Example 1: Watch the Movie, Write the Payoff Matrix. Is there a dominant strategy? It is weakly dominant or strongly dominant? Is there a Nash equilibrium?

http://www.youtube.com/watch?v=p3Uos2fzIJ0&feature=player_embedded

Example 2. You have all played Rock, Paper, Scissors. Simply put, Rock Beats Scissors, Paper beats Rock and Scissors beats Paper. Try removing the rock, so you can only display one of two signs, either paper or scissors. You can then succinctly represent the outcomes in the form of a two by two. If one person wins, they get +1 and the other gets -1. If they both show the same sign, they both get 0. Write the Payoff Matrix. Is there a Pure Strategy Nash equilibrium? Try a full rock paper scissors game ( a 3 by 3 matrix). Is there a Pure Strategy Nash equilibrium?

3. You and a friend play the following game. You can contribute a dollar to a benevolent leader or you can decide not to. The leader will give take your money, triple the sum of the money that you both give to her and split that amount equally between you. Can you draw the payoff matrix? Can you tell what is the Nash Equilibrium?

Example 4: (We will do this together)

Three pirates (A, B, and C) arrive from a lucrative voyage with 100 pieces of gold. They will split up the money according to an ancient code dependent on their leadership rules. The pirates are organized with a strict leadership structure—pirate A is stronger than pirate B who is stronger than pirate C.

The voting process is a series of proposals with a lethal twist. Here are the rules:

  1. The strongest pirate offers a split of the gold. An example would be: “0 to me, 10 to B, and 90 to C.”
  2. All of the pirates, including the proposer, vote on whether to accept the split. The proposer holds the casting vote in the case of a tie.
  3. If the pirates agree to the split, it happens.
  4. Otherwise, the pirate who proposed the plan gets thrown overboard from the ship and perishes.
  5. The next strongest pirate takes over and then offers a split of the money. The process is repeated until a proposal is accepted.

Pirates care first and foremost about living, then about getting gold. How does the game play out?

http://www.traileraddict.com/clip/the-dark-knight/first-6-minutes