Consider the following auction problem. One indivisible good is to be auctioned off. There are two bidders, bidders 1 and 2. Each bidder has quasi-linear utility, that is, her payoff is vt if she obtains the good and pays t to the auctioneer, and t if she does not obtain the good and pays t. The auction format is the all-pay auction, i.e., the bidder who makes a higher bid wins the good (and wins the good with probability one half if both bidders bid the same amount), and the bidder pays the amount she bids whether or not she wins the good. 1. Assume that the two bidders differ in their valuations: Assume v1>v2>0 where vi is bidder i 's valuation of the good. These values are exogenously given constants and common knowledge. (a) (8 points) Identify a pure-strategy Nash equilibrium of this game if there exists any. If not, then prove nonexistence. (b) (8 points) Identify a Nash equilibrium. (c) (8 points) Now, assume that there is a cap on the bidding at m where m is an exogenously given constant such that 0v2>0 and 0v2>0 where vi is bidder i 's valuation of the good. These values are exogenously given constants and common knowledge. (a) (8 points) Identify a pure-strategy Nash equilibrium of this game if there exists any. If not, then prove nonexistence. (b) (8 points) Identify a Nash equilibrium. (c) (8 points) Now, assume that there is a cap on the bidding at m where m is an exogenously given constant such that 0v2>0 and 0