Game+Theory+14

Should I Push the Button??
 * Name of the Game:**

The game is a game between two people that have clickers and are competing against each other to win money. The rules of the game are as follows: 1. Both people are in separate rooms (this means they can't see each other or know what the other is going to do). 2. Both have clickers that they can decide whether to push the button or not push the button. //And the payoffs are as follows:// 1. Both can push the button, and they both win with $0. 2. One can push the button and win $50, and the other looses $50 that they have gained (or goes negative). 3. If they both don't push the button they both win $40. 4. The game ends after ten rounds.
 * General Description and Rules of the Game:**

1. A way for each person to not see or know what the other players move is. 2. A way for each player to show the other what their move was. 3. And a way to keep track of the score Different Ideas on how to do this: 1. This could be done with cards: black = push, red = don't push.* 2. Actual clickers could be used and the players could be in different rooms.* 3. The players could stand back to back, and on three and turn the other player with hand gestures their move (fist with thumb in = push, and thumbs up = don't push)*
 * Materials Required:**
 * All games could keep each players score on a piece of paper for each of the 10 rounds*****

//The following is the payoff matrix://
 * Predicted Results:**
 * Player 1**
 * ~ Player 2 ||~ Push ||~ Don't Push ||
 * ~ Push ||= $0, $0 ||= $50 , -$50 ||
 * ~ Don't Push ||= -$50, $50 ||= $40 , $40 ||

The most likely result of this game is that both players would walk away with $0. That is to say that the players do what is best for them, and if they do collude that they each then cheat on that agreement. This is because each player has a dominant strategy, and that strategy is to push the button. This can be seen from both players perspectives because the payoffs are the same for each player. If player 1 pushes the button, player two has the incentive to push the button so they don't loose $50. But, if player 1 doesn't push the button player, player two should still push the button to make $50, rather than only $40. And vice verse for player 1. Therefore, the Nash Equilibrium for this game is the box in which both players push the button (both making $0). This is because the Nash Equilibrium is the box in which both players will end up if they use their dominant strategies (which is to push the button in this game).