperate with each other in different political regimes, such as democracy, dictatorship, monarchy, or anarchy. It can also help analyze how voters or citizens make choices under uncertainty, ignorance, or manipulation. Moreover, it can help design optimal rules or mechanisms for achieving political goals, such as representation, accountability, legitimacy, or stability in various contexts, such as elections, voting systems, coalitions, bargaining, wars, or international relations. How Game Theory Applies to Oligopoly Game theory is a useful tool for analyzing the behavior and outcomes of oligopolistic firms. It can help model the interdependence and strategic behavior of the firms in different scenarios and identify the possible equilibria and payoffs that may result from their decisions. It can also help evaluate the advantages and disadvantages of being a leader or a follower in the market and the effects of collusion or competition on the industry and society. Interdependence and Strategic Behavior As we have seen, the firms in an oligopoly are interdependent and engage in strategic behavior. They have to consider not only their own costs and benefits, but also those of their rivals when making their decisions. For example, they have to decide how much to produce and what price to charge for their products. If they produce too much or charge too low, they will start a price war that will reduce their profits. If they produce too little or charge too high, they will lose market share to their rivals who may take advantage of the opportunity to increase their sales and profits. One way to model this situation is by using a payoff matrix that shows the payoffs for each firm based on their choices. For example, consider a duopoly (an oligopoly with two firms) that produces a homogeneous product (such as bottled water) and faces a linear demand curve (such as Q = 100 - P). The marginal cost of production for each firm is constant at $10 per unit. The table below shows the payoff matrix for this duopoly: Firm B Low price ($20) High price ($40) --- --- --- Firm A Low price ($20) A: $100 B: $100 A: $150 B: $50 High price ($40) A: $50 B: $150 A: $200 B: $200 The payoff matrix shows the profits for each firm based on their price choices. For example, if both firms choose a low price ($20), they will each earn a profit of $100 (calculated as (20 - 10) x 10). If both firms choose a high price ($40), they will each earn a profit of $200 (calculated as (40 - 10) x 10). If one firm chooses a low price and the other chooses a high price, the low-price firm will earn a profit of $150 (calculated as (20 - 10) x 15) and the high-price firm will earn a profit of $50 (calculated as (40 - 10) x 5). The payoff matrix illustrates the interdependence and strategic behavior of the firms. Each firm has to anticipate what the other firm will do and choose its best response accordingly. For example, if firm A expects firm B to choose a low price, its best response is to choose a low price as well (to avoid losing market share and profits). If firm A expects firm B to choose a high price, its best response is to choose a high price as well (to avoid starting a price war and reducing profits). Similarly, if firm B expects firm A to choose a low price, its best response is to choose a low price as well. If firm B expects firm A to choose a high price, its best response is to choose a high price as well. The Prisoner's Dilemma The payoff matrix above also illustrates a famous game theory concept called the prisoner's dilemma. The prisoner's dilemma is a situation where two players have an incentive to cooperate but also have an incentive to defect and betray each other. As a result, they end up choosing an outcome that is worse for both of them than if they had cooperated. In this case, the prisoner's dilemma occurs because both firms have an incentive to charge a high price and earn a high profit ($200 each), but they also have an incentive to charge a low price and undercut their rival and earn a higher profit ($150 each). However, if both firms charge a low price, they will end up earning a lower profit ($100 each) than if they had charged a high price. Thus, the high price-high price outcome is the cooperative outcome and the low price-low price outcome is the non-cooperative outcome. The prisoner's dilemma shows that the rational and self-interested behavior of the firms leads to a suboptimal outcome for both of them. This is because they fail to take into account the externalities or spillovers of their actions on the other firm. If they could somehow coordinate or communicate with each other and agree to charge a high price, they would both be better off. However, this is not possible or legal in most cases, as we will see in the next section. Nash Equilibrium and Dominant Strategies Another important game theory concept that applies to oligopoly is the Nash equilibrium. A Nash equilibrium is a set of strategies that represents mutual best responses to the other strategies. In other words, if every firm is playing its part of a Nash equilibrium, no firm has an incentive to unilaterally change its strategy. A Nash equilibrium can be found by looking for the strategies that are underlined in the payoff matrix. In this case, there are two Nash equilibria: one where both firms charge a low price and one where both firms charge a high price. These are the only outcomes where neither firm can improve its profit by changing its price, given what the other firm is doing. For example, if both firms charge a low price, neither firm can increase its profit by charging a high price, because it will lose market share and earn only $50. Similarly, if both firms charge a high price, neither firm can increase its profit by charging a low price, because it will start a price war and earn only $150. A Nash equilibrium can also be found by looking for dominant strategies. A dominant strategy is a strategy that is optimal for a firm regardless of what the other firm does. In other words, it is a strategy that always yields the highest payoff for a firm, no matter what the other firm chooses. A dominant strategy can be found by comparing the payoffs for each strategy across the rows or columns of the payoff matrix. Collusion and Cartels As we have seen, the prisoner's dilemma shows that the firms in an oligopoly have an incentive to cooperate and charge a high price, but they also have an incentive to defect and charge a low price. This creates a tension between cooperation and competition among the firms. One way to resolve this tension is by colluding or forming a cartel. Collusion occurs when oligopoly firms make joint decisions and act as if they were a single firm. Collusion requires an agreement, either explicit or implicit, between cooperating firms to restrict output and achieve the monopoly price. This causes the firms to be interdependent, as the profit levels of each firm depend on the firms own decisions and the decisions of all other firms in the industry. This strategic interdependence is the foundation of game theory. A cartel is a group of colluding firms that act as a monopoly. A cartel is formed when firms jointly fix prices and outputs with a view to maximizing total industry profits. A cartel can be either formal or informal. A formal cartel is an organization that has a legal status and a governing body that enforces the agreement among the members. An example of a formal cartel is OPEC (Organization of Petroleum Exporting Countries), which controls the supply and price of oil in the world market. An informal cartel is an arrangement that has no legal status and no governing body that enforces the agreement among the members. An example of an informal cartel is the diamond industry, which is dominated by a few large firms that control the supply and price of diamonds in the world market. The figure below shows how a cartel works in an oligopoly: ![Cartel](https://www.economicsdiscussion.net/wp-content/uploads/2016/03/clip_image0021.jpg) The figure shows the demand curve (D) and the marginal revenue curve (MR) for the industry, as well as the marginal cost curve (MC) for each firm. The cartel acts as a monopoly and sets the output level where MR = MC for the industry, which is Qc units. The cartel then sets the price Pc that corresponds to Qc on the demand curve. The cartel then allocates the output Qc among its members according to some rule, such as equal shares or proportional shares based on capacity or market share. The cartel


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