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?
| Table Expected utility payoffs for states θ1 and θ2 |
|
Decision
|
θ1
|
θ2
|
|
α
|
15
|
90
|
|
β
|
B
|
75
|
|
γ
|
55
|
40
|