Assignment:
Consider a 2-person private value, ?rst-price auction. The object is worth $10,000 to bidder 1 who knows that bidder 2's value is uniformly distributed between 0 and $40,000. Assume that bidder 2 is going to use his equilibrium bidding strategy.
a) What is bidder 1's optimal bid for his value $10,000 and what is his expected payoff?
b) Assume that bidder 1 learns that the object is worth $22,000 to bidder 2 and in turn, bidder 2 is not aware that bidder 1 has this information and would therefore stick to his equilibrium strategy. How much should bidder 1 bid and what is his expected payoff?
c) Assume that bidder 1 learns that the object is worth $14,000 to bidder 2 and in turn, bidder 2 is not aware that bidder 1 has this information and would therefore stick to his equilibrium strategy. How much should bidder 1 bid and what is his expected payoff?