1. (3 points) We want to analyze an all-pay auction. For this consider an auction environment with 2 bidders and independent private values. Values v; are distributed uniformly on [0,1]. Players submit a bid (in a sealed and whoever submits the highest bid wins the object. Irrespective on whether or not a bidder won, she always has to pay her bid. (a) Specify what a strategy for each player is. (b) Given a strategy for the other bidder s_; derive the (interim) payoffs for a bidder who bids b; and has value Vi. (c) Solve for the Bayes-Nash equilibrium in symmetric, quadratic strategies. (Hint: Quadratic means a strategy takes the form s; (vi) = av? with a > 0. With this, and the previous step, you can solve for the BNE (and in particular for a) following very much they same steps we used to derive the BNE in a first-price independent private value auction.) (d) Derive the expected revenue for a given valuation vi. Does this auction format generate the same revenue as the first- and second-price auction we discussed in class? (e) Does the winner's curse arise?