Zero sum game
From DDL Wiki
Contents |
Background
The individual that was most associated with Game Theory is John von Neumann. Game Theory is a very broad subject. It is the study of situations where multiple decision makers influence one another. It is the study of the interactions between players, and the outcomes it produces under certain preferences (or Utility). One area that this entry will focus on is related to one of his first major contribution in the minimax theorem. The minimax theorem describes a technique to minimize the maximum possible loss (and in turn, maximizing the minimum gain).
Zero Sum Game
If there were a situation with two players involved, the gain of one player will be directly balanced by the loss of another player. So the sum of all the losses and all the wins of players involved will be zero. Some examples of circumstances that exhibit the zero-sum idea are chess and tic-tac-toe. The zero-sum theory has its applications in more than just games, its applications extends further into economics and psychology.
Example
Rock, Paper, Scissors is a game that illustrates the zero-sum game quite well. In this game, there are two players involved: Player I and Player II. On the count of three, the two players are to simultaneously hold out their hands in a position that represents either a rock, a paper, or scissors.
After each turn, one player will lose and one player will win the round based on the following rules:
1. Rock breaks Scissors - Rock wins, Scissors loses
2. Scissors cuts Paper - Scissors wins, Paper loses
3. Paper covers Rock - Paper wins, Rock loses
4. If both players choose the same object, it is a tie.
The above is a matrix that represents all the possible outcomes of the game. For instance, if Player I chose Scissors and Player II chose Rock, Player I will lose and Player II will win. This is represented by (-1, +1). If Player I were to win, then the outcome is represented by (+1, -1). An outcome of (0,0) symbolizes a tie.
Essentially, a gain is represented by +1, while a loss is represented by a -1. As mentioned earlier, a zero sum game is when the sum of all the loses and gains are zero, which is exactly what the table is showing.
Restrictions and Limitations
A zero sum game is possible only when the decision makers are making random choices without any influences from previous knowledge. For instance, tic-tac-toe is a zero sum game. However, there are strategies that players use to allow them to win. In such cases, the game is not a zero sum game.
Links
http://en.wikipedia.org/wiki/Zero-sum_game
