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# Class_3 - GameTheory Lecture 3 Followup From yesterday e...

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Econ 171 – Introduction to  Game Theory Lecture 3

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Follow-up From yesterday, e) What beliefs must P1 have about P2 in order for her to mix strategies?
Follow-up From yesterday, e) If > 2/3, P1 will choose A. If 2/3 > > 1/3, P1 will choose B. If < 1/3, P1 will choose C.

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Practice If P1 has beliefs ={1/2,1/4,1/4} about P2, what strategy should P1 choose? a) A b) B c) C d) Can’t tell.
Practice What strategy is never a best response for P1? a) A b) B c) C d) All can be a best response.

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Practice P1 tries mixing strategies A and B to dominate C. No matter strategy P2 chooses, how could P1 mix A and B? a) (1/2,1/2) b) (3/4,1/4) c) (1/4,3/4) d) Can’t tell.
Practice Suppose p is the probability P1 chooses A and (1- p ) is the probability of B. For A and B to dominate C given any P2 strategy, we must satisfy the following conditions: 1. If P2 chooses X, EU= 6p+0(1-p) > 2 2. If P2 chooses Y, EU= 5p+4(1-p) > 3 3. If P2 chooses Z, EU= 0p+6(1-p) > 2

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Classical games: Battle of the Sexes Matching Pennies New solution concept: Nash Equilibrium (NE). Lots of examples using classic Normal Form games.
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Class_3 - GameTheory Lecture 3 Followup From yesterday e...

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