Consider the ascending-price auction with bidders who are drawing their values independently from a uniform distribution on [0, 1]. The auctioneer continuously raises the price from 0 to 2. If neither bidder has dropped out when the price is 2, one of the bidders is randomly selected to receive the object at that price.
(a) What is the strategy space for each bidder in this Bayesian game? Hint: Be careful!
(b) Are there any strictly dominate strategies? Show what they are, or explain why there aren't any.
(c) Find a Bayesian Nash equilibrium in which the auctioneer's expected revenue is zero. Hint: consider asymmetric equilibrium (i.e., players play different strategies).