Three (3) bidders participate in a first price, sealed bid auction satisfying all the assumptions of the independent private values model. Each knows his own value v ? [0, 1], but does not know anyone else's, and so must form beliefs. Suppose everyone thinks it is more likely a rival's value is high than low. Specifically, each player believes any other player's value is distributed on [0, 1] according to the cumulative distribution function F(v) = v3, and this is common knowledge. Now consider the induced game under this auction format and its symmetric (Bayesian) Nash equilibrium.

a. What is the equilibrium bidding function, b(v)?

b. Does the bidding rule in (a) call for the bidder with value v to bid the expectation of the next-highest bidder's value, conditional on v being the highest (Please provide me with justification).

c. How much (expected) revenue should the seller anticipate if he were to run this auction?