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Suppose three individuals i = 1, 2,3 value an object for sale in an auction according to ti, where it is common knowledge that t; is independently and identically uniformly distributed on the unit interval. The three bidders i = 1, 2,3 receive payoffs from bidding b; according to: (ti - b;)" if i wins 0 if not where r E (0, 1) is a parameter measuring risk-aversion. Assume that bidder i bids according to a linear strategy. (a) Suppose this is a first-price sealed-bid auction. Find the equilibrium of this game and discuss how the optimal bid for player i depends on the parameter r. What is the appropriate solution concept? (b) Suppose instead that this is a second-price auction. Carefully show what the equilibrium is in this case. Is it different from the result in (a)