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第1行： − 此词条暂由彩云小译翻译，翻译字数共1421，未经人工整理和审校，带来阅读不便，请见谅。+ 第11行：
第11行： − 在博弈论和经济理论中，零和博弈是一种数学描述，其中每个参与者的效用收益与其他参与者的效用收益的损失完全平衡。如果将参与者的总收益加起来，再减去总损失，则它们之和为零。因此，如果所有的参与者都平等地评价每一块蛋糕，那么切蛋糕就是一个零和游戏，切一块蛋糕会减少给其他人的蛋糕数量，同时也会增加给那个接受者的边际效用。+ 第19行：
第19行： − 相比之下，非零和描述了一种情况，在这种情况下，相互作用的各方的总体收益和损失可能小于或大于零。零和博弈也称为严格竞争博弈，而非零和博弈可以是竞争博弈，也可以是非竞争博弈。零和博弈通常是用极大极小定理来解决的，这个定理与线性规划二元性密切相关,+ + + 第31行：
第33行： − + − 参与者可以共同获益或共同受苦的情况称为非零和。因此，如果一个国家有过量的香蕉与另一个国家进行交易以换取其过剩的苹果，而这两个国家都从交易中受益，那么这个国家就处于一种非零和情况。其他非零和博弈是这样一种博弈，在这种博弈中，参与者的得与失之和有时大于或小于他们开始时的水平。+ 第43行：
第45行： − 在零和博弈中，帕累托最优收益的概念引出了一个广义的相对自私的理性标准，即惩罚对手的标准，在这个标准中，双方总是以对自己有利的代价来寻求最小化对手的收益，而不是偏好多于少。惩罚对手标准可以用在零和游戏中。战争游戏，国际象棋)和非零和游戏(例如:。集合选择游戏)。+ 第55行：
第57行： − 对于双人有限零和对策，纳什均衡点、极大极小和极大的不同对策理论解概念都给出了相同的解。如果允许参与者采用混合策略，博弈总是存在均衡。+
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此词条暂由水流心不竞初译，翻译字数共1421，未经审校，带来阅读不便，请见谅。
{{short description|Mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants}}
{{short description|Mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants}}
In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. 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 larger 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 (see marginal utility).
In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. 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 larger 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 (see marginal utility).
在博弈论和经济理论中，'''<font color="#ff8000"> 零和博弈Zero-sum game</font>'''是一种数学描述，其中每个参与者的效用收益与其他参与者的效用收益的损失完全平衡。如果将参与者的总收益加起来，再减去总损失，则它们之和为零。因此，如果所有的参与者都平等地评价每一块蛋糕，那么切蛋糕就是一个零和游戏，切一块蛋糕会减少给其他人的蛋糕数量，同时也会增加给那个接受者的边际效用。
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,
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,
相比之下，非零和描述了（另）一种情况，在这种情况下，相互作用的各方的总体收益和损失可能小于或大于零。零和博弈也称为严格竞争博弈，而非零和博弈可以是竞争博弈，也可以是非竞争博弈。零和博弈通常是用极大极小定理来解决的，这个定理与线性规划二元性密切相关,
Many people have a [[cognitive bias]] towards seeing situations as zero-sum, known as [[zero-sum bias]].
Many people have a [[cognitive bias]] towards seeing situations as zero-sum, known as [[zero-sum bias]].
许多人对将情况视为零和有[[认知偏差]]，称为[[零和偏差]]。
Zero-sum games are a specific example of constant sum games where the sum of each outcome is always zero. Such games are distributive, not integrative; the pie cannot be enlarged by good negotiation.
Zero-sum games are a specific example of constant sum games where the sum of each outcome is always zero. Such games are distributive, not integrative; the pie cannot be enlarged by good negotiation.
== Definition ==
== Definition 定义==
Situations where participants can all gain or suffer together are referred to as non-zero-sum. Thus, a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, is in a non-zero-sum situation. Other non-zero-sum games are games in which the sum of gains and losses by the players are sometimes more or less than what they began with.
