there are only 2 bidders: let's call them bidder A and B each bidder knows how much they value the item, but are uncertain about their rival's valuation each bidder may have a valuation for the item of either $4 or $5 o valuations are independent across bidders o the probability that a bidder has a valuation of $4 is 20% and the probability that a bidder has a valuation of $5 is 80% bidders can only bid whole amounts, that is, their bids can only take one of the following values 0, 1, 2, 3, ... the auction's format is second-price sealed-bid (that is, bidders submit their bids in a sealed envelope, the highest bidder wins the item and pays an amount equal to the second-highest bid) if the bidders are tied, the seller flips a (fair) coin to determine the winner (d) Define what we mean by a symmetric Bayesian Nash Equilibrium (BNE) in this game. (e) Show that bidding truthfully (that is, submitting a bid equal to your value for the item) is a (symmetric) BNE. there are only 2 bidders: let's call them bidder A and B each bidder knows how much they value the item, but are uncertain about their rival's valuation each bidder may have a valuation for the item of either $4 or $5 o valuations are independent across bidders o the probability that a bidder has a valuation of $4 is 20% and the probability that a bidder has a valuation of $5 is 80% bidders can only bid whole amounts, that is, their bids can only take one of the following values 0, 1, 2, 3, ... the auction's format is second-price sealed-bid (that is, bidders submit their bids in a sealed envelope, the highest bidder wins the item and pays an amount equal to the second-highest bid) if the bidders are tied, the seller flips a (fair) coin to determine the winner (d) Define what we mean by a symmetric Bayesian Nash Equilibrium (BNE) in this game. (e) Show that bidding truthfully (that is, submitting a bid equal to your value for the item) is a (symmetric) BNE