The concept of zero-sum game
Zero-sum games are a type of game theory developed in the 1940s by John von Neumann and Oskar Morgenstern. In these types of games, if one player gains, another player must lose; any gains or losses cannot be divided, hence the name zero-sum game.
A zero-sum game only involves two players, a winner and a loser - where ones legal move is exactly countered by an opponents move such that no net gain is made by either participant. The sum of all point gains and loses across all parts of the game must equal zero. If a player can secure a net gain over the other participant, then the game is referred to as a non-zero sum game.
In zero-sum games, the most important factor determining which player will win or lose is the initial state of the game. The outcome of the game is completely determined by how the boards resources are allocated at the very beginning, even before any moves are made.
A zero-sum game is typically used in transactions or negotiations with a fixed amount of resources. This can range from a two-player board game to situations like gambling, or stocks and shares. Any money gained or lost by one player is the same amount lost or gained by the other player or players. Taking this concept of gain being equivalent to anothers loss to its extreme, war is a zero-sum game.
For analytical reasons, in game theory a game is usually classified as zero-sum if it is strictly between two players, because a three-plus-player game can also involve cooperative aspects. In such a game, the structure is more complicates and gains and losses can be shared across the participants.
Regardless of whether the game is zero-sum or not, game theory can help identify the optimal strategies of each participant in any game, whether it is chess, casino, stock market, or any other game or transaction. Zero-sum games are an important part of game theory, and underlie much of economic and political decision-making. When two countries make decisions that could involve a loss for one of them, the situation can often be described as a zero-sum game. Therefore, understanding the mathematical components at work in the game can help to resolve such issues.
