3. Consider two bidders with private values, where u,- .131 U [[1, EDD]. Under this distributional assumption, Pr(i.!.- 1} = Prfug (I) = % E[highest 11,-] = 133.33 E[2nd highest 11,-] = 66.6? Conditional payos are: a?\" = u.- (amount paid) 14:0 {a} What is the seller's expected revenue in the Nash equilibrium of a second price auction? (b) Suppose that the bidders participate in a rstprice auction Furthermore, suppose that bidder 1 believes that bidder 2's bidding strategy is to bid his value. That is, bztg) = 112. If bidder 1 bids in, what is the probability bidder 1 will win the auction? {This should depend on b.) {c} What is bidder 1's expected payo' when she bids b and believes that bidder 2 will bid b2{u2] = v2? (d) What is bidder 1's optimal bidding strategy, re) when she believes that bidder 2 will bid infra] = U2? {e} Consider the following strategy prole: both bidders will bid their valuation. Is this a Nash equilibrium of the rstprice auction? {1'} What is the seller's expected revenue in the Nash equilibrium of the rst-price auction? {g} What is the seller's expected revenue in the Nash equilibrium of an English (Ascending) auction? What about a Dutch (Descending) auction? (lnt: assume that the bidder with the highest valuation will win each auction}