3. Consider a sealed bid second prioe common value auction. The difference to the standard common value setting is that there is uncertainty about the value of the good being auctioned c. In particular, the value of v is not known and assumed to follow a normal distribution with mean If] and variance 1. Every bidder 1' receives a piece of intormation about 1:, that we call signal 55,-, which is distributed normal with mean 1: and variance 1 (note that Em) = 1:}. Each bidder 2' receives its own signal mi which may be different that the one received by other bidders. All signals as are independent and identically distributed (lid) and all bidders know. on top of their own signal, that v is distributed Nut}, 1], that their signal and that of others are distributed N(c, 1) and that signals are iid. Once the auction is over the value of v is revealed to the bidders and the payoffs are zero for whoever lost the auction and v minus the price paid for whoever won. For example. say that there are 2 bidders. Bidder 1 receives signal at, = 3 and bidder 2 receives signal 172 = 8. Bidder 1 observes his own signal but not that at bidder 2 and bidder 2 observes his own signal but not that of bidder 1. Bidders then simultaneously submit bids in = 5 and 112 = 4 which means bidder 1 wins and pays price p = 4. The value of c is then revealed to be c = T and thus the profits are 3 {Y - 4) for bidder 1 and 0 for bidder 2. Assume that the number of bidders tends to infinity, is a situation where all bidders bid their signal (by; = 9:; for all 2') an equilibrium? Please explain (intuitivety or tormally} your answer. Hint: The particular value for the mean for c and variance for 1} and all It is irrelevant. [15 marks]