game theory is the science of strategy. It attempts to determine mathematically and logically the actions that “players” should take to secure the best outcomes for themselves in a wide array of “games.” The games it studies range from chess to child rearing and from tennis to takeovers. But the games all share the common feature of interdependence. That is, the outcome for each participant depends on the choices (strategies) of all. In so-called zero-sum games the interests of the players conflict totally, so that one person’s gain always is another’s loss. More typical are games with the potential for either mutual gain (positive sum) or mutual harm (negative sum), as well as some conflict.

都具有相互依赖的共同特征。也就是说，每个参与者的结果取决于所有人的选择（策略）。在所谓的零和游戏中，玩家的利益是完全冲突的博弈论是战略的科学。它试图从数学和逻辑上确定“玩家”应采取的行动，以确保他们在各种“游戏”中获得最佳成果。所研究的游戏包括从国际象棋到儿童饲养，从网球到收购。但是这些游戏，所以一个人的收益总是另一个人的损失。更典型的是有相互收益（正数）或相互伤害（负数）的博弈，以及一些冲突。

Game theory was pioneered by Princeton mathematician john von Neumann. In the early years the emphasis was on games of pure conflict (zero-sum games). Other games were considered in a cooperative form. That is, the participants were supposed to choose and implement their actions jointly. Recent research has focused on games that are neither zero sum nor purely cooperative. In these games the players choose their actions separately, but their links to others involve elements of both competition and cooperation.

博弈论由普林斯顿数学家约翰·冯·诺曼先生开创。早期的重点是纯粹的冲突游戏（零和游戏）。其他比赛以合作形式考虑。也就是说，参与者应该共同选择和实施他们的行动。最近的研究集中在既不是零和也不是纯合作的游戏。在这些游戏中，玩家分别选择他们的行为，但他们与其他人的联系涉及竞争与合作的要素。

Games are fundamentally different from decisions made in a neutral environment. To illustrate the point, think of the difference between the decisions of a lumberjack and those of a general. When the lumberjack decides how to chop wood, he does not expect the wood to fight back; his environment is neutral. But when the general tries to cut down the enemy’s army, he must anticipate and overcome resistance to his plans. Like the general, a game player must recognize his interaction with other intelligent and purposive people. His own choice must allow both for conflict and for possibilities for cooperation.

游戏与中性环境下的决策有着根本的区别。为了说明这一点，想一想伐木工人的决定与一般人的决定之间的区别。当伐木工人决定如何砍木头时，他并不指望木头能够反击; 他的环境是中立的。但是当将军试图削减敌人的军队时，他必须预见并克服对他的计划的抵抗。和一般人一样，玩家必须认识到他与其他聪明和有目的的人的互动。他自己的选择必须同时允许冲突和合作的可能性。

The essence of a game is the interdependence of player strategies. There are two distinct types of strategic interdependence: sequential and simultaneous. In the former the players move in sequence, each aware of the others’ previous actions. In the latter the players act at the same time, each ignorant of the others’ actions.

游戏的本质是玩家策略的相互依赖性。战略相互依存有两种截然不同的类型：顺序式和同时式。在前者中，球员依次移动，每个人都意识到其他人以前的行为。在后者中，参与者同时行动，每个人都无知其他人的行为。

A general principle for a player in a sequential-move game is to look ahead and reason back. Each player should figure out how the other players will respond to his current move, how he will respond in turn, and so on. The player anticipates where his initial decisions will ultimately lead and uses this information to calculate his current best choice. When thinking about how others will respond, he must put himself in their shoes and think as they would; he should not impose his own reasoning on them.

玩家在顺序移动游戏中的一般原则是向前看，回头看。每个玩家都应该弄清楚其他玩家将如何回应他目前的行动，他将如何反应，等等。玩家预期他最初的决定将最终导致并使用这些来计算他当前的最佳选择。当想到别人会如何回应时，他必须放下自己的想法，按照自己的想法去思考; 他不应该对他们施加他自己的推理。

In principle, any sequential game that ends after a finite sequence of moves can be “solved” completely. We determine each player’s best strategy by looking ahead to every possible outcome. Simple games, such as tic-tac-toe, can be solved in this way and are therefore not challenging. For many other games, such as chess, the calculations are too complex to perform in practice—even with computers. Therefore, the players look a few moves ahead and try to evaluate the resulting positions on the basis of experience.

