Please help me solve this problem set.

Show all work and explain your answers. No credit will be given for questions that do not show work,but partial credit will be given where applicable.

Bargaining with Uncertainty about Value (100 points)

Suppose a hacker has captured a victim's data. He does not know how valuable his data are to identityfraud criminals. With probability q, he believes it to be worth V > 0; with probability 1q, he believesit to be worth V1> 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 hackeraccepts, the victim earns x and the hacker earns x.
• If he rejects, the payoffs depend on the value ofthe data.
• If the data were valuable (with probability 1q), the victim earns V1, and the hacker earns V1-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.

1. What is the victim's optimal offer? You may assume that the hacker accepts when indifferent.Your answer should be in terms of V, V1, c, and q.
2. What is the "price of uncertainty" in this game? (Calculate the victim's expected value of thegame. Then subtract that amount from the victim's expected value for the game in which he knowsthe value of the data.)
3. How does the probability of a deal being reached change as c increases?
4. How does the probability of a deal being reached change as V increases?