Y7

Problem 1 Consider the following game known as a second-price sealed-bid auction. A certain object is going to be sold at an auction. Two people are interested in buying it. Let 1?,- be each person's valuation of the object, with 171 > 192 > 0. Each person is going to submit a bid stating how much she is prepared to pay (13,-) in a closed envelope. Then, the two envelopes are going to be opened at the same time and the person that submits the highest bid will win the object (assume that, in case of a tie, person 1 wins the object); the price that person will have to pay will be equal to the bid submitted by the other person. Therefore, the payoff for the player that wins the object is 17; by. The payoff for the other player is zero. 3. Suppose now that everything is as before except that the winner of the auction will pay the amount he proposed, so that his payoff is v,- 1),. Find at least one Nash equilibrium of this game