Suppose Players 1 and 2 are participating in a first-price sealed bid auction with private, independent valuations. Each player's valuation of the object to be sold, which is assumed to be worth 0 to the seller, is either 100, 60 or 40 with equal probabilities.
Each player knows her own valuation but only the probability distribution on the other
Player's valuation. Bids are restricted to be either 100, 60 or 40. Remember bids are chosen simultaneously, the highest bidder wins and pays the amount of his bid. If two bidders bid the same amount, one of them gets the object with probability 0.5.
What is a strategy for a player in this game? Describe strategies that are in Bayes Nash equilibrium.