MG3212 Strategy: Game Theory I Notes

MG3212 Strategy: Game Theory I - Simultaneous Games

What is Strategy?

  • Definition of Strategy:

    • Strategy is the set of decisions that allow a firm to achieve its long-term goals.
    • It also involves evaluating the opportunities and threats present in a firm’s environment (Part I of the Course).
    • It requires evaluating the strengths and weaknesses of the firm’s internal environment (Part II of the Course).

  • Game Theory:

    • Game theory is a mathematical tool used to model and study strategic interactions involving coordination, cooperation, and conflict.

Overview of Course Content

  • Part I:
    • How do firms compete?
    • Mechanisms of competition:
    • Static Models of Imperfect Competition (Market Structure: Oligopoly)
    • Dynamic Competition (Dynamic Collusive Pricing; Entry, Exit, and Dynamics)
    • Game Theory I: Simultaneous Games
    • Game Theory II: Dynamic Games

Game Theory: Terminology

  • Players: Each firm comprises a player.
  • Actions: Each player has a set of actions they can take at each instance of the game.
  • Profiles of Actions: A profile of actions determines an outcome. For every outcome, each player receives a payoff, leading to players’ preferences over outcomes.
  • Strategy Definition:
    • A strategy for each player is "a contingent, complete plan of action specifying an action that the player would take in every contingency of the game that they may encounter."
  • Best Response:
    • A best response for a player is the best strategy that can be followed given the belief about the other player’s strategy. Notably, there may be more than one best response.
  • Dominant Strategy:
    • A dominant strategy is a strategy for a player that strictly outperforms any other strategy, regardless of the beliefs they hold about the other player's strategy.
  • Dominated Strategy:
    • A player has a dominated strategy if there exists another strategy yielding a strictly higher payoff regardless of the choices made by others.
  • Equilibrium:
    • Equilibrium predicts the outcome of the game. It is a profile of strategies where:
    • Players play a best response to what they believe others are playing.
    • These beliefs must be correct.

Example of Game Theory in Action

  • Payoff Matrix Example:
    • Players choose strategies which lead to multiple outcomes, each with associated payoffs:
      | | Player 2: H | Player 2: L |
      |-----------|--------------|--------------|
      | Player 1: H | (10, 5) | (6, 6) |
      | Player 1: L | (5, 2) | (10, 8) |
Players Determine Best Response
  1. If Player 2 chooses H, Player 1’s best response is to choose H for a payoff of (10, 5).
  2. If Player 2 chooses L, Player 1’s best response is to choose L for a payoff of (10, 8).
  3. Player 1 will seek the optimal response based on Player 2's action.

Analyzing Dominant Strategies and Equilibria

  • Characteristics of Dominant Strategy:
    • Certain strategies consistently outperform their alternatives, resulting in predictable player behavior.
  • Nash Equilibrium:
    • A Nash equilibrium occurs when:
    • Each player is choosing the optimal strategy based on the strategy chosen by the other player.
    • There are no profitable deviations available.
  • Mixed Strategy Nash Equilibria:
    • Employed when players face uncertainty. Players randomize over strategies, which makes them less predictable to their opponents.

Application: Problem Sets in Game Theory I

  • Problem Set I, Part I: Questions 1-4 cover simultaneous game scenarios.
  • Problem Set I, Part II: Analyze scenarios regarding nuclear standoffs and strategic interactions.

Assignment Content Breakdown

  1. Assignment Problem Set, Part I - Question 1:
    • Examine a matrix representing the game between Players R and C, identifying dominant and dominated strategies. For example:
      • Player R > Q=100; Dominated Strategies identified as Q=50.
  2. Question 2:
    • Analyze two firms in the chocolate market and determine Nash equilibria and the outcome maximizing joint surplus.
  3. Profit Matrix for Question 2:
    • Identification of payoffs based on quality choice.
  4. Question 3:
    • Assess possible product introduction outcomes among competing firms.
  5. Question 4:
    • Critically assess generalized assumptions about Nash Equilibrium.

Conclusion and Key Learnings

  • Rationality in Game Theory: Players must acknowledge rationality in Decision Theory to predict outcomes effectively.
  • Mixed Strategies: Understanding the implications of mixing strategies enables players to optimize payoffs and minimize losses across various competitive environments.
  • Game Theory remains a pivotal analytical tool in understanding strategic interactions across a multitude of scenarios including economics, politics, and personal decision-making processes.

Advanced Game Theory Analysis

  • Using Mixed Strategies: Offers unpredictability and strategic advantages, as players randomize decisions based on expected responses of their opponents.
  • Iterative Deletion of Dominated Strategies: A crucial methodology for narrowing down potential strategy profiles to determine probable outcomes.

Reflective Insights

  • When dealing with multiple competing strategies, such as the nuclear standoff, recognizing potential cooperative outcomes is vital for mitigating adverse effects.
  • Strategic Interaction Outcomes: Must be critically analyzed, questioning assumptions of rationality and assessing potential payoffs in both cooperative and non-cooperative frameworks.