原则上，在有限的一系列动作之后结束的任何连续游戏都可以完全“解决”。我们通过展望每一个可能的结果来确定每个玩家的最佳策略。简单的游戏，如井字游戏，可以用这种方式解决，因此不具有挑战性。对于许多其他游戏，如国际象棋，计算过于复杂，无法在实践中执行 - 即使使用计算机。因此，球员们会看到前进的几​​步，并尝试根据经验评估所得到的位置。

In contrast to the linear chain of reasoning for sequential games, a game with simultaneous moves involves a logical circle. Although the players act at the same time, in ignorance of the others’ current actions, each must be aware that there are other players who are similarly aware, and so on. The thinking goes: “I think that he thinks that I think . . .” Therefore, each must figuratively put himself in the shoes of all and try to calculate the outcome. His own best action is an integral part of this overall calculation.

与连续游戏的线性推理链不同，具有同时移动的游戏涉及逻辑循环。虽然玩家同时行动，但无视别人目前的行为，每个人都必须意识到还有其他玩家同样意识到，等等。这个想法是：“我认为他认为我想。。。“因此，每个人都必须形象地把自己置于所有人的脚下，并试图计算结果。他自己的最佳行为是整体计算的一个组成部分。

This logical circle is squared (the circular reasoning is brought to a conclusion) using a concept of equilibrium developed by the Princeton mathematician john nash. We look for a set of choices, one for each player, such that each person’s strategy is best for him when all others are playing their stipulated best strategies. In other words, each picks his best response to what the others do.

使用普林斯顿数学家约翰纳什开发的均衡概念，将这个逻辑圆平方（圆形推理得出结论）。我们寻找一套选择，每个选手都有一个选择，这样当其他人都在玩他们规定的最佳策略时，每个人的策略对他来说都是最好的。换句话说，每个人都会对他人所做的最好的回应。

Sometimes one person’s best choice is the same no matter what the others do. This is called a “dominant strategy” for that player. At other times, one player has a uniformly bad choice—a “dominated strategy”—in the sense that some other choice is better for him no matter what the others do. The search for an equilibrium should begin by looking for dominant strategies and eliminating dominated ones.

无论别人做什么，有时一个人的最佳选择是一样的。这被称为该球员的“主导战略”。在其他时候，一个球员有一个统一的不好的选择 - 一个“主导策略” - 在某种意义上，无论别人怎么做，其他选择对他都更好。寻求均衡应首先寻找主导策略并消除主导策略。

When we say that an outcome is an equilibrium, there is no presumption that each person’s privately best choice will lead to a collectively optimal result. Indeed, there are notorious examples, such as the prisoners’ dilemma (see below), where the players are drawn into a bad outcome by each following his best private interests.

当我们说结果是一种均衡时，并不假设每个人的私人最佳选择将导致集体最优结果。事实上，有一些臭名昭着的例子，比如囚徒困境（见下文），在这些情况下，玩家被各自追求最好的私人利益而陷入糟糕的结局。

Nash’s notion of equilibrium remains an incomplete solution to the problem of circular reasoning in simultaneous-move games. Some games have many such equilibria while others have none. And the dynamic process that can lead to an equilibrium is left unspecified. But in spite of these flaws, the concept has proved extremely useful in analyzing many strategic interactions.

纳什的均衡概念仍然是解决同步移动游戏中循环推理问题的不完全解决方案。一些游戏有很多这样的均衡，而其他游戏则没有。并且可以导致均衡的动态过程未指定。但是，尽管存在这些缺陷，但这一概念在分析许多战略互动中证明是非常有用的。

It is often thought that the application of game theory requires all players to be hyperrational. The theory makes no such claims. Players may be spiteful or envious as well as charitable and empathetic. Recall George Bernard Shaw’s amendment to the Golden Rule: “Do not do unto others as you would have them do unto you. Their tastes may be different.” In addition to different motivations, other players may have different information. When calculating an equilibrium or anticipating the response to your move, you always have to take the other players as they are, not as you are.

