Bargaining with Uncertainty about Value(50 points)

Suppose a hacker has captured a victim's data. He does not know how valuable his data are to identity fraud criminals. With probability q, he believes it to be worth V > 0; with probability 1 q, he believes it to be worth V I > V . The hacker, however, knows how much the data are worth.

The victim makes an offer to "buy" the data back. Specifically, he offers x 0. If the hacker accepts, the victim earns x and the hacker earns x. If he rejects, the payoffs depend on the value of the data. If the data were valuable (with probability 1 q), the victim earns V I and the hacker earns V I c, where c > 0 represents the transaction cost the hacker has to pay to find a buyer for the identity information. If the data were not valuable (with probability q), these payoffs are V and V c instead.

a) Whatis the victim's optimal offer? You may assume that the hacker accepts when indifferent. Your answer should be in terms of V, V I, c, and q. (Please solve the critical cutpoint in terms of q.)

b) What is the "price of uncertainty" in this game? (Calculate the victim's expected value of the game. Then subtract that amount from the victim's expected value for the game in which he knows the value of the data.)

c) How does the probability of a deal being reached change as c increases?

d) How does the probability of a deal being reached change as V increases?