Zero-sum Game and Non-zero-sum Game (Positive-sum Game and Negative-sum Game)

A zero-sum game is one in which no wealth is created or destroyed. So, in a two-player zero-sum game, whatever one player wins, the other loses. Therefore, the player share no common interests. There are two general types of zero-sum games: those with perfect information and those without.

In a game with perfect information, every player knows the results of all previous moves. Such games include chess, tic-tac-toe, and Nim. In games of perfect information, there is at least one “best” way to play for each player. This best strategy does not necessarily allow him to win but will minimize his losses. For instance, in tic-tac-toe, there is a strategy that will allow you to never lose, but there is no strategy that will allow you to always win. Even though there is an optimal strategy, it is not always possible for players to find it. For instance, chess is a zero-sum game with perfect information, but the number of possible strategies is so large that it is not possible for our computers to determine the best strategy.

In games with imperfect information, the players do not know all of the previous moves. Often, this occurs because the players play simultaneously.

The theory of zero-sum games is vastly different from that of non-zero-sum games because an optimal solution can always be found. However, this hardly represents the conflicts faced in the everyday world. Problems in the real world do not usually have straightforward results. The branch of Game Theory that better represents the dynamics of the world we live in is called the theory of non-zero-sum games. Non-zero-sum games differ from zero-sum games in that there is no universally accepted solution. That is, there is no single optimal strategy that is preferable to all others, nor is there a predictable outcome. Non-zero-sum games are also non-strictly competitive, as opposed to the completely competitive zero-sum games, because such games generally have both competitive and cooperative elements. Players engaged in a non-zero sum conflict have some complementary interests and some interests that are completely opposed.

Positive-sum game, in game theory, a term that refers to situations in which the total of gains and losses is greater than zero. A positive sum occurs when resources are somehow increased and an approach is formulated in which the desires and needs of all concerned are satisfied. One example would be when two parties both gain financially by participating in a contest, no matter who wins or loses. Positive-sum outcomes occur in instances of distributive bargaining where different interests are negotiated so that everyone’s needs are met.

In contrast to the positive-sum game are the zero-sum game and the negative-sum game. The term zero-sum game refers to situations in which the total of wins and losses adds up to zero, and thus one party benefits at the direct expense of another. The term negative-sum game describes situations in which the total of gains and losses is less than zero, and the only way for one party to maintain the status quo is to take something from another party. It is in the context of negative-sum games that the most serious competition tends to occur.

A negative-sum game is a situation that destroys value as opposed to creating it. This doesn’t mean that all participants lose, it just means that total losses exceed total winnings.