Two individuals, Player 1 and Player 2, are competing in an auction to obtain a valuable object. Each player bids in a sealed envelope, without knowing the bid of the other player. The bids must be in multiples of $100 and the maximum they can bid is $500 (lowest 0). The object is worth $400 to player 1 and $300 to player 2. The highest bidder wins the object. In case of a tie player 1 gets the object. The winner pays a price p to be specified below. So, if the value of the object for player i is x and player i wins the object her payoff is x-p; If she does not win her payoff is zero.
(First price auction) In this case, the winner of the object pays the price he bids.
Answer the following questions for the first price auction:
(a) Write down the strategic form of this game
(b) Identify any strictly dominating and weakly dominating strategies for both players.
(c) What is the Nash equilibrium using IEDS?