. Players 1 and 2 compete in an auction for a valuable object, for example a painting. Each player writes a bid in a sealed envelope, without knowing the other player's bid. The bids start from 0, are multiples of 100, and the maximum bid is 500 euros. That is, if we denote by by player i's bid {i = 1,2] then b,- can only take one of these values: 0, 100, 200, 300, 400, 500. The valuation of the object is 400 euros for player 1 {v.- = 400) and 300 euros for player 2 [v2 = 300). The player making the highest bid wins the auction, gets the object, and pays a price equal to her bid (this is called a rst price auction). In case of a tie, each player has a 50% chance of winning the auction. If by > bjthen player E's payoff is v; by, and playerj's payoff is zero. If by = by (tie), then player i's expected . 1 . . payoff IS 3(1), by). Players' valuations as well as the rules of the auction are common knowledge. a. Write the game in normal form. b. Find the players' best responses c. Find all Nash equilibria in pure strategies