2 Auctions Consider an auction for a single item. There are two bidders. Each bidder has a privately known value, drawn from a uniform distribution on (0,100). Suppose the bidders are asked to submit sealed bids. The high bidder wins the auction, and is required to pay two thirds of their own bid plus one third of the losing bid. In other words, if bidder one wins, they pay {b + {b2. 1 1. Write down the probability that bidder 1 wins as a function of their bid. 2. Write down bidder l's payoffs in the event that they win and in the event they do not 3. Solve for the Bayesian Nash equilibrium. 4. Calculate the expected auction revenue and compare it to the the first price and second price sealed bid auctions (as discussed in class). 2 Auctions Consider an auction for a single item. There are two bidders. Each bidder has a privately known value, drawn from a uniform distribution on (0,100). Suppose the bidders are asked to submit sealed bids. The high bidder wins the auction, and is required to pay two thirds of their own bid plus one third of the losing bid. In other words, if bidder one wins, they pay {b + {b2. 1 1. Write down the probability that bidder 1 wins as a function of their bid. 2. Write down bidder l's payoffs in the event that they win and in the event they do not 3. Solve for the Bayesian Nash equilibrium. 4. Calculate the expected auction revenue and compare it to the the first price and second price sealed bid auctions (as discussed in class)