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Suppose that utility payoffs depend on decisions and states as shown in Table 1.3. Letp(θ1,),p(θ2)) denote the decision-makers subjective probability distribution over Ω = {θ1 ,θ2}.
a. Suppose first that B = 35. For what range of values of p(θ1) is a optimal? For what range is 13 optimal? For what range is y optimal? Is any decision strongly dominated? If so, by what randomized strategies?
b. Suppose now that B = 20. For what range of values of p(θ1 ) is a optimal? For what range is 13 optimal? For what range is y optimal? Is any decision strongly dominated? If so, by what randomized strategies?
c. For what range of values for the parameter ß is the decision 13 strongly dominated?
Decision
θ1
θ2
α
15
90
β
B
75
γ
55
40
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