Consider the common-value auction described in this chapter, where Y = y₁ + y₂ and y₁ and y₂ are both uniformly distributed on [0, 10]. Player i privately observes yi . Players simultaneously submit bids and the one who bids higher wins.

(a) Suppose player 2 uses the bidding strategy b₂(y₂) = 3 + y₂ . What is player 1's best-response bidding strategy?

(b) Suppose each player will not select a strategy that would surely give him/her a negative payoff conditional on winning the auction. Suppose also that this fact is common knowledge between the players. What can you conclude about how high the players are willing to bid?

(c) Show that for every fixed number z / 0, there is no Bayesian Nash equilibrium in which the players both use the bidding strategy bi = yi + z.