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Oligopoly games & strategies: Prisoners dilemma

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Intros
Lessons
  1. Oligopoly Games & Strategies: Prisoner's Dilemma
  2. Definition of a Game
    • Rules
    • Strategies
    • Payoffs
    • Outcome
    • We will see these in Prisoner's Dilemma
  3. Rules of Prisoner's Dilemma, and Strategies
    • Background of Prisoner's Dilemma
    • Rules of each prisoner
    • Strategies of each player
    • Possible Outcomes
  4. The Payoff Matrix & Nash Equilibrium
    • What each player gains/loss in each outcome
    • Predicting the Outcome
    • Nash equilibrium
    • Best choice given the action of prisoner B
    • Best choice given the action of prisoner A
    • Equilibrium of the Game: Worst Outcome
  5. Prisoner's Dilemma in Duopoly
    • Collusive Agreement (Comply or Cheat)
    • Possible Outcomes for Complying or Cheating
    • What happens to each firm in each outcome
    • Payoff Matrix & Nash Equilibrium of Duopoly
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Examples
Lessons
  1. Understanding Game Definitions
    Determine whether each action is allowed in a prisoner's dilemma.
    1. Accuse each other
    2. Stay silent
    3. Communicate with each other
    4. Negotiate with the police
    5. Accuse first, then stay silent
    6. Stay silent first, and then accuse.
  2. Determine whether each statement is true or false in a prisoner's dilemma.
    1. There are always 4 outcomes
    2. Players can have more than two strategies
    3. The players cannot communicate with each other.
    4. Players always make choices base on their personal gain.
  3. Calculating the Payoff Matrix & Nash Equilibrium in Prisoner's Dilemma
    Suppose there is a two-player game in which they cannot communicate. Each player is asked a question and must answer honestly or lie. If both answer honestly, then each receives $100. If one answers honestly and one lies, then the liar receives $500 and the honest player gets nothing. If both lie, then each player receives $50.
    1. Describe the strategies and outcomes
    2. Make the payoff matrix.
    3. What is the Nash equilibrium?
  4. Suppose there are two prisoners in which they cannot communicate. Each prisoner is interrogated by the police. If both prisoners stay silent, then both will be sentenced to jail for 2 years. If both accuse each other, then both will be sentenced to jail for 4 years. If one accuses and the other stays silent, then one of them will be sentenced to jail for 7 years, and the other prisoner will be free.
    1. Describe the strategies and outcomes.
    2. Make the payoff matrix.
    3. What is the Nash equilibrium?
  5. Calculating the Payoff Matrix & Nash Equilibrium with Duopoly
    Firm A and firm B are both producers of soft drinks. Both firms are trying to figure out how much soft drinks is needed to be produced. They know the following:
    1. If both limit productions to 10,000 gallons a week, they will make a maximum attainable profit of $100,000. So, each firm gains $50,000 a week.
    2. If one firm produces 10,000 gallons a week and the other firm produces 5,000 gallons a week, then the one who produces 10,000 gallons will gain an economic profit of $100,000, while the other will incur an economic loss of $25,000.
    3. If both increases their production 10,000 gallons a week, both firms will gain zero economic profit.

    1. Construct a payoff matrix.
    2. Find the Nash equilibrium.
  6. Firm A and firm B are both producers of wallets. The firms decide to collude and form a cartel to share the market equally. If neither firm cheat on the agreement, then each makes $2 million profit. If one firm cheats, then the cheater make a profit of $3 million and the complier will lose $1 million. If both cheats, they will both break even. Assume that none of the firms can monitor the other actions.
    1. What are the strategies of the game?
    2. Construct the payoff matrix.
    3. What is the Nash equilibrium?
Topic Notes
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Introduction to Oligopoly Games and Strategies

Welcome to our exploration of oligopoly games and strategies, with a special focus on the famous Prisoner's Dilemma! In this section, we'll dive into the fascinating world of game theory and how it applies to oligopolies. The Prisoner's Dilemma is a classic example that beautifully illustrates the strategic decision-making in oligopolistic markets. Our introduction video provides a clear and engaging overview of these concepts, making it an essential starting point for understanding oligopoly dynamics. As we progress, you'll see how firms in an oligopoly must consider their competitors' actions when making decisions, much like the prisoners in our dilemma. This interdependence creates a complex web of strategies and outcomes, which we'll unravel together. By mastering these concepts, you'll gain valuable insights into real-world market behaviors and competitive strategies. So, let's begin this exciting journey into the world of oligopoly games and the Prisoner's Dilemma!