人们经常认为，博弈论的应用要求所有参与者都是超理性的。这个理论没有提出这样的说法。玩家可能是恶毒或嫉妒，以及慈善和同情。回想萧伯纳对黄金法则的修正案：“不要像别人那样对待他人。他们的口味可能不同。“除了不同的动机外，其他玩家可能会有不同的信息。当计算均衡或预测对你的举动的反应时，你总是必须让其他玩家保持原样，而不是像现在这样。

The following examples of strategic interaction illustrate some of the fundamentals of game theory.

下面的战略交互例子说明了博弈论的一些基本原理。

The prisoners’ dilemma. Two suspects are questioned separately, and each can confess or keep silent. If suspect A keeps silent, then suspect B can get a better deal by confessing. If A confesses, B had better confess to avoid especially harsh treatment. Confession is B’s dominant strategy. The same is true for A. Therefore, in equilibrium both confess. Both would fare better if they both stayed silent. Such cooperative behavior can be achieved in repeated plays of the game because the temporary gain from cheating (confession) can be outweighed by the long-run loss due to the breakdown of cooperation. Strategies such as tit-for-tat are suggested in this context.

囚犯的困境。两名嫌疑人分别受到质疑，每个人都可以坦白或保持沉默。如果嫌疑人A保持沉默，那么怀疑B可以通过承认获得更好的交易。如果A承认，B最好承认避免特别苛刻的治疗。认罪是B的主导策略。A也是如此，因此在平衡中都承认。如果两人都保持沉默，两人的表现都会更好。这种合作行为可以在游戏的重复中实现，因为由于合作中断而造成的长期损失可以超过作弊（忏悔）的暂时收益。在这种情况下，建议采取针锋相对的策略。

Mixing moves. In some situations of conflict, any systematic action will be discovered and exploited by the rival. Therefore, it is important to keep the rival guessing by mixing your moves. Typical examples arise in sports—whether to run or to pass in a particular situation in football, or whether to hit a passing shot crosscourt or down the line in tennis. Game theory quantifies this insight and details the right proportions of such mixtures.

混合动作。在一些冲突的情况下，任何系统性行动都会被对手发现并利用。因此，通过混合你的动作来保持对手猜测是很重要的。典型的例子出现在体育运动中 -无论是在足球的特定情况下跑步还是传球，还是在网球场上击中传球射门或下线。博弈论量化了这种见解，并详细说明了这种混合物的正确比例。

Strategic moves. A player can use threats and promises to alter other players’ expectations of his future actions, and thereby induce them to take actions favorable to him or deter them from making moves that harm him. To succeed, the threats and promises must be credible. This is problematic because when the time comes, it is generally costly to carry out a threat or make good on a promise. Game theory studies several ways to enhance credibility. The general principle is that it can be in a player’s interest to reduce his own freedom of future action. By so doing, he removes his own temptation to renege on a promise or to forgive others’ transgressions.

战略举措。玩家可以使用威胁和承诺来改变其他玩家对未来行为的期望，从而诱使他们采取有利于他的行动，或阻止他们采取行动伤害他。要成功，威胁和承诺必须可信。这是有问题的，因为到时候，执行威胁或承诺承诺通常是昂贵的。博弈论研究几种提高可信度的方法。总的原则是，为了降低自己未来行动的自由，符合玩家的利益。通过这样做，他消除了自己的背叛，或者原谅别人的过失的诱惑。

For example, Cortés scuttled all but one of his own ships on his arrival in Mexico, purposefully eliminating retreat as an option. Without ships to sail home, Cortés would either succeed in his conquest or perish. Although his soldiers were vastly outnumbered, this threat to fight to the death demoralized the opposition, who chose to retreat rather than fight such a determined opponent. Polaroid Corporation used a similar strategy when it purposefully refused to diversify out of the instant photography market. It was committed to a life-or-death battle against any intruder in the market. When Kodak entered the instant photography market, Polaroid put all its resources into the fight; fourteen years later, Polaroid won a nearly billion-dollar lawsuit against Kodak and regained its monopoly market. (Polaroid’s focus on instant film products later proved costly when the company failed to diversify into digital photography.)

