Supposed 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 0 or 2 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 0, 1, or 2. 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
A) What is a strategy for a player in this game?
B) A bidder decides in advance of knowing his value to bid 0 if his value turns out to be 0 and 1 if his value turns out to be 2. If both bidders decide to behave in this fashion, would their strategies constitute a Nash Equilibrium?