Understanding Game Theory in Oligopoly

Game theory is a fascinating concept that has found significant application in understanding oligopoly markets. At its core, game theory is about strategic decision-making in situations where the outcome depends not just on your own choices, but also on the choices of others. In the context of oligopolies, where a few large firms dominate the market, game theory provides valuable insights into how these firms interact and compete.

Let's break down the four common features of a game to better understand how game theory works:

  1. Rules: These are the guidelines that govern the game. In an oligopoly, rules might include legal regulations, market conditions, or industry standards. For example, in the smartphone industry, patent laws and technological standards act as rules that companies like Apple and Samsung must follow.
  2. Strategies: These are the possible actions that players can take. In an oligopoly, strategies could involve pricing decisions, product differentiation, or marketing campaigns. For instance, a soft drink company might choose between a low-price strategy or a premium branding strategy.
  3. Payoffs: These are the rewards or consequences associated with different combinations of strategies. In business terms, payoffs are often measured in profits or market share. If two rival airlines both decide to lower their prices, the payoff might be increased market share but lower profits for both.
  4. Outcomes: These are the final results of the game, determined by the strategies chosen by all players. In an oligopoly, outcomes could be changes in market share, profitability, or even market structure.

To illustrate these concepts, let's consider a simple example in the cola market, dominated by two major players: Cola A and Cola B. Both companies are deciding whether to increase their advertising budget or keep it the same. This scenario can be represented as a game with the following elements:

  • Rules: Each company can only choose to increase advertising or maintain current levels.
  • Strategies: Increase advertising or maintain current advertising.
  • Payoffs: Profits for each company based on their combined decisions.
  • Outcomes: The resulting market shares and profits after both companies make their choices.

If both companies maintain their current advertising, they might each keep their existing market share and profits. If one increases advertising while the other doesn't, the one that increases might gain market share at the expense of the other. However, if both increase advertising, they might end up with similar market shares but lower profits due to increased costs.

Game theory helps predict how firms in an oligopoly might behave, considering the potential actions of their competitors. It explains why companies sometimes engage in price wars, why they might collude (even though it's often illegal), or why they might focus on non-price competition like advertising or product differentiation.

Understanding game theory can be incredibly valuable for both business strategists and policymakers. For businesses, it provides a framework for making strategic decisions in competitive environments. For policymakers, it offers insights into how market structures like oligopolies function, helping inform regulations to promote fair competition and consumer welfare.

In conclusion, game theory is a powerful tool for analyzing strategic interactions in oligopoly markets. By breaking down these interactions into rules, strategies, payoffs, and outcomes, we can gain a deeper understanding of why companies make certain decisions and how these decisions shape market dynamics. Whether you're a student of economics, a business professional, or simply curious about how markets work, game theory offers valuable insights into the complex world of strategic decision-making.

The Prisoner's Dilemma: A Classic Example

Understanding the Prisoner's Dilemma

The Prisoner's Dilemma is a fundamental concept in game theory that illustrates the conflict between individual and collective rationality. This thought experiment, developed by mathematicians Merrill Flood and Melvin Dresher in 1950, explores decision-making processes and their consequences in a competitive scenario.

The Setup

Imagine two suspects, Alice and Bob, are arrested for a crime. The police lack sufficient evidence to convict them of the main charge but have enough to convict them on a lesser charge. The suspects are separated and offered the same deal: betray your accomplice by testifying against them, or remain silent.

The Rules and Possible Outcomes

The rules of the Prisoner's Dilemma create four possible outcomes:

  1. If both Alice and Bob betray each other, they each serve 2 years in prison.
  2. If Alice betrays Bob, but Bob remains silent, Alice goes free while Bob serves 3 years.
  3. If Bob betrays Alice, but Alice remains silent, Bob goes free while Alice serves 3 years.
  4. If both remain silent, they each serve 1 year on the lesser charge.

Decision-Making Process

Each prisoner must make their decision without knowing what the other will do. This uncertainty is crucial to the dilemma. From an individual perspective, betraying seems like the best option regardless of what the other person does. If the other person betrays, betraying limits your sentence to 2 years instead of 3. If the other person remains silent, betraying allows you to go free instead of serving 1 year.

The Paradox

The paradox arises because if both prisoners follow this seemingly rational logic and betray each other, they end up worse off than if they had both remained silent. This outcome, where both serve 2 years, is less desirable than the 1 year they would serve if they had cooperated by staying silent.

Nash Equilibrium

The outcome where both prisoners betray each other is known as the Nash Equilibrium, named after mathematician John Nash. It represents a stable state where neither player can unilaterally improve their situation by changing their strategy, assuming the other player's strategy remains unchanged.

Payoffs and Game Theory

The Prisoner's Dilemma is often represented in a payoff matrix, showing the years of imprisonment (negative payoffs) for each combination of choices. This matrix is crucial in game theory analysis, helping to visualize and calculate optimal strategies.

Real-World Applications

While the Prisoner's Dilemma is a simplified model, it has far-reaching implications in various fields:

  • Economics: It explains phenomena like price wars and collective bargaining.
  • Politics: It illustrates challenges in international relations and arms races.
  • Environmental studies: It helps understand issues like overfishing and pollution control.
  • Psychology: It provides insights into trust, cooperation, and social behavior.

Strategies and Iterations

In real-life scenarios, the Prisoner's Dilemma is often iterated, meaning the game is played multiple times. This introduces the possibility of developing strategies based on past behavior, such as tit-for-tat, where a player copies the opponent's previous move. These iterations can lead to more cooperative outcomes over time.

Conclusion

The Prisoner's Dilemma remains a powerful tool for understanding complex decision-making processes. It highlights the tension between individual and collective interests, demonstrating how rational self-interest can lead to suboptimal outcomes for all parties involved. By studying this concept, we gain valuable insights into human behavior, strategic thinking, and the delicate balance

Nash Equilibrium in the Prisoner's Dilemma

Let's dive into the fascinating world of game theory and explore the concept of Nash Equilibrium, particularly as it applies to the classic Prisoner's Dilemma. Imagine you're tutoring a friend on this topic that's the approach we'll take to make it accessible and engaging!

First, what exactly is Nash Equilibrium? Named after mathematician John Nash, it's a situation in a game where each player is making the best decision for themselves, given what their opponents are doing. In other words, no player can benefit by changing only their own strategy.

Now, let's apply this to the Prisoner's Dilemma. Picture two suspects, Alice and Bob, arrested for a crime. They're interrogated separately and given two choices: betray their partner or remain silent. This is where the payoff matrix comes into play.

A payoff matrix is a table that shows the outcomes for each combination of choices. In the Prisoner's Dilemma, it might look like this:

  • If both remain silent: Each gets 1 year in prison
  • If one betrays and one remains silent: The betrayer goes free, the silent one gets 3 years
  • If both betray: Each gets 2 years in prison

To find the Nash Equilibrium, we need to look at each player's optimal strategy given what the other might do. Let's walk through Alice's thought process:

  1. If Bob remains silent, Alice's best move is to betray (0 years vs 1 year)
  2. If Bob betrays, Alice's best move is still to betray (2 years vs 3 years)

Interestingly, Bob's reasoning will be identical. No matter what the other does, betraying always leads to a better individual outcome. This is why mutual betrayal is the Nash Equilibrium in the Prisoner's Dilemma.

But why is this equilibrium so important? It shows us that in certain situations, rational self-interest can lead to a suboptimal outcome for everyone involved. If Alice and Bob could cooperate and both stay silent, they'd each only serve 1 year. But the structure of the game pushes them towards mutual betrayal and 2 years each.

This concept extends far beyond hypothetical prisoners. It helps explain behaviors in economics, politics, and even everyday life. Think about arms races between countries, or companies deciding whether to engage in price wars. In each case, the Nash Equilibrium might not be the best outcome for all parties, but it's the stable result of everyone pursuing their own interests.

The beauty of the Nash Equilibrium is that it provides a way to predict outcomes in complex interactive situations. By understanding where these equilibria lie, we can better design systems, policies, and incentives to encourage cooperation and achieve better overall results.

Remember, while the Prisoner's Dilemma is a simplified model, it captures a fundamental tension between individual and collective interests. Next time you're in a situation where your choices affect others (and vice versa), think about the payoff matrix and where the Nash Equilibrium might lie. It could give you valuable insights into why people behave the way they do and how to navigate complex social situations.

In conclusion, the Nash Equilibrium in the Prisoner's Dilemma illustrates how rational self-interest can sometimes lead to suboptimal outcomes. By understanding this concept, we gain powerful tools for analyzing strategic interactions in various fields, from economics to social policy. So next time you're faced with a tricky decision involving others, remember Alice and Bob and choose wisely!

Applying Prisoner's Dilemma to Oligopoly Markets

The Prisoner's Dilemma, a classic concept in game theory, provides valuable insights into the dynamics of oligopoly markets, particularly in the case of duopolies. In an oligopoly, a small number of firms dominate the market, and their decisions significantly impact one another. This interdependence creates a scenario similar to the Prisoner's Dilemma, where firms must choose between cooperation and competition.

In a duopoly, where only two firms control the market, the Prisoner's Dilemma becomes even more pronounced. These firms often face the temptation to engage in collusive agreements or form cartels to maximize their collective profits. A collusive agreement is an arrangement between competing firms to control prices, limit production, or divide markets. Cartels are formal organizations of producers or suppliers that agree to fix prices, limit supply, or engage in other anti-competitive practices.

To illustrate how the Prisoner's Dilemma applies to oligopolies, let's consider the example from the video. Imagine two firms in a duopoly market that have formed a collusive agreement to maintain high prices and limit production. Each firm now faces a crucial decision: to comply with the agreement or to cheat by lowering prices or increasing output.

The payoff matrix for this scenario might look like this:

  • If both firms comply with the agreement, they each earn high profits (let's say $10 million each).
  • If one firm cheats while the other complies, the cheating firm earns very high profits ($15 million) while the complying firm suffers losses ($5 million).
  • If both firms cheat, they each earn moderate profits ($8 million each).

This payoff structure creates a dilemma for both firms. While collective compliance would yield the highest total profits, each firm has an individual incentive to cheat. If a firm believes its competitor will comply, it can increase its profits by cheating. Conversely, if a firm suspects its competitor might cheat, it's better off cheating as well to avoid significant losses.

The Prisoner's Dilemma in oligopoly markets often leads to a breakdown of collusive agreements. Even though both firms would benefit from cooperation, the fear of being exploited and the temptation to gain an advantage often result in both firms choosing to compete. This outcome, where both firms cheat on the agreement, is known as the Nash equilibrium a state where neither firm can unilaterally improve its position.

However, unlike the classic Prisoner's Dilemma, which is typically a one-time game, oligopoly markets involve repeated interactions. This repetition can sometimes lead to more stable collusive agreements. Firms may develop strategies like tit-for-tat, where they start by cooperating and then mirror their competitor's previous move. Over time, this can foster a more cooperative environment, although it remains inherently unstable.

The application of the Prisoner's Dilemma to oligopoly markets highlights several key aspects of these market structures:

  1. Interdependence: Firms in oligopolies must constantly consider their competitors' actions when making decisions.
  2. Tension between cooperation and competition: While cooperation can lead to higher profits, the temptation to compete is always present.
  3. Instability of collusive agreements: The individual incentive to cheat often undermines attempts at cooperation.
  4. Potential for price wars: If trust breaks down, firms may engage in aggressive price cutting, leading to lower profits for all.

Understanding these dynamics is crucial for both firms operating in oligopoly markets and regulators tasked with maintaining fair competition. For firms, it underscores the importance of strategic decision-making and the potential consequences of their actions. For regulators, it highlights the need for vigilance against anti-competitive practices while recognizing the complex motivations that drive firm behavior in these markets.

In conclusion, the Prisoner's Dilemma provides a powerful framework for analyzing oligopoly markets, especially duopolies. It illuminates the challenges of maintaining collusive agreements and the constant tension

Analyzing Firm Behavior in Oligopoly Games

In the complex world of oligopolies, firm behavior plays a crucial role in determining market outcomes. Let's examine the different scenarios that can unfold when firms interact in these concentrated markets. We'll explore the economic consequences of compliance and cheating, shedding light on why firms might be tempted to deviate from agreements.

Scenario 1: Both Firms Complying

When both firms in an oligopoly choose to comply with agreements, we often see a stable market environment. This scenario typically results in moderate economic profits for both parties. By adhering to agreed-upon prices or production levels, firms can maintain a balance that benefits all players. Market prices remain relatively stable, and consumers experience predictable pricing. While profits may not be as high as in a monopoly situation, they are generally above what would be seen in perfect competition.

Scenario 2: One Firm Cheating, One Complying

This scenario introduces an interesting dynamic. When one firm decides to cheat on an agreement while the other remains compliant, we often see a short-term advantage for the cheating firm. By lowering prices slightly or increasing production beyond agreed levels, the cheating firm can capture a larger market share and potentially higher economic profits. Meanwhile, the complying firm may experience economic losses or reduced profits as their market share diminishes. This situation creates an unstable market environment and can lead to a breakdown of trust between firms.

Scenario 3: Both Firms Cheating

When both firms choose to cheat on their agreements, we often witness a race to the bottom. In this scenario, economic profits for both firms typically decrease as they engage in aggressive price cutting or overproduction. Market prices can fall dramatically, benefiting consumers in the short term but potentially leading to long-term instability in the industry. This situation can result in economic losses for both firms if prices fall below production costs.

The Temptation to Cheat

Understanding why firms might be tempted to cheat on agreements is crucial. The primary motivation is often the potential for short-term gains in market share and profits. By slightly undercutting a competitor's price or producing more than agreed, a firm can attract more customers and boost its bottom line. This temptation is particularly strong when firms believe they can act without detection or when the potential gains outweigh the risks of retaliation.

Moreover, the pressure to meet shareholder expectations or outperform competitors can drive firms towards cheating. In highly competitive markets, even a small advantage can make a significant difference in financial performance. The fear of being left behind if other firms are suspected of cheating can also push companies to preemptively break agreements.

However, it's important to note that cheating often leads to unstable market conditions and can trigger retaliatory actions from competitors. This can result in a less profitable environment for all firms involved in the long run. The potential for regulatory scrutiny and damage to reputation are additional factors that firms must consider when contemplating whether to cheat on agreements.

In conclusion, the behavior of firms in oligopoly games significantly impacts market dynamics and economic outcomes. While the temptation to cheat for short-term gains exists, firms must carefully weigh the potential consequences against the benefits. Understanding these scenarios helps both businesses and policymakers navigate the complex landscape of oligopolistic markets, striving for a balance that promotes healthy competition and economic stability.

Conclusion

Understanding oligopoly games and strategies is crucial in the world of economics. The Prisoner's Dilemma, as explored in our introduction video, serves as a cornerstone for grasping these complex interactions. This concept illuminates how firms in an oligopoly market make decisions, balancing cooperation and competition. By studying these games, we gain insights into real-world economic behaviors and outcomes. The strategies employed in oligopolies often mirror those in the Prisoner's Dilemma, highlighting the importance of anticipating competitors' moves. We encourage you to delve deeper into game theory, as it offers powerful tools for analyzing various economic scenarios. Remember, the principles learned here extend far beyond oligopolies, influencing diverse fields within economics. Your journey into the fascinating world of game theory has just begun, and we're excited for you to discover its wide-ranging applications in economics and beyond.

Oligopoly Games & Strategies: Prisoner's Dilemma

Oligopoly Games & Strategies: Prisoner's Dilemma Definition of a Game

  • Rules
  • Strategies
  • Payoffs
  • Outcome
  • We will see these in Prisoner's Dilemma

Step 1: Introduction to Oligopoly and Game Theory

Welcome to this section where we delve into the fascinating world of oligopoly and game theory. Oligopoly is a market structure characterized by a small number of firms whose decisions are interdependent. This interdependence often leads firms to engage in strategic behavior, akin to playing games. These games are not for entertainment but are strategic interactions aimed at achieving economic profit. Understanding how these games are played and the types of games involved is crucial for comprehending the dynamics of oligopolistic markets.

Step 2: Definition of a Game

Before diving into specific games like the Prisoner's Dilemma, it is essential to understand the basic components that define a game. A game in economic terms has four common features:

  • Rules: These are the laws or guidelines that all players must follow. In the context of oligopoly, rules could include market regulations, legal constraints, and the basic principles governing the interactions between firms.
  • Strategies: These are the possible actions that a player can take. In an oligopoly, strategies could involve pricing decisions, product launches, marketing campaigns, and other competitive actions.
  • Payoffs: This refers to the gains or losses resulting from a player's actions. Payoffs are crucial as they determine the incentives for each player. In an oligopoly, payoffs could be measured in terms of profits, market share, or other economic benefits.
  • Outcome: The outcome is the result of the actions taken by all players. It is the collective result of the strategies employed by each firm in the market. The outcome could be a stable market equilibrium, a price war, or any other market condition resulting from the strategic interactions.

Step 3: Applying the Game Definition to Prisoner's Dilemma

Now that we have a clear understanding of what constitutes a game, we can apply these concepts to the Prisoner's Dilemma, a classic example in game theory. The Prisoner's Dilemma illustrates the challenges of cooperation and competition in an oligopoly. Heres how the four features of a game apply to the Prisoner's Dilemma:

  • Rules: In the Prisoner's Dilemma, the rules are simple. Two players (or firms) must decide independently whether to cooperate or defect. The decision must be made without knowing the other player's choice.
  • Strategies: Each player has two strategies: to cooperate (remain silent) or to defect (betray the other). In an oligopoly, this could translate to strategies like maintaining current prices (cooperate) or cutting prices to gain market share (defect).
  • Payoffs: The payoffs in the Prisoner's Dilemma are structured such that mutual cooperation leads to moderate benefits for both, mutual defection leads to moderate losses, and one-sided defection leads to a significant gain for the defector and a significant loss for the cooperator. In an oligopoly, this could mean stable profits for mutual cooperation, reduced profits for mutual defection, and a competitive advantage for the defector if the other firm cooperates.
  • Outcome: The outcome of the Prisoner's Dilemma depends on the choices made by both players. If both cooperate, they achieve a collectively better outcome. If both defect, they end up worse off. If one defects while the other cooperates, the defector gains significantly at the expense of the cooperator. In an oligopoly, this dynamic can lead to various market outcomes, including stable collusion, price wars, or competitive imbalances.

Step 4: Conclusion and Implications for Oligopoly

Understanding the Prisoner's Dilemma and its application to oligopoly provides valuable insights into the strategic behavior of firms. It highlights the tension between cooperation and competition and the potential for suboptimal outcomes when firms act in their self-interest. By analyzing these dynamics, firms can better navigate the complexities of oligopolistic markets and make more informed strategic decisions.

FAQs

  1. What is the Prisoner's Dilemma and how does it relate to oligopoly markets?

    The Prisoner's Dilemma is a classic game theory scenario that illustrates the conflict between individual and collective interests. In oligopoly markets, it represents the strategic decision-making process firms face when choosing between cooperation and competition. Just as prisoners must decide whether to betray or remain silent, firms in an oligopoly must decide whether to comply with agreements or cheat for potential short-term gains.

  2. What is Nash Equilibrium in the context of oligopoly games?

    Nash Equilibrium, named after mathematician John Nash, is a state in a game where each player is making the best decision for themselves, given what their opponents are doing. In oligopoly games, it often represents a situation where firms choose to compete rather than cooperate, even though cooperation might lead to better overall outcomes. This equilibrium helps explain why firms might engage in price wars or other competitive behaviors that ultimately reduce profits for all parties involved.

  3. Why do firms in oligopolies sometimes form cartels, and why are these agreements often unstable?

    Firms in oligopolies may form cartels to maximize collective profits by controlling prices, limiting production, or dividing markets. However, these agreements are often unstable because each firm has an individual incentive to cheat. By slightly undercutting agreed prices or increasing production, a firm can potentially capture a larger market share and higher profits. This temptation to cheat, coupled with the fear of being exploited by others, makes cartel agreements inherently unstable.

  4. How does game theory help in understanding and predicting firm behavior in oligopoly markets?

    Game theory provides a framework for analyzing strategic interactions between firms in oligopoly markets. It helps predict how firms might behave by considering the potential actions and reactions of competitors. Through concepts like the Prisoner's Dilemma and Nash Equilibrium, game theory explains why firms might choose certain strategies, such as price cutting or product differentiation, even when these choices lead to suboptimal outcomes for the industry as a whole.

  5. What are the key differences between one-time and repeated oligopoly games?

    One-time oligopoly games often result in non-cooperative outcomes, as firms have no incentive to consider future interactions. In contrast, repeated games allow for the development of strategies based on past behavior, such as tit-for-tat. This repetition can sometimes lead to more cooperative outcomes over time, as firms learn to trust each other and recognize the long-term benefits of cooperation. However, the threat of cheating and the temptation for short-term gains still exist, making even repeated games potentially unstable.

Prerequisite Topics

Understanding the foundations of oligopoly games and strategies, particularly the Prisoner's Dilemma, is crucial for students delving into advanced economic concepts. While there are no specific prerequisite topics listed for this subject, it's important to recognize that a solid grasp of basic economic principles and game theory fundamentals can significantly enhance your comprehension of this complex topic.

The Prisoner's Dilemma, a cornerstone of oligopoly games and strategies, builds upon several key economic concepts. A strong understanding of basic economics is essential, as it provides the context for how firms interact in markets with limited competition. Familiarity with microeconomics is particularly valuable, as it focuses on individual firm behavior and decision-making processes.

Additionally, a basic knowledge of game theory can greatly aid in grasping the intricacies of the Prisoner's Dilemma. Game theory explores strategic decision-making, which is at the heart of oligopoly interactions. Understanding concepts such as Nash equilibrium and dominant strategies will provide a solid foundation for analyzing the Prisoner's Dilemma in the context of oligopolies.

Moreover, familiarity with market structures is crucial. Oligopoly is a specific type of market structure, and comparing it to other structures like perfect competition and monopoly can help in appreciating its unique characteristics. This knowledge will enable students to better understand why firms in an oligopoly might face dilemmas similar to the Prisoner's Dilemma.

While not strictly prerequisites, having a background in statistics and probability can be beneficial. These mathematical tools are often used in analyzing game outcomes and predicting firm behaviors in oligopolistic markets. They can help in quantifying the risks and potential payoffs associated with different strategies in the Prisoner's Dilemma scenario.

Lastly, an understanding of business ethics can provide valuable context for discussing the moral implications of decisions made in oligopoly games. The Prisoner's Dilemma often raises questions about cooperation, trust, and the balance between self-interest and collective benefit, which are central themes in business ethics.

By building a strong foundation in these related areas, students will be better equipped to tackle the complexities of oligopoly games and strategies, particularly the Prisoner's Dilemma. This comprehensive understanding will not only enhance their grasp of the topic but also enable them to apply these concepts to real-world economic scenarios and business decision-making processes.

Definition of a Game

In an economic sense, firms in an oligopoly market play a game with each other to try to achieve economic profit.

Lets first try to investigate the features of a game, and then later see how it relates to Prisoners Dilemma and Duopoly.

There four common features in a game:
  1. Rules: laws that need to be followed.
  2. Strategies: possible actions for a player.
  3. Payoffs: the gains and loss of a player from his actions.
  4. Outcomes: the result gained from the action of all players.

Rules of Prisoners Dilemma, and Strategies

Background: Suppose two people are suspects of a crime, and now must become prisoners. We will call them prisoners A and B. The police do not know who committed the crime, so they force the prisoners to play a game to see if they stay silent or betray each other.

Note: Assume that the prisoners are not friends, and do not know each other.

