1 博弈论概述

Glossary
Zero-sum game零和博弈 A game is said to be zero-sum if for any outcome, the sum of the payoffs to all players is zero. In a two-player zero-sum game, one player’s gain is the other player’s loss, so their interests are diametrically opposed. 一个博弈称为零和博弈，当对于任何结果，所有参与人 的支付总和为零。在一个两人零和博弈中，一个参与 人的所得是另一个参与人的损失，所以他们的利益是 直接对立的。
Glossary
Strategic form战略式 A game in strategic form, also called normal form, is a compact representation of a game in which players simultaneously choose their strategies. The resulting payoffs are presented in a table with a cell for each strategy combination. 一个战略式博弈也称为标准式博弈，它用紧凑的形式来 表示博弈，博弈中参与人同时选择战略。作为结果的 支付用表格的形式来表示，每一个单元格表示一个战 略组合。
Glossary术语
Common knowledge共同知识 A fact is common knowledge if all players know it, and know that they all know it, and so on. The structure of the game is often assumed to be common knowledge among the players. 如果一个事实被所有的参与人知道，并且每个参与 人都知道所有的人都知道，并且每个参与人都知道每 个参与人都知道所有的人都知道，如此等等，以致无 穷，那么，这个事实就是共同知识。
Glossary
Dominating strategy占优战略 A strategy dominates another strategy of a player if it always gives a better payoff to that player, regardless of what the other players are doing. It weakly dominates the other strategy if it is at least as good. 参与人的某个战略相对另一个战略占据优势，如果这 个战略总是带给他更好的支付，不管其他的参与人如 何选择。该战略称为占优战略。如果这个战略所带来 的支付至少是最好的，那么，这个战略就成为弱占优 战略。
Glossary
Payoff支付 A payoff is a number, also called utility, that reflects the desirability of an outcome to a player, for whatever reason. When the outcome is random, payoffs are usually weighted with their probabilities. The expected payoff incorporates the play’s attitude towards risk. 支付是一个数字，也称为效用。支付反映了一个参与人 对一种结果的希求。当结果是随机的时候，支付通常 用它们的概率来表示。期望支付体现了该参与人对待 风险的态度。
Glossary
Mixed strategy混合战略 A mixed strategy is an active randomization, with given probabilities, that determines the player’s decision. As a special case, a mixed strategy can be the deterministic choice of one of the given pure strategies.
Glossary
Player参与人 A player is an agent who makes decisions in a game. 一个参与人是一个博弈中作出选择的代理人。
Glossary
Rationality理性 A player is said to be rational if he seeks to play in a manner which maximizes his own payoff. It is often that the rationality of all players is common knowledge. 一个参与人是理性的，如果他寻求最大化自己的支付。 所有参与人都是理性的通常被作为一种共同知识来对 待。
Glossary
Strategy战略 In a game in strategic form, a strategy is one of the given possible actions of player. In an extensive game, a strategy is a complete plan of choice, one for each decision point of the player. 战略式博弈中，一个战略是一个参与人给定的可能行动 中的一个。在扩展博弈中，一个战略是关于行动的一 个完整计划，它描述了一个参与者在每一个决策点上 对可行行动的选择。
混合战略是一种积极的随机选择。给定概率，然后决定 参与人的选择。作为特例，一个混合战略可以是给定 纯战略的一个确定性选择。
Glossary
Nash equilibrium纳什均衡 A Nash equilibrium, also called strategic equilibrium, is a list of strategies, one for each player, which has the property that no player can unilaterally change his strategy and get a better payoff. 纳什均衡，也称战略均衡，是一系列战略的组合，该战 略组合具有这样的性质：没有参与人能够通过单方面 改变他的战略得到更好的支付。
Glossary
Perfect information完美信息 A game has perfect information when at any point in time one player makes a move, and knows all the actions that have been made until then. 一个博弈拥有完美信息，当一个参与人在每一点上 行动，他及时知道直到该点之前的所有行动。
Glossary
Game博弈 A game is a formal description of a strategic situation. 博弈是对战略形势的标准描述。
Glossary
Game theory博弈理论 Game theory is the formal study if decisionmaking where several players must make choices that potentially affect the interests of the other players. 博弈论是对多人决策问题的标准研究，在这种决策中， 每个参与人必须做出选择，他的选择潜在的影响了其 他参与人的利益。
Game Theory博弈论
Biblioteka Baidu
How to decide.如何做决定
Glossary术语
Backward induction逆向归纳 Backward induction is a technique to solve a game of perfect information. It first considers the moves that are the last in the game, and determines the best move for the player in each case. Then, taking these as given future actions, it proceeds backwards in time, again determining the best move for the respective player, until the beginning of the game is reached. 逆向归纳是解决完美信息博弈的一种技术。它首先考虑博弈的最 后一步，决定每种场合下参与人的最优行动。然后，把这些作 为给定的未来行动，依次向后推导决定每一个参与人的最优行 动，直到博弈的开头。
History and impact of game theory 博弈论的历史及其影响
The earliest example of a formal game-theoretic analysis is the study of a duopoly by Antoine Cournot in 1838. The mathematician Emile Borel suggested a formal theory of games in 1921, which was furthered by the mathematician John von Neumann in 1928 in a “theory of parlor games.” Game theory was established as a field in its own right after the 1944 publication of the monumental volume Theory of Games and Economic Behavior by von Neumann and the economist Oskar Morgenstern. This book provided much of the basic terminology and problem setup that is still in use today.
Glossary
Extensive game扩展博弈 An extensive game(or extensive form game)describes with a tree how a game is played. It depicts the order in which players make moves, and the information each player has at each decision point. 扩展博弈（或扩展式博弈）用树型结构来表述博弈，它 表示了参与人的顺序及每个参与人在每个决策点上所 拥有的信息。
1 What is game theory?什么是博弈？
Game theory is the formal study of conflict and cooperation. Game theoretic concepts apply whenever the actions of several agents are interdependent. These agents may be individuals, groups, firms, or any combination of these. The concepts of game theory provide a language to formulate, structure, analyze, and understand strategic scenarios. 博弈论是对冲突与合作的标准研究。只要多个代理人之 间的行动是互相依赖的时候，博弈的理论观念就起作 用。这些代理人可以是个人、组织、公司或它们的组 合。博弈论的思想提供了一种表述、构造、分析和理 解战略情景的语言。