Chapter06序贯博弈和同时博弈的结合

序贯博弈和同时博弈的结合 Combining Sequential and Simultaneous Moves第6章 Chapter 6

序贯博弈和同时博弈的结合 Combining Sequential and Simultaneous Moves博弈类型 Game Type概念 Concepts分析技术 Techniques of Analysis博弈树(扩展形式) Game Trees (Extensive form)收益表(策略形式) Payoff tables (Strategic form)

纯粹序贯博弈反转均衡 Purely Sequential- Rollback move games equilibrium纯粹同时博弈 Purely Simultaneousmove games纳什均衡 Nash equilibrium

Slide 2

序贯博弈和同时博弈的结合 Combining Sequential and Simultaneous Moves在现实中，许多策略环境包含了这两种相互作用的成分。 In reality, many strategic situations contain elements of both types of interaction.而且，我们还可以使用扩展形式或策略形式分析任何一种博弈(可以交叉使用)。 Also, we can use either extensive form or strategic form for any type of game.Slide 3

内容提要 Outline兼具同时和序贯行动的博弈 Games with both simultaneous and sequential moves改变博弈中的行动顺序 Changing the order of moves in a game !改变分析方法 Change in the method of analysis *三人博弈 Three-player gamesSlide 4

兼具同时和序贯行动的博弈 Games with Both Simultaneous and Sequential Moves典型的例子一般都是博弈者在一段比较长的时间内相互作用。 The most obvious examples are those between players over an extended period of time.这样的博弈是同时利用博弈树和反转，以及收益表和纳什均衡的工具来分析的。 Such games are analyzed by combing the tools of trees and rollback, and payoff tables and Nash Equilibrium.Slide 5

兼具序贯和同时行动的一个两阶段博弈 A Two-stage Game Combining Sequential and Simultaneous Moves有两个可能成为电信巨头的企业：C和G。 There’re two would-be telecom giants, CrossTalk and GlobeDialog.每个企业都需要同时选择是否投资100亿以购置光纤网。 Each can choose whether to invest$10 billion in the purchase of a fiberoptic network, simultaneously.如果一个企业投资了而另一个没有，投资的企业需要确定其电信服务的定价。 If one invests and the other does not, then the investor has to make a pricing decision for its telecom service.如果两个企业都投了，那么他们的定价选择成为一个第二阶段的同时博弈。 If both invest, then their pricing choices become a second simultaneous-move game.Slide 6

兼具序贯和同时行动的一个两阶段博弈 A Two-stage Game Combining Sequential and Simultaneous MovesFirst stage: Investment Game GLOBEDIALOG Don’t CROSSTALK Don’t Invest 0, 0,0 Invest 0, GLOBALDIALOG High Second stage: GlobalDialog’s pricing decision

14

Low Second stage: pricing game

6

Second stage: GlobalDialog’s pricing decision High

GLOBEDIALOG High Low -10, 6 -2, -2 Slide 7

CROSSTALK

14

CROSSTALK

High L

ow

2, 2 6,-10

Low

6

兼具序贯和同时行动的一个两阶段博弈 A Two-stage Game Combining Sequential and Simultaneous MovesTwo Nash Equilibria: A chicken game GLOBEDIALOG Don’t CROSSTALK Don’t Invest 0, 0 14, 0 Invest 0, 14 -2, -2

Stage one Investment Game (After Substituting Rolled-Back Payoffs from the Equilibrium of the Second Stage)

Slide 8

子博弈 Subgames一个子博弈是整个博弈的一部分，它自身就构成一个完备博弈，具有完整的结构：博弈者、策略和收益。 A subgame is a part of a full game, which is also a full-fledged game in its own right, with a fully specified structure of players, strategies, and payoffs.更一般的，一个子博弈是多行动博弈的一部分，它开始于原博弈的某一个节点。 More generally, a subgame is the part of a multimove game that begin at a particular node of the original game.一个多行动博弈具有的子博弈数目等于其决策点数目。 A multimove game has as many subgames as it has decision nodes.Slide 9

多阶段博弈的构成：例子 Configurations of Multistage Games: Examples假设G事先已经投了100亿了 Suppose GlobalDialog has already made the$10 billion investment……CROSSTALK High Low GLOBEDIALOG High 2, 2 6,-10 Low -10, 6 -2, -2

Invest

CROSSTALKDon’t GLOBALDIALOG

High

0, 14

Low

0, 6Slide 10

多阶段博弈的构成：例子 Configurations of Multistage Games: Examples德国女足防守阵形中国女足防守阵形进攻阵形 1 3进攻阵形 2

反应德国女足

1 2

变阵中国女足不变阵 -1

不反应

Simultaneous-move First Stage Followed by Sequential MovesSlide 11

多阶段博弈的构成：例子 Configurations of Multistage Games: Examples德国女足防守阵形中国女足防守阵形进攻阵形 1 3进攻阵形 2 1

No pure strategy Nash equilibrium. It turns out our Chinese team should choose the attack lineup with probability 1/3. (Shown in Ch7)

Slide 12

改变博弈中的行动顺序 Changing the Order of Moves in a Game序贯博弈可以变成同时的，如果参与者在做出自己的选择时，不能观察到对手的行动。 Sequential-move games become simultaneous if the players cannot observe moves made by their rivals before making their own choices.这样，我们就得去寻找纳什均衡而非反转均衡。 In that case, we would analyze the game by searching for a Nash equilibrium rather than for a rollback equilibrium.Slide 13

改变博弈中的行动顺序 Changing the Order of Moves in a Game同时博弈也可以变成序贯的，如果某一参与者能够在做出自己选择前观察到其他人的行动。 A simultaneous-move game could become sequential if one playe …… 此处隐藏：13087字，全部文档内容请下载后查看。喜欢就下载吧 ……