Module 12.1 Strategies and Payoffs Lecture

Understanding Game Theory

• Introduction to Game Theory

  • Examines decision making where outcomes are influenced by the actions of others.

  • Important for understanding behaviors when payoffs depend on interactions between individuals.

  • Utilized in various fields, including economics and sports.

Elements of a Game

• Players

  • Example: Steph and Tanya, roommates with shared interests.

• Strategies

  • Complete action plans available to players.

  • Example: Each can choose to either clean the apartment or play video games.

• Payoffs

  • Rewards for each combination of strategies.

  • Payoffs represent happiness or utility rather than just monetary value.

Payoff Matrix

• Simultaneous Move Game

  • Players make decisions without knowledge of the other's choice.

  • This assumption helps explore less-than-ideal outcomes.

• Payoff Example:

  Strategy / Tanya	Play Video Games	Clean
  Play Video Games	(2, 2)	(10, 0)
  Clean	(0, 10)	(6, 6)

• Payoff Analysis:

  • Both play video games: payoffs of $2 each (disliked outcome - dirty apartment).

  • One cleans, one plays: the cleaner has a lower payoff (0); the player has a higher payoff (10).

  • Both clean results in highest mutual payoff of $6 each.

Dominant Strategy

• Definition:

  • A strategy that is best for a player regardless of what the other does.

• Analysis for Steph:

  • If Tanya plays video games, Steph’s payoffs are (2, from video games) and (0, from cleaning), supporting playing video games.

  • If Tanya cleans, Steph gets (6 from cleaning) or (10 from video games), so also chooses to play video games.

• Similarly, analyze Tanya's decisions:

  • She finds playing video games is her best choice, regardless if Steph plays or cleans.

Dominant Strategy Equilibrium

• Outcome:

  • Both players choosing to play video games leads to payoffs of $2 each.

  • Despite not being the optimal choice (could achieve $6 each from cleaning together), each player’s strategy keeps them in a suboptimal equilibrium.

Applications of Game Theory

• Prisoner’s Dilemma:

  • Classic example where mutual cooperation leads to better outcomes but individual strategies lead to suboptimal results.

  • Situations include nuclear arms races and pricing strategies among competitors.

Conclusion

• Understanding how to analyze interactions through game theory can help avoid breakdowns in rational behavior and foster cooperation among individuals.