Question
An agent must pick one of two possible designs (A or B) for a new device. The agent knows that the value of the device
An agent must pick one of two possible designs (A or B) for a new device. The agent knows that the value of the device when using design k {A,B} is a random variable xk [0,1], where xk is an independent draw from a uniform distribution in [0,1]. The agent can learn the realization of the random variable xk by paying a cost c 0.
- (a)What is the expected payoff of picking A or B without paying the cost c to learn the value of either of the alternatives?
- (b)Suppose the agent knows that the value of design A is xA. At this point, the agent could implement design A, implement design B without paying to learn its value, or pay c to learn the value of design B, and then implement the design with the highest value. Compute the agent's payoff in each one of these cases.
- (c)Suppose the agent knows that the value of design A is xA. Under what condition will the agent pay c to learn the value of design B?
(d) Assume that c = 1/32. Suppose that the agent does not the value of A or B and she decides to learn the value of some design, she always learns the value of A first and subsequently decides whether to learn the value of B. Under what condition will the agent pay the cost c to learn the value of A?
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