I need help with the following question: In a first-price sealed-bid auction with two players, both the player's type/valuations are taken from the set $\{10,20,30,40,50\}$ with the assumption that probabilities are all equal and these are common knowledge. So what should be the optimal bid?
What I understand is that the bidder’s valuation can take one of five values occurring with probabilities of 0.2. The bidder’s payoff becomes zero when they lose and on winning it becomes the valuation minus her bid. I understand how to find the optimal bid for a continuous case, but in discrete case how do i find the optimal bid?