One unit of object is going to be sold via auction. There are two bidders, A and B. Their willingness to pay are known to be either of 10,20,30,40,50 and bids are also restricted to those values. Suppose A's WTP is 20 and B's is 40. Ties are broken by coin flip and assume they are risk neutral.
(1) Consider the first price auction. Write down the payoff matrix and find all Nash equilibria.
(2) Consider the second price auction. Write down the payoff matrix and find dominant strategy equilibrium.