In an average price sealed-bid auction, potential buyers submit bids in sealed envelops. The object is assigned to the participant who submitted the highest bid, and the winner pays a price equal to the average submitted bid. (For example, if three participants submit bids of $3, $4 and $2 respectively, the participant who bids $4 receives the object and pays a price of $3 = (3+4+2)/3.) Suppose there are N > 1 bidders, and their private valuations for the object are independent draws from the uniform distribution on the interval [0,1]. a) Is bidding your own valuation a dominant strategy? b) Assume that the equilibrium bidding strategies are increasing and linear in the valuations (i.e. they take the form B(v) = av, with a > 0.) Using the revenue equivalence theorem, find an equilibrium of the average price auction. (I am asking you to provide the equi- librium bidding strategy as a function of the number of participants i.e. N. For partial marks you can find the equilibrium for an example with a fixed N e.g N = 2 or N = 3 etc.) In an average price sealed-bid auction, potential buyers submit bids in sealed envelops. The object is assigned to the participant who submitted the highest bid, and the winner pays a price equal to the average submitted bid. (For example, if three participants submit bids of $3, $4 and $2 respectively, the participant who bids $4 receives the object and pays a price of $3 = (3+4+2)/3.) Suppose there are N > 1 bidders, and their private valuations for the object are independent draws from the uniform distribution on the interval [0,1]. a) Is bidding your own valuation a dominant strategy? b) Assume that the equilibrium bidding strategies are increasing and linear in the valuations (i.e. they take the form B(v) = av, with a > 0.) Using the revenue equivalence theorem, find an equilibrium of the average price auction. (I am asking you to provide the equi- librium bidding strategy as a function of the number of participants i.e. N. For partial marks you can find the equilibrium for an example with a fixed N e.g N = 2 or N = 3 etc.)