经济博弈论课件3

1

序贯博弈

Games with Sequential Moves

第3章

Chapter 3

Slide 2

序贯博弈

Sequential-move Games

序贯博弈要求一个有严格博弈顺序的策略环境。Sequential-move games entail strategic situations in which there is a strict order of play.

参与者按顺序出招，并且他们知道在他们之前的那些参与者都干了什么。

Players take turns making their moves, and they know what players who have gone before them have done.

Slide 3

序贯博弈

Sequential-move Games

无论何时采取行动，参与者都需要考虑他们当前的行动会如何影响未来的行动，包括对手和自己的行动。

Whenever actions are taken, players need to think about how their current actions will influence future actions, both for their rivals and for themselves.

参与者在计算未来后果的基础上，决定现在如何出招。

Players thus decide their current moves on the basis of calculations of future consequences.

Slide 4

博弈树

Game Trees

博弈树，或博弈的扩展式，是用来表示和分析序贯博弈的图形方法。

A game tree, or the extensive form of a game is a graphical technique for displaying and analyzing sequential-move games.

它表明了所有参与者能够采取的所有可能的行动，指出了博弈的所有可能结果。

It illustrate all of the possible actions that can be taken by all of the players and indicate all of the possible outcomes from the game.

Slide 5

决策树与博弈树

Decision Trees vs. