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Unraveling Oligopoly Games: The Prisoner's Dilemma
Dive into the world of oligopoly games and strategies, with a focus on the Prisoner's Dilemma. Understand strategic decision-making in oligopolistic markets and gain insights into real-world competitive behaviors.

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Now Playing:Prisoners dilemma – Example 0a
Intros
  1. Oligopoly Games & Strategies: Prisoner's Dilemma
  2. Oligopoly Games & Strategies: Prisoner's Dilemma
    Definition of a Game
    • Rules
    • Strategies
    • Payoffs
    • Outcome
    • We will see these in Prisoner's Dilemma
  3. Oligopoly Games & Strategies: Prisoner's Dilemma
    Rules of Prisoner's Dilemma, and Strategies
    • Background of Prisoner's Dilemma
    • Rules of each prisoner
    • Strategies of each player
    • Possible Outcomes
Examples
  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.

Oligopoly games & strategies: Prisoners dilemma
Jump to:NotesConceptFAQsPrerequisites
Notes
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. 
Concept

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!

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.

Prerequisites

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.