Rule: Each prisoner is placed in an isolated room, and the prisoners cannot communicate with each other. Each prisoner is told that they are suspected of committing the crime, and are told the following
  1. If both do not accuse each other of committing the crime and stay silent, then both will be sentenced to jail for 3 years.
  2. If the prisoner accuses the other prisoner of committing the crime and the other stays silent, then the accuser is free, and the other prisoner is sentenced to jail for 10 years.
  3. If both prisoners accuse each other, then both will be sentenced to jail for 5 years.

Strategies: Prisoner A and B have two possible actions
  1. Stay silent to the crime.
  2. Accuse the other prisoner.

Outcomes: Since there are two prisoners and each have two strategies
  1. Both stay silent
  2. Prisoner A accuses, Prisoner B stays silent
  3. Prisoner A stays silent, Prisoner B accuses
  4. Both prisoners accuse each other

The Payoff Matrix, & Nash Equilibrium

A payoff matrix is a table that shows all the strategies each player can make, and lists the gains/losses of each player for every outcome.
The Payoff Matrix, & Nash Equilibrium


Nash Equilibrium: is the equilibrium where each players strategy is optimal when given the strategies of all other players.

Lets look at the optimal strategy for prisoner A.
  • Case 1: Prisoner A assumes Prisoner B stays silent about the crime.

    If prisoner A chooses.

    1. \enspace Stay silent  \, →  \, 3 years in jail
    2. \enspace Accuses  \, →  \, 0 years in jail

    The best choice is to accuse prisoner B.
    • Case 2: Prisoner A assumes Prisoner B accuses.

  • If prisoner A chooses.

    1. \enspace Stay silent  \, →  \, 10 years in jail
    2. \enspace Accuses  \, →  \, 5 years in jail

    The best choice is to accuse prisoner B.


So, whether prisoner B stays silent or accuses, prisoner As best action is to accuse.

Lets look at the optimal strategy for prisoner B.
  • Case 1: Prisoner B assumes Prisoner A stays silent about the crime.

    If prisoner B chooses.

    1. \enspace Stay silent  \, →  \, 3 years in jail
    2. \enspace Accuses  \, →  \, 0 years in jail

    The best choice is to accuse prisoner A.
    • Case 2: Prisoner B assumes Prisoner A accuses.

  • If prisoner B chooses.

    1. \enspace Stay silent  \, →  \, 10 years in jail
    2. \enspace Accuses  \, →  \, 5 years in jail

    The best choice is to accuse prisoner A.


So, whether prisoner A stays silent or accuses, prisoner Bs best action is to accuse.

Hence, the Nash equilibrium is for both prisoners accuse each other. This outcome will lead both prisoners to go to jail for 5 years.

Prisoners Dilemma in Duopoly

The same idea in prisoners dilemma holds for duopoly.

Collusive Agreement: an agreement between two firms to form a cartel and act as a monopoly.

Suppose there is firm A and firm B, and the demand and costs for the product is below.

Collusive Agreement

Strategies: Each firm can either
  1. Comply
  2. Cheat .

Outcomes:
  1. Both firms Comply: then they enter a collusive agreement and act as a monopoly. Both firms produce an output of 15, and sell each outprice for $5.

    2. Both firms Comply Collusive Agreement act as a monopoly

    Result: Both firms gain an economic profit of $7.50

  2. Firm A Complies, and Firm B Cheats: Then firm B produces 10 more than firm A, thus lowering the price to $4.
    3. Collusive Agreement Firm A Complies, and Firm B Cheats

    Result: Firm B gains an economic profit of $37.50, and Firm A incurs an economic loss of -$7.50.

    Collusive Agreement Firm A Complies, and Firm B Cheats

  3. Firm B Complies, and Firm A Cheats: Vice versa happens in outcome b.

  4. Both Firms Cheat: They break the collusive agreement and both firms will increase their output to 25, thus lowering the price to $2.50. Both firms will gain no profit.
Collusive Agreement Both Firms Cheat

Payoff: With the listed outcomes, we can create a payoff matrix.
Collusive Agreement payoff matrix outcomes

The Nash equilibrium will be for both firms to cheat.