We are going to show that the auctioneer's revenues are the same in a first (FPA) and a second (SPA) price auction. This result is an example of the more general Revenue Equivalence Theorem.

The set up is the following: there are two bidders 1 and 2 , and each has private valuation vi U[0,1],i = 1,2. The strategy of a bidder is her bidding function bi (vi).

-Assume player i uses strategy bi = vi. What is the expected payoff of player i in FPA? and Find a symmetric Nash equilibrium of the FPA.

-Show that it is a dominant strategy for player i to bid vi in SPA.

-Compute the auctioneer's revenue in both FPA and SPA and show that it is equal

in both cases. Use that E (max {X1, X2}) = 23 and E (min {X1, X2}) = 13 when X1,X2 U[0,1]