Zero-Sum and Non-Zero Sum Games

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A zero-sum game is a game where the total payoffs are fixed, where one player’s gain is another player’s loss. An excellent example of this is a poker game where the players contribute money into a pot and someone “wins” it after all the bets are tallied and the winning hand is revealed. However, nobody actually “won” the pot of money, rather all the other players lost money that another player gained. The total amount of money available will never change in this game. The simplest form of a zero-sum game consists of two players and two strategies because a one-player game is not a game and only having one choice of strategies is not really a choice. The only way for a player to win is for the other player to lose, no cooperation is possible. That is, in order to be a true zero-sum game, the expected payoff for one player must equal the expected cost for the other player (if I gain $1, you must lose $1) for a sum of zero.

NON-ZERO SUM GAMES

A non-zero sum game where one player's gain does not necessarily mean the other player's loss; these games are actually more complex because there is usually more than one rational strategy. They are referred to as "non-zero sum" because the sum of the two player's payoffs does not always equal zero. Furthermore, non-zero sum games are not forced to be non-cooperative. That is, sometimes cooperation between the players leads to the optimal solution. The greatest example of a non-zero sum game is the prisoner's dilemma (I'll explain it in a later post). Essentially, each player is acting in his own self-interest, but that doesn't necessarily mean that the one player's gain is the other player's loss. Depending on how much the prisoner's cooperate with each other, that will determine each player's individual strategy. Furthermore, examples of non-zero sum games are more prevalent in real world situations, which makes them more useful to game theorists.