Market Failure: Game Theory

Game Theory

Overview

• Course: ECO 2023: Introductory Microeconomics

• Instructor: Viviana Rodriguez

• Semester: Fall 2025

Prologue

• Date: 2/22

Chapter Focus

• Chapter 13: Oligopoly and Strategic Behavior

  • Note: Oligopoly part not covered

  • Reading Assignment: Pages 405-418

  • Main Theme: How does Game Theory explain strategic behavior?

Definition of Game Theory

• Game Theory: A framework of analysis where two or more players compete for payoffs.

  • Player's Payoff Dependents:

  1. Her decisions.

  2. Decisions of all other players.

  • Applications of Game Theory:

  • Useful for understanding various competitive and cooperative scenarios, including:

    • Competitive Scenarios: Politics, collective bargaining, war, sports, etc.

    • Cooperative Scenarios: Resource management, public goods (discussed in next week’s topic).

Key Components of a Game

• **Definition of a Game Requirements:

  • Players: Individuals or groups involved in the game.

  • Example Players:

    • Donald Trump and Kamala Harris in the 2024 election.

    • OPEC countries such as Saudi Arabia and Venezuela.

    • Historical superpowers like the USA and USSR.

  • Strategies: Options available to each player.

  • Example Strategies:

    • Focus on specific states in an election, e.g., Pennsylvania or Georgia.

    • Colluding to restrict oil output or competing to increase oil output.

    • Developing a nuclear arsenal or choosing not to.

  • Payoffs: Outcomes associated with each strategy combination.

  • Examples of Payoffs:

    • Winning the presidential election (POTUS) or losing.

    • Splitting higher revenues or incurring lower revenues.

    • Continue to exist or risk total annihilation.

The Prisoner's Dilemma

• Scenario Overview: An interrogator keeps two prisoners (Prisoner 1 and Prisoner 2) in separate cells and interviews them separately.

  • Available Actions for Each Prisoner:

  • Deny the charges.

  • Accuse the other prisoner.

  • Implications of Choices:

  • Leads to an analysis of strategic behavior.

Analysis of the Prisoner's Dilemma

1. Step 1: Quantify the payoffs in the situation.

2. Step 2: Determine each prisoner’s best response based on the strategy played by the other prisoner.

   • Finding: Both players exhibit a dominant strategy to accuse their counterpart.

3. Step 3: Identify the Nash equilibrium.

   • Nash Equilibrium: (Accuse, Accuse)

     • Explanation of Equilibrium Logic:

     • Given that Prisoner 1 chooses to accuse, Prisoner 2 has a greater payoff by also accusing.

     • Conversely, if Prisoner 2 opts to accuse, Prisoner 1 benefits by choosing to accuse.

Cooperation versus Defection

• Participation Scenario: Participants can choose to cooperate or defect.

  • Outcome of Cooperative Choices:

  • If all cooperate, each participant receives 2 bonus participation points.

  • Outcome of Defection:

  • If one defects while others cooperate, the defector earns 6 points while others earn nothing.

  • If multiple defect, all receive 0 points.

  • Strategy Options:

  • A. Cooperate

  • B. Defect

Equilibrium Strategies in Different Contexts

• Cournot Game:

  • Equilibrium Explanation:

  • (Low Price, Low Price) is the equilibrium strategy, even when mutual deviation could be beneficial.

Modifications in the Prisoner's Dilemma

• Prisoner’s Dilemma 2.0:

  • Scenario Change:

  • Similar to the initial prisoner's dilemma, but now includes a pre-heist contract.

  • New Equilibrium Strategies:

  • Two equilibria identified: (Accuse, Accuse) and (Deny, Deny).

  • This scenario transitions from a prisoner's dilemma to a coordination game.

Matching Pennies Game

• Game Structure:

  • Players: 2 players, each having a penny.

  • Action: Each player secretly turns their penny to heads or tails.

  • Winning Conditions:

  • If the pennies match (both heads or both tails), player Even wins and keeps both pennies.

  • If they do not match (one heads and one tails), player Odd wins and keeps both pennies.

  • Equilibrium Strategy:

  • No mutual best responses exist; the only equilibrium strategy necessitates randomization.

Sequential Games

• Understanding Sequential Games:

  • Sequential decisions: Not all games involve simultaneous actions; one player might move before another.

  • Backward Induction:

  • A method to deduce backward from the end of a scenario to derive a sequence of optimal decisions.

Market for Smartphones Scenario

• Situation Description:

  • Samsung (S) has developed a new smartphone.

  • Pricing Strategies: Samsung's pricing will influence market dynamics.

  • High Price Outcome: High price could lead to substantial profits but attracts competition from Apple (A).

  • Low Price Outcome: May suppress potential profits but discourage competition.

Market Dynamics with Specific Strategies

• 
  

• Strategies Summary:
  

  Samsung Price	Apple's Action	Payoff for Samsung
  High Price	Enter	16%
  High Price	Don't Enter	30%
  Low Price	Enter	5%
  Low Price	Don't Enter	-2%
  Backward Induction Application in Market for Smartphones

  • Using Backward Induction:

    • Samsung (S) evaluates possible outcomes based on its pricing strategy:

    • If set to high price: Apple (A) will enter and Samsung will achieve a 16% return.

    • If set to low price: Apple (A) will not enter, enabling Samsung to receive a 20% return.

    • Final Decision: Samsung ultimately chooses to set a low price.