Homework ch4 Introduction to Game Theory – Sergio Turner 55 points 2. 10 points Suppose the nfg, where we ignore 2’s payoffs and parameterize 1’s by z: H L X z,# 0, # Y z,# 10,# Exercise: Suppose 1’s belief is θ2=(½,½). What are u1(H,θ2), u1(L,θ2)? Which z equalizes these, i.e. makes 1 indifferent between H,L for such a belief? 4. 25 points For the mixed strategies σ1=(½,½) =(½,½)=σ2 in the nfg’s of lecture 3, compute u1(σ1, σ2): (a) Matching pennies (b) Prisoners’ dilemma (c) Battle of the Sexes (d) Hawk-Dove (e) Pigs 6. 20 points Suppose ui(σi,θ-i)=5 for some mixed strategy and belief. Must there be a pure strategy for which ui(si,θ-i)≥5? Prove or,, by example, disprove your answer.
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