1. Auctions. Consider the following connnon value auction. There are two bidders, 1 and 2, whose types 92- for both 3' E {1, 2}, are independently drawn from a uniform distribution on [0: 200]. The value of the object to both bidders is the sum of the types, Le. 61 + 62. The object is offered for sale in a rst price auction. Hence the payoffs depend on the bids fit- and types as follows (assume a coin toss if b; = bi): 95+6jb1'1fbi> bj' 1L1 (bi,f)j,9i,6j)= %(61'+63bi) 1fbi=bj. 0 otherwise. (a) Show that strategies 521055;) = 9i- for i = 1,2 (i.e. the players bid their own type) form a Bayes Nash equilibrium in this game. To show that this is a BNE, do the following: i) formulate player is expected payoff when player j bids 133- = I513- and player 3' bids b1- and has a type 61' (remember that player 1' does not know 93- but uses that it is drawn from U [03200])g ii) show that bi = 9%- niaidniizes the expected payoff. (b) If 9?; = 1, the equilibrium bid is 1, but it might seem that the expected value of the object is 1 + 100 = 101. Why doesn't the bidder behave more aggressively (informal discussion is enough)