Justin Wolf

Two men are arrested, but the police do not possess enough information for a conviction. Following the separation of the two men, the police offer both a similar deal—if one testifies against his partner (defects/betrays), and the other remains silent (cooperates/assists), the betrayer goes free and the cooperator receives the full one-year sentence. If both remain silent, both are sentenced to only one month in jail for a minor charge. If each ‘rats out’ the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept quiet. What should they do?

∴ ”[R]egardless of what the other decides, each prisoner gets a higher pay-off by betraying the other.”

the stability, the equilibrium, will only happen if everyone involved behave selfishly. Because if they cooperate, then the results become unpredictable and dangerous.

1. Starting a game:
   1. Each player takes 7 chips of one color (Cards of one suit from a deck work equally well).
   2. No two players may start with the same color chips.
   3. Someone is randomly selected as the first player to move.
   4. This player places a chip onto the playing area, and selects anyone to be the next person to move.
2. Playing the game:
   1. Move by playing a chip of any color onto the playing area (starting a new pile), or on top of any existing chip(s) in the playing area.
   2. If no chips are captured (see below), the player selects the next person to move, so long as that person’s starting chip color is not in the stack just played on (this may be the same person, if that person used a captured chip). However, if all four colors are in the stack just played on, the next person must be the player whose most-recently-played chip (by color) is furthest down in the stack
   3. Chips are captured by playing two chips of the same color consecutively on one pile. The player designated by that color must kill one chip of his choice out of that pile, and take the rest. Then he gets the next move. Killed chips are taken out of the game.
   4. A chip is a prisoner when held by a player other than the original owner.
   5. Any prisoner in a player’s possession may be killed or transferred to another player at any time. Such transfers are unconditional and cannot be retracted. A player may not transfer or kill chips of his own color.
   6. A player is defeated when given the move, but has no chips in his possession (and hence is unable to play).
      1. Defeat is not final until every player holding prisoners has refused to rescue him by transferring chips.
      2. After defeat, the move returns to the player who gave the defeated player the move.
      3. The defeated player’s chips remain in play as prisoners, but are ignored in determining the order of play.
      4. If a pile is captured by the chips of a defeated player, the entire pile is killed, and the move rebounds to the capturing player.
   7. Players must keep their chips in view at all times.
3. Order of play:
   1. If a capture occurs: the player whose color made the capture gets the next move.
   2. If a player is defeated: move returns to the player who gave the defeated player the move. If this should also defeat that player in turn, whoever gave that player the move will get the next turn, etc.
   3. Otherwise, the next player to move is decided by last player to have moved as follows:
      1. They may give the move to any player (including themselves) whose color is not represented in the pile just played upon.
      2. If all players are represented in that pile, the move goes to the player whose most-recently-played chip is furthest down in the pile.
4. Strategy:
   1. Coalitions, or agreements to cooperate, are permitted, and may take any form.
   2. No penalty for failure to live up to an agreement.
   3. Players are freely allowed to confer only at the table during the game— no secret or prior agreements are allowed.
5. Winning the game:
   1. The winner is the last surviving player (after the others have been defeated).
   2. A player can win even if they hold no chips and all of their chips have been killed.