# Two individuals, player 1 and player 2, are competing in an auction to obtain a valuable object.

## Write down the payoff matrix, Applied Statistics

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 that they can bid is \$500. 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 auction is a First Price Auction, i.e., the winner of the object pays whatever price p she bid. So, if the value of the object for a player is x and the player wins, her payoff is x - p. If she loses, her payoff is zero.

(a) Write down the payoff matrix of this game.

(b)  Is there a dominant strategy equilibrium? Is there a weakly dominant strategy equilibrium?

(c) What are the strategy profiles that survive Iterated Elimination of Strictly Dominated strategies?

(d) What are the strategy profiles that survive Iterated Elimination of Weakly Dominated strategies?

(e) Find the Nash equilibria.

(f) What is the difference between profiles that answer both (d) and (e) and profiles that only answer (e)?

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