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The Theory of Rational Choice

The Theory of Rational Choice. The Theory of Rational Choice. A rational decision-maker chooses the best action according to her preferences, among the actions available to her. Set of available actions Preferences Complete Consistent (transitive) Rational  Selfish.

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The Theory of Rational Choice

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  1. The Theory of Rational Choice

  2. The Theory of Rational Choice A rational decision-maker chooses the best action according to her preferences, among the actions available to her. Set of available actions Preferences Complete Consistent (transitive) Rational  Selfish

  3. The Theory of Rational Choice Payoff function: associates a number with each action in such a way that actions with the higher number are preferred. a and bA u(a) > u(b) if and only if the decision-maker prefers a to b

  4. The Theory of Rational Choice Example: A = {Coke, Pepsi, Sprite} = {C, P, S} Decision-maker prefers C to P and P to S • u(C)=3, u(P)=2, u(S)=1 Or • u(C)=10, u(P)=0, u(S)=-2

  5. The Theory of Rational Choice Preferences  Ordinal information v is another payoff function that represents the same preferences as u if v(c) > v(p) u(c) > u(p) Any monotonically increasing function of u represents the same preferences

  6. The Theory of Rational Choice Example: u(C)=3, u(P)=2, u(S)=1 u(C)=3 > u(P)=2 > u(S)=1 f(x)=2*x v(x) = f(u(x)) v(C) = f(u(C)) = f(3)=6, v(P)=4, v(S)=2 v(C)=6 > v(P)=4 > v(S)=2

  7. The Theory of Rational Choice The action chosen by a decision-maker is at least as good, according to her preferences, as every other available action. Example: If A={P,C} and she always chooses C If A’={P,C,S} and she chooses P • Inconsistent with the Theory of Rational Choice To be consistent she must choose C or S - See the Weak Axiom of Revealed Preference (WARP)

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