摘要翻译：
这篇短文演示了如何定义一个非零和博弈到零和博弈的转换，从而使达到均衡的最优混合策略始终存在。这种转换相当于把一个被动的参与者引入一个博弈（一个拥有单一纯策略集的参与者），其收益取决于主动参与者的行动，它是由博弈中的效用守恒定律证明的。在一个变换的游戏中，每个参与者与所有其他玩家比赛，包括被动玩家。这种方法的优点是变换后的博弈是零和的，并且有一个均衡解。然而，新博弈的最优策略和价值可能不同于原始博弈中的理性策略。我们用囚徒困境的例子来证明这一原理。
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英文标题：
《Conservation Law of Utility and Equilibria in Non-Zero Sum Games》
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作者：
Roman V. Belavkin
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最新提交年份：
2010
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Computer Science and Game Theory        计算机科学与博弈论
分类描述：Covers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games (which may overlap with Learning), foundations of agent modeling in games (which may overlap with Multiagent systems), coordination, specification and formal methods for non-cooperative computational environments. The area also deals with applications of game theory to areas such as electronic commerce.
涵盖计算机科学和博弈论交叉的所有理论和应用方面，包括机制设计的工作，游戏中的学习（可能与学习重叠），游戏中的agent建模的基础（可能与多agent系统重叠），非合作计算环境的协调、规范和形式化方法。该领域还涉及博弈论在电子商务等领域的应用。
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一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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英文摘要：
  This short note demonstrates how one can define a transformation of a non-zero sum game into a zero sum, so that the optimal mixed strategy achieving equilibrium always exists. The transformation is equivalent to introduction of a passive player into a game (a player with a singleton set of pure strategies), whose payoff depends on the actions of the active players, and it is justified by the law of conservation of utility in a game. In a transformed game, each participant plays against all other players, including the passive player. The advantage of this approach is that the transformed game is zero-sum and has an equilibrium solution. The optimal strategy and the value of the new game, however, can be different from strategies that are rational in the original game. We demonstrate the principle using the Prisoner's Dilemma example.
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PDF链接：
https://arxiv.org/pdf/1010.2439