(Negative externality) The holder of a patent on a cost reducing process is considering the possibility of licensing it to one of two firms. The two firms are competitors in the same industry and so if firm 1 obtains the license,its profits will increase by X1 while those of firm 2 will decrease by αX2,where α is a known parameter satisfying 0<α<1. This is because if firm 1 gets the license, firm 2 will have a cost disadvantage relative to firm 1.Similarly, if firm 2 obtains the license, its profits will increase by X2 while those of firm 1 will decrease by αX1. The variables X1 and X2 are uni-formly and independently distributed on [0, 1]. Firm 1 knows the realized value x1 of X1 and only that X2 is uniformly distributed, and similarly for firm 2.
a. Suppose that the license will be awarded on the basis of a first-price auc-tion. What are the equilibrium bidding strategies? What is the expected revenue of the seller, that is, the holder of the patent?
b. Find the payments in the VCG mechanism associated with this prob-lem. Are the expected payments the same as in a first-price auction?
c. Suppose that the patent holder is a government laboratory and it wants to ensure that the license is allocated efficiently and that the net pay-ments of the buyers add up to zero-that is, the "budget" is balanced.What is the associated "expected externality" mechanism for this prob-lem? Is it individually rational? Does there exist an efficient, incentive compatible, and individually rational mechanism that also balances the budget?