zero-sum game (idea)

A zero sum game is one in which the total amount of 'points' remains constant. One player's loss is the other player's gain. Payments are made only to the other players.

The simplest of zero sum games is the classic matching coins game.

• Two players agree to one being "even" and the other being "odd".
• Each player shows a penny.
  • Pennies are shown simultaneously
  • Each player may show a head or a tail.
• If both show the same side, then "even" wins the penny from "odd".
• If each shows a different side, then "odd" wins the penny from "even".

Or, the payoff for the game.

         ._______odd______.
         |  Head  |  Tail |
Even Head|  1,-1  |  -1,1 |
     Tail|  -1,1  |  1,-1 |

Adding up the payoffs in each cell, the sum of them is 0, hence, a zero sum game.

Formally this is defined as: If all the wins and losses in a game are totaled, treating losses as negatives, the sum for each set of strategies chosen is 0.

Or, less formally, a zero sum game is one in which one player's winnings equal the other player's losses.