Situations where participants can all gain or suffer together are referred to as non-zero-sum. Thus, a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, is in a non-zero-sum situation. Other non-zero-sum games are games in which the sum of gains and losses by the players are sometimes more or less than what they began with.
参与者可以共同获益或共同受苦的情况称为'''<font color="#ff8000"> 非零和Non-zero-sum</font>'''。因此，如果一个国家有过量的香蕉与另一个国家进行交易以换取其过剩的苹果，而这两个国家都从交易中受益，那么这个国家就处于一种非零和情况。其他'''<font color="#ff8000"> 非零和博弈</font>'''是这样一种博弈，在这种博弈中，参与者的得与失之和有时大于或小于他们开始时的水平。
The idea of Pareto optimal payoff in a zero-sum game gives rise to a generalized relative selfish rationality standard, the punishing-the-opponent standard, where both players always seek to minimize the opponent's payoff at a favorable cost to himself rather to prefer more than less. The punishing-the-opponent standard can be used in both zero-sum games (e.g. warfare game, chess) and non-zero-sum games (e.g. pooling selection games).
The idea of Pareto optimal payoff in a zero-sum game gives rise to a generalized relative selfish rationality standard, the punishing-the-opponent standard, where both players always seek to minimize the opponent's payoff at a favorable cost to himself rather to prefer more than less. The punishing-the-opponent standard can be used in both zero-sum games (e.g. warfare game, chess) and non-zero-sum games (e.g. pooling selection games).
在零和博弈中，帕累托最优收益的概念引出了一个广义的相对自私的理性标准，即惩罚对手的标准，在这个标准中，双方总是以对自己有利的代价来寻求最小化对手的收益，而不是偏好多于少。惩罚对手标准可以同时用在零和游戏（例如战争游戏，国际象棋)和非零和游戏(例如:集合选择游戏)。
| 2L = Choice 1 | 2R = Choice 2 |
| 2L = Choice 1 | 2R = Choice 2 |
For two-player finite zero-sum games, the different game theoretic solution concepts of Nash equilibrium, minimax, and maximin all give the same solution. If the players are allowed to play a mixed strategy, the game always has an equilibrium.
For two-player finite zero-sum games, the different game theoretic solution concepts of Nash equilibrium, minimax, and maximin all give the same solution. If the players are allowed to play a mixed strategy, the game always has an equilibrium.
对于双人有限零和对策，'''<font color="#ff8000"> 纳什均衡点Nash equilibrium</font>'''、极大极小和极大的不同对策理论解概念都给出了相同的解。如果允许参与者采用混合策略，博弈总是存在均衡。
The zero-sum property (if one gains, another loses) means that any result of a zero-sum situation is [[Pareto optimal]]. Generally, any game where all strategies are Pareto optimal is called a conflict game.<ref>{{cite book |first=Samuel |last=Bowles |title=Microeconomics: Behavior, Institutions, and Evolution |url=https://archive.org/details/microeconomicsbe00bowl |url-access=limited |location= |publisher=[[Princeton University Press]] |pages=[https://archive.org/details/microeconomicsbe00bowl/page/n47 33]–36 |year=2004 |isbn=0-691-09163-3 }}</ref>
The zero-sum property (if one gains, another loses) means that any result of a zero-sum situation is [[Pareto optimal]]. Generally, any game where all strategies are Pareto optimal is called a conflict game.<ref>{{cite book |first=Samuel |last=Bowles |title=Microeconomics: Behavior, Institutions, and Evolution |url=https://archive.org/details/microeconomicsbe00bowl |url-access=limited |location= |publisher=[[Princeton University Press]] |pages=[https://archive.org/details/microeconomicsbe00bowl/page/n47 33]–36 |year=2004 |isbn=0-691-09163-3 }}</ref>