In a number of countries, government contracts are awarded by means auctions in which the winner is the bidder whose bid is closest to the average bid. Consider such an auction with three bidders competing to win a single object. Bidder i has a valuation vi for the object, where U > U > V3 > 0. Bidders simultaneously submit bids b; 20. The bidder whose bid is closest to the average of b,b, and b3 wins the object and pays her own bid (thus if i is the winning bidder, her payoff is vi- b;). In case of a tie, the bidder with the highest valuation wins the object. Losing bidders receive a payoff of 0. (a) Find all (pure strategy) Nash equilibria of this game. (b) Show that in every Nash equilibrium in which the three players do not submit identical bids, at least one player plays a weakly dominated strategy.