Penalty Kicks: Imagine a kicker and a goalie who confront each other in a penalty kick that will determine the outcome of a soccer game. The kicker can kick the ball left or right, while the goalie can choose to jump left or right. Because of the speed of the kick, the decisions need to be made simultaneously. If the goalie jumps in the same direction of the kick, then the goalie wins and the kicker loses. If the goalie jumps in the opposite direction of the kick, then the kicker wins and goalie loses. Model this as a normal form game and write down the matrix that represents the game you modeled. Meeting Up: Two old friends plan to meet at a conference in San Francisco, and they agree to meet by "the tower." After arriving in town, each realizes that there are two natural choices: Sutro Tower or Coit Tower. Not having cell phones, each must choose independently which tower to go to. Each player prefers meeting up to not meeting up, and neither cares where this would happen. Model this as a normal-form game and write down the matrix form of the game. 4.3 Discrete First-Price
Auction: An item is up for auction. Player 1 values the item at 3 while player 2 values the item at 5. Each player can bid either 0, 1, or 2. If player į bids more than player j then i wins the good and pays his bid, while the loser does not pay. If both players bid the same amount then a coin is tossed to determine who the winner is, and the winner gets the good and pays his bid while the loser pays nothing.
A. Write down the game in matrix form.
B. Does any player have a strictly dominated strategy?
C. Which strategies survive IESDS?