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Game Theory

Game Theory. Yen-Chia Huang Mentor : Quanyuan Zhu. What is game theory?. A theory that helps us understand situations in which decision makers interact with each other. What elements do game theory have?.

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Game Theory

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  1. Game Theory Yen-Chia Huang Mentor : Quanyuan Zhu

  2. What is game theory? • A theory that helps us understand situations in which decision makers interact with each other.

  3. What elements do game theory have? • A set of actions that are available for each player. • Preferences and payoff functions. • We use payoff functions to represent preferences of players. For example : for player A payoff(I) > payoff(II) if and only if player A prefers action I to action II.

  4. Strategic Games • A strategic game is a model of interacting decision makers. • A strategic game consist of 1. A set of players. 2. For each player, a set of actions. 3. For each player, preferences over the set of action profiles.

  5. Example : 2x2 matrix.

  6. Nash Equilibrium

  7. Three different types I • Prisoner's Dilemma

  8. Three different types II • Bach & Stravinsky

  9. Three different types II • Head & Tail

  10. Fictitious Play • During the game, each player assumes that his/her opponents use the stationary strategy. • At each round, each player selects an action that optimizes his/her payoff based on historical frequency of actions of his/her opponents.

  11. Fictitious Play • Prisoner's Dilemma

  12. Fictitious Play • Bach & Stravinsky

  13. Fictitious Play • Head & Tail

  14. How does it work?

  15. Prisoner's Dilemma • Rationality of Player A = 90%

  16. Prisoner's Dilemma • Rationality of Player A = 80%

  17. Prisoner's Dilemma • Rationality of Player A = 70%

  18. Prisoner's Dilemma • Rationality of Player A = 60%

  19. Bach & Stravinsky • Rationality of Player A = 90%

  20. Bach & Stravinsky • Rationality of Player A = 80%

  21. Bach & Stravinsky • Rationality of Player A = 70%

  22. Bach & Stravinsky • Rationality of Player A = 60%

  23. Head & Tail • Rationality of Player A = 90%

  24. Head & Tail • Rationality of Player A = 80%

  25. Questions?

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