State whether each of the following is true /false and provide a brief explanation.

1. Consider the first price sealed bid auction with two players having valuations v1 and v2 where, v1 > v2, and all other assumptions the same as discussed in class. Is the following statement True/False?

There can be no strategy profile which constitutes a Nash equilibrium where player 2 wins. (True/False explain briefly)

2. Let time be a continuous variable that starts at 0 and runs indefinitely. Assume that the value party i attaches to the object in dispute is vi > 0 and the value it attaches to a 50% chance of obtaining the object is vi /2. Each unit of time that passes before the dispute is settled (i.e. one of the parties concedes) costs each party one unit of payoff. Thus if player i concedes first, at time ti, her payoff is -ti (she spends ti units of time and does not obtain the object). If the other player concedes first, at time tj , player i's payoff is vi - tj (she obtains the object after tj units of time). If both players concede at the same time, player i's payoff is vi /2 - t, where t is the common concession time.

The pure strategy Nash equilibrium is where both players are going to hold the object until their valuations. i.e. (v1, v2)

(True/False explain briefly)