例如，科尔特斯在抵达墨西哥时凿沉了他自己的所有船只中的一艘，并有目的地消除了撤退。如果没有船舶回家，科尔特斯要么成功征服，要么灭亡。尽管他的士兵数量众多，但这种与死亡作斗争的威胁使反对派士气低落，他们选择撤退而不是与这样坚定的对手作战。宝丽来公司在有意拒绝从即时摄影市场多元化时采用了类似的策略。它致力于对抗市场上的任何入侵者的生死战。当柯达进入即时拍摄市场时，宝丽来将所有资源投入到战斗中; 14年后，宝丽来赢得了对柯达的近亿美元的诉讼并重新获得了垄断权市场。（宝丽来专注于即时胶片产品的后来证明，当该公司未能实现数字摄影多样化时，昂贵的成本。）

Another way to make threats credible is to employ the adventuresome strategy of brinkmanship—deliberately creating a risk that if other players fail to act as you would like them to, the outcome will be bad for everyone. Introduced by Thomas Schelling in The Strategy of Conflict, brinkmanship “is the tactic of deliberately letting the situation get somewhat out of hand, just because its being out of hand may be intolerable to the other party and force his accommodation.” When mass demonstrators confronted totalitarian governments in Eastern Europe and China, both sides were engaging in just such a strategy. Sometimes one side backs down and concedes defeat; sometimes tragedy results when they fall over the brink together.

另一种使威胁可信的方法是采用冒险的冒险策略 - 故意制造一种风险，即如果其他玩家没有按照自己的愿望行事，结果将会对每个人都不利。托马斯谢林在“冲突战略”中介绍说，“边缘战术”是故意让局势略微失控的策略，仅仅是因为它的失控可能让对方无法忍受，并迫使他们的住所。“当群众示威者面对时东欧和中国的极权政府双方都在制定这样的战略。有时一方支持并承认失败; 有时候会一起陷入濒临崩溃的悲剧结局。

Bargaining. Two players decide how to split a pie. Each wants a larger share, and both prefer to achieve agreement sooner rather than later. When the two take turns making offers, the principle of looking ahead and reasoning back determines the equilibrium shares. Agreement is reached at once, but the cost of delay governs the shares. The player more impatient to reach agreement gets a smaller share.

讨价还价。两名球员决定如何分割一个馅饼。每个人都希望有更大的份额，并且都希望尽早达成协议，而不是晚些时候。当两人轮流提出要约时，展望未来和推理的原则决定了均衡份额。协议立即达成，但延迟的成本支配股份。玩家更不耐烦达成协议的份额较小。

Concealing and revealing information. When one player knows something that others do not, sometimes he is anxious to conceal this information (his hand in poker) and at other times he wants to reveal it credibly (a company’s commitment to quality). In both cases the general principle is that actions speak louder than words. To conceal information, mix your moves. Bluffing in poker, for example, must not be systematic. Recall Winston Churchill’s dictum of hiding the truth in a “bodyguard of lies.” To convey information, use an action that is a credible “signal,” something that would not be desirable if the circumstances were otherwise. For example, an extended warranty is a credible signal to the consumer that the firm believes it is producing a high-quality product.

隐藏和揭示信息。当一个玩家知道其他人不知道的东西时，有时候他会急于隐藏这些信息（他的手在扑克中），有时候他想要可靠地揭示它（公司对质量的承诺）。在这两种情况下，总的原则是行动胜于言语。要隐藏信息，请混合您的动作。例如，扑克中的虚张声势不能是系统性的。回想一下温斯顿丘吉尔在“谎言的保镖”中隐瞒真相的言论。为了传递信息，请使用一种可信的“信号”，如果情况不是这样的话，这是不可取的。例如，延长保修期对消费者来说是一个可靠的信号，即该公司认为它正在生产高质量的产品。

Recent advances in game theory have succeeded in describing and prescribing appropriate strategies in several situations of conflict and cooperation. But the theory is far from complete, and in many ways the design of successful strategy remains an art.

博弈论的最新进展已经成功地描述和规定了在若干冲突与合作情况下的适当策略。但是这个理论远未完成，在许多方面，成功策略的设计仍然是一门艺术。

英文原文来源：http://www.econlib.org/library/Enc/GameTheory.html

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