Question

Four bidders participate in first price auction for a single object that is of the following value to them:

V1 = 150,          V2 = 100,          V3 = 90,            V4 = 80

The information above is known to all (i.e., each bidder knows not only his own valuation but also that of the other bidders). If two bidders or more bidders place the same bid, one of them is selected at random to be the winner. Select all that apply

	a.	There's a Nash Equilibrium where the bids are: b1 = 103, b2 = 102, b3 = 84. b4 = 74
	b.	There's a Nash Equilibrium where the bids are: b1 = 150, b2 = 100, b3 = 90, b4 = 80.
	c.	There is a NE in which player 1 wins the object
	d.	There's a Nash Equilibrium where the bids are: b1 = 99, b2 = 98, b3 = 90, b4 = 80
	e.	There's a Nash Equilibrium where each bidder offers half of his value of the object.

Answer 1

C.

There is a NE in which player 1 wins the object

d>There's a Nash Equilibrium where the bids are: b1 = 103, b2 = 102, b3 = 84. b4 = 74

Reason

Since the first agent has the highest value, there will be a Nash equilibrium where agent 1 gets the object and e> is a NE because to win the object, agent 1 must pay at least 103 and others get zero payoff which is the best that they can get.