Lecture3-Slides - 9/2/08 Game Theory and Hamilton's Rule...

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9/2/08 1 Game Theory and Hamilton’s Rule The mathematical theory of the evolution of social interactions. The goal of every scientific discipline is to describe, predict, and explain phenomena with the aid of theoretical models that picture the essential relationships between these phenomena and their causes.
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9/2/08 2 Virtues of mathematical models • Force one to be explicit about assumptions • Allow analysis of complex causal networks • Generate precise, quantitative predictions Evolutionary game theory • A mathematical apparatus for predicting the combinations of social behaviors that should be exhibited by interacting organisms as the result of natural selection • Organisms are pictured as players in games, with the payoffs of the game being units of fitness • Especially useful when behavioral strategies have frequency-dependent fitness
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9/2/08 3 Class simulation: two strategies • Raise your hand ( R ) • Don’t raise your hand (NR) Situation 1 • You receive $1 if you raise your hand. • You receive $0 if you don’t raise your hand.
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9/2/08 4 Frequency of hand-raising (R) Payoffs payoff for R payoff for NR Frequency-independent fitness Situation 2 • If you raise your hand, you receive $1 for every hand that is raised. • If you don’t raise your hand, you receive $0.
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9/2/08 5 Frequency of hand-raising (R) Payoffs payoff for R payoff for NR Positively frequency-dependent fitness Situation 3 • If you raise your hand, you receive $1 for every hand that is NOT raised. • If you don’t raise your hand, you receive $1 for every hand that IS raised.
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6 Frequency of hand-raising (R) Payoffs payoff for R payoff for NR Negatively frequency-dependent fitness 1/2 stable equilibrium Situation 4 • If you raise your hand, you receive $1 for every hand that is raised. • If you don’t raise your hand, you receive
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Lecture3-Slides - 9/2/08 Game Theory and Hamilton's Rule...

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