3. (35 pts) Consider a rst price auction with three players. Each bidder has a valuation 1),; uniformly drawn on interval [5, 10], so that the utility for player 1 is 1J1 bl if b1 is the highest bid and 0 if ()2 > bl or 53 > bl. The payoffs of the other bidders are symmetric. 1. (10 pts) We are looking for a symmetric equilibrium in linear strategies. We therefore start by assuming that bidders 2 and 3 bid in accordance to 15' (111') = c + aim. First, write down the condition for which bid 51 wins in terms of ()1, c, d, 1:3, and v3. Then, derive the probability that In wins in terms of bl, c, and d. 2. (15 pts) Formulate the best response problem for player 1 and derive the optimality (rst order) condition. 3. (10 pts) Combine the optimality condition above with the initial guess to nd the symmetric linear equilibrium of the model