科技英语第二次课_game_theory

它试图以数学和逻辑的方法帮助博弈者作出决策， 它试图以数学和逻辑的方法帮助博弈者作出决策，使他 以数学和逻辑的方法帮助博弈者作出决策 们在一系列纷繁复杂的博弈中保证利益的最大化。 们在一系列纷繁复杂的博弈中保证利益的最大化。
zero-sum games
In game theory and economic theory, zerosum describes a situation in which a participant's gain or loss is exactly balanced by the losses or gains of the other participant(s). Examples:赌博 赌博
More typical are games with the potential for either mutual gain or mutual harm, as well as some conflict.
更多具有代表性的例子可能会导致共同得利博弈和共 同损失博弈，同样的情况还会发生在另外一些冲突中。 同损失博弈，同样的情况还会发生在另外一些冲突中。
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”.
When thinking about how others will respond, one must put oneself in their shoes, and think as they would; one should not impose one’s own reasoning on them.
Nash equilibrium
纳什均衡，又称为非合作博弈均衡 纳什均衡 又称为非合作博弈均衡 A Nash equilibrium, named after John Nash, is a set of strategies, one for each player, such that no player has incentive to unilaterally change her action.
John von NeBiblioteka Baidumann
A Hungarian-born American mathematics and made contribution to quantum physics, functional analysis, set theory, economics, computer science, topology, numerical analysis, hydrodynamics, statistics and may other mathematical fields as one of word history’s outstanding mathematicians.
Game theory was pioneered by Princeton mathematician John von Neumann.
更多具有代表性的例子可能会导致共同得利博弈和共同损 失博弈，同样的情况还会发生在另外一些冲突中。 失博弈，同样的情况还会发生在另外一些冲突中。
Princeton
纳什关于均衡的概念还不能完全解决联立策略博弈中逻 辑循环的问题。 辑循环的问题。
And the dynamic process that can lead to an equilibrium is left unspecified.
纳什均衡还没有清除地说明关于导致均衡的动态过程。 纳什均衡还没有清除地说明关于导致均衡的动态过程。
在考虑其他博弈者会如何应对时，博弈者必须能设身处 在考虑其他博弈者会如何应对时， 地地换位思考，而不能把自己的主观判断强加于人。 地地换位思考，而不能把自己的主观判断强加于人。
tic-tac-toe 井字棋
Tic-tack-toe is a penciland-paper game in which two players alternately put crosses(0) and circles(×) in one of the compartments of a square grid of nine spaces. The player who succeeds in placing three respective marks in a horizontal, vertical or diagonal row wins the game.
John Nash
John Forbes Nash Jr. (born June 13, 1928) is an American mathematician and economist whose works in game theory, differential geometry, and partial differential equations have provided insight into the forces that govern chance and events inside complex systems in daily life.
Prisoners’ dilemma
囚徒困境
In game theory, the prisoners’ dilemma is a type of non-zero game in which two players can cooperate with or defect the other player.
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League and is considered one of the Colonial Colleges.
当我们把博弈的结果表述为一种均衡的时候，并不能假 当我们把博弈的结果表述为一种均衡的时候， 定博弈的每个参与者的个人最佳策略将带来共同的最优 化结果。 化结果。
Nash’s notion of equilibrium remains an incomplete solution to the problem of circular reasoning in simultaneous-move games.
Text A
Game Theory
博弈论
Game Theory
Game theory is the mathematical analysis of any situation involving a conflict of interest, with the intent of indicating the optimal choices that, under given conditions, will lead to a desired outcome.
Unit 1
Mathematics
Warming-up
Mathematics has a wide application, such as computer, economy. Now it has been broaden theoretically and applied to many social problems. It has driven a revolution in economic theory. It has also found application in sociology and psychology, and established links with evolution and biology. One significant application is Game Theory which received special attention with the awarding of the Nobel Prize in economics to John Nash.
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.
Prisoners’ dilemma
Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (defects from the other) for the prosecution against the other and the other remains silent (cooperates with the other), the betrayer goes free and the silent accomplice receives the full 8-year sentence. If both remain silent, both prisoners are sentenced to only one year in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. If we assume that each player cares only about minimizing his or her own time in jail, how should the prisoners act?
In contrast to the linear chain of reasoning for sequential games, a game with simultaneous moves involves a logical circle.
与连续策略博弈的线性思维不同，联立策略的博弈涉及 与连续策略博弈的线性思维不同， 逻辑循环。 逻辑循环。
警方逮捕A、 两名嫌疑犯 但没有足够证据指控二人入罪。 两名嫌疑犯， 警方逮捕 、B两名嫌疑犯，但没有足够证据指控二人入罪。于是 警方分开囚禁嫌疑犯，分别和二人见面， 警方分开囚禁嫌疑犯，分别和二人见面，并向双方提供以下相同的 选择： 选择： 若一人认罪并作证检举对方（相关术语称“背叛”对方），而对方 若一人认罪并作证检举对方（相关术语称“背叛”对方），而对方 ）， 保持沉默，此人将即时获释，沉默者将判监8年 保持沉默，此人将即时获释，沉默者将判监 年。 若二人都保持沉默（相关术语称互相“合作”），则二人同样判监 若二人都保持沉默（相关术语称互相“合作”），则二人同样判监 一年。 一年。 若二人都互相检举（互相“背叛”），则二人同样判监5年 若二人都互相检举（互相“背叛”），则二人同样判监 年。 则二人同样判监 囚徒困境假定每个参与者（ 囚徒困境假定每个参与者（即“囚徒”）都是利己的，即都寻求最 囚徒” 都是利己的， 大自身利益，而不关心另一参与者的利益。 大自身利益，而不关心另一参与者的利益。