Zero-sum game
Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two competing entities, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one’s gain is equivalent to player two’s loss, with the result that the net improvement in benefit of the game is zero.
If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Thus, cutting a cake, where taking a more significant piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if all participants value each unit of cake equally. Other examples of zero-sum games in daily life include games like poker, chess, sport and bridge where one person gains and another person loses, which results in a zero-net benefit for every player. In the markets and financial instruments, futures contracts and options are zero-sum games as well.
In contrast, non-zero-sum describes a situation in which the interacting parties’ aggregate gains and losses can be less than or more than zero. A zero-sum game is also called a strictly competitive game, while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality, or with Nash equilibrium. Prisoner’s Dilemma is a classic non-zero-sum game.
A zero-sum game is a situation in game theory where one participant’s gain is exactly equal to another’s loss, resulting in a net sum of zero. This competitive dynamic can be seen in games like poker, chess, and Tennis, where the total amount of wealth or points remains constant and is simply redistributed among players. Examples include a bet where one person’s winnings are the other’s exact loss, or a market where one company’s gain in market share is an equivalent loss for a competitor.
Key characteristics
- Constant total value: The total wealth, points, or payoff available to all players remains constant.
- Win-lose dynamic: For a player to gain, another player must lose an equivalent amount.
- No net change: The sum of all gains and losses is always zero, meaning no new wealth is created or destroyed in the system.
Examples of zero-sum games
- Poker: The money won by some players is a direct loss for the others, with the total pot remaining the same.
- Chess: A win for one player is a loss for the other, and in some scoring systems, the points gained by one are taken directly from the other (e.g., ELO ratings).
- Tennis: A win by one player is the direct loss of the other.
- Futures and options contracts: One party’s profit is the other party’s loss.
- Elections: One candidate winning means other candidates lose votes, which is a zero-sum situation for votes.
- Status
AI responses may include mistakes.
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[12] https://brilliant.org/wiki/zero-sum-games/
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