Suppose there is one item up for auction in a sealed bid , first price auction . There are two allowable bids : 0 and 0.4 . There are two risk- neutral bidders each with private valuation ti "-U" [ 0,1 ] . Of course each bidder knows his own valuation but not the other He only knows the distribution of other's valuations . The highest bidder wins and pays his bid . In the case of a tie , a coin is flipped to determine the winner . Find the Bayesian Nash Equilibrium of the game .