Game+Theory+6

**__ General Description of Game __** Your friend has challeneged to you to re-enact a historic duel. You have to choose whether or not to fire at your friend, trusting that he will also not fire, or chose to fire and beat him to "the kill"! **__ Rules of the Game __** If you fire your gun, your opponent will die and you will live. If your opponent fires his gun, you will die and he will live. If you both fire your guns, both of you die. If neither of you fire your guns, you both live. Assume that: **__ Materials Required __** Option 1: Grab and friend and two guns. Start by facing each other, then, execute an about face and each walk 10 paces. Lastly, turn around and decide whether or not to kill your best friend.
 * __ The Duel __**
 * if neither friend shoots, each player gets 5 points
 * if one player shoots, the player who shoots gets 6 points, and the one who dies looses 2 points
 * if both players shoot, each player looses 1 point

Option 2: Each player needs two index cards; one that says "SHOOT" and the other that says "DON'T SHOOT." On the count of three, each player will lay down their choice. Add point totals as necessary.

You can play multiple rounds using Option 2 and decide a winner using the point totals described in the rules. **__ Predicted Results __**
 * ||  || Player 2 ||   ||
 * ||  || SHOOT || DON'T SHOOT ||
 * Player 1 || SHOOT || -1, -1 || 6, -2 ||
 * || DON’T SHOOT || -2, 6 || 5, 5 ||

The Result: Both players will end up shooting each other. This is because the dominant strategy for both players is to shoot. Why is this, you might ask? This is because, no matter what the other player does, the benefit of shooting for that player is greater than it would be if they did not shoot. This, in turn, means that the Nash Equilibrium is the [-1, -1] box.

This is too bad! That's because if both players were able to collude AND actually **keep** their agreement, both would come out better off!