Suppose two bidders compete for a single indivisible item (e.g., a used
car, a piece of art, etc.). We assume that bidder 1 values the item at $v1, and bidder 2 values the item at $v2. We assume that v1 > v2.
Suppose you use a first price auction to sell the item, which proceeds as follows. Each player i = 1, 2
simultaneously chooses a bid bi ≥ 0. The higher of the two bidders wins, and pays exactly what they bid.
(In case of a tie, suppose the item goes to bidder 1.) If a bidder does not win, their payoff is zero; if the
bidder wins, their payoff is their value minus their bid.
 

 

a) Do bidders have a (weak or strict) dominant strategy in this auction? Explain why or why not.