1. First Price Auction. Suppose a particular object is being auctioned off and two players, Mary and Larry, are bidding for the item. Let Mary's valuation be $V_{Mary} = 10$ and Larry's be $V_{Larry} = 9$. Let the bidding intervals be restricted to $1 intervals. The game is depicted below.
$8
Larry
$9
$10
Mary
$8
1, 5
0, 0
0, -1
$9
1, 0
5, 0
0, -1
$10
0, 0
0, 0
0, -5
(1.A) If Mary and Larry both bid $9, explain how the payoffs in the relevant cell are calculated.
(1.B) If Mary bids $9 and Larry bids $10, explain how the payoffs in the relevant cell are calculated.
(1.C) Using iterated dominance and the concept of dominated strategies and dominant strategies, weak or strong, find the Nash Equilibrium bidding strategies and payoffs for both players. You need to show or explain how you got your answers, either by crossing columns and rows and/or which strategies are dominated by which strategies, etc....
(1.D) What can you say about Mary's bidding Strategy? What can you say about Larry's bidding strategy? Compare them to their own true valuation and/or to each other's.
