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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 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? • 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.
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.
Three different types I • Prisoner's Dilemma
Three different types II • Bach & Stravinsky
Three different types II • Head & Tail
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.
Fictitious Play • Prisoner's Dilemma
Fictitious Play • Bach & Stravinsky
Fictitious Play • Head & Tail
Prisoner's Dilemma • Rationality of Player A = 90%
Prisoner's Dilemma • Rationality of Player A = 80%
Prisoner's Dilemma • Rationality of Player A = 70%
Prisoner's Dilemma • Rationality of Player A = 60%
Bach & Stravinsky • Rationality of Player A = 90%
Bach & Stravinsky • Rationality of Player A = 80%
Bach & Stravinsky • Rationality of Player A = 70%
Bach & Stravinsky • Rationality of Player A = 60%
Head & Tail • Rationality of Player A = 90%
Head & Tail • Rationality of Player A = 80%