Game Theory Problem

[scotty34]

Here was a game theory question posed today in my economics class. Can anyone figure it out?

There are two companies, Company A and Company B. Company A wishes to acquire Company B. Company B is about to undertake an oil exploration project.

-If the exploration is a complete success, Company B's shares will be worth $100 each
-If the exploration is a complete failure, Company B's shares will be worth $0 each
-Any value in between these is also possible, and no outcome is any more likely than any of the others
-Under Company A's management, Company B's shares will be worth 50% more

Here are the rules of the acquisition:

Company A must make a proposal for how much money they will pay for each share of Company B
Company A must make this proposal before the exploration project begins
Company B will decide whether or not to accept Company A's proposal after they have learned the results of the exploration project
Company B will only accept an offer greater than the value of its share price

Assume Company A wants to maximize profits, how much should they offer per share?