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 persons gain always is anothers 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 enemys 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信息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 players 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 practiceeven 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 loo