Mixed Strategy Nash Equilibrium Using Game of Thrones

Objectives:

1. Understand the concept of a Mixed Strategy Nash Equilibrium (MSNE) in game theory.
2. Analyze strategic interactions where players randomize over strategies.
3. Evaluate how MSNE applies to decision-making under uncertainty.
4. Apply MSNE concepts to scenarios from Game of Thrones.

Materials:

• Video: “Game Theory in House of the Dragon: A Mixed Strategy for the Prince’s Life”
• Whiteboard or presentation slides for game theory diagrams.

Procedures:

Introduction (5 minutes):

1. Begin by discussing how uncertainty and strategy play a role in decision-making.
2. Introduce the concept of a Mixed Strategy Nash Equilibrium (MSNE) as a situation where players randomize their choices to make opponents indifferent to their strategies.

Instruction (30 minutes):

1. Introduce why many games only have a MSNE:
   • Explain how some games have a Nash equilibrium in pure strategies, like a prisoner’s dilemma game, but other games do not have one.
   • Provide a simple example, such as rock-paper-scissors, where each player chooses their actions with equal probability.
2. Video Analysis:
   • Show the video “Game Theory in House of the Dragon: A Mixed Strategy for the Prince’s Life.”
   • Ask students to identify the strategic situation described in the video.
3. Group Discussion:
   • Divide students into small groups to analyze:
     • What strategies were available to the Prince and his adversaries?
     • How does randomization ensure survival or success in this scenario?
     • Was the outcome influenced by information asymmetry or imperfect information?
   • Have each group present their findings.
4. Game Theory Diagrams:
   • Use the whiteboard or slides to map out the strategies and payoffs for each player.
     • Note, different groups could come up with different payoffs here. Some might use numbers and others might use “live/die”, for example. This is OK and gives a educators good opportunity to discuss how defining the payoffs is important (and not always easy).
   • For those who provided numbers, calculate the MSNE, showing how each player’s choices influence the others.

Conclusion (10 minutes):

1. Recap the key concepts of MSNE, including the role of randomization in strategy.
2. Emphasize the practical applications of MSNE in competitive and uncertain environments.

Follow-Up Activity:

Assign students to find a real-world example where players use mixed strategies (e.g., business pricing strategies, sports tactics). Have them prepare a brief analysis of the strategies and potential equilibria to share in the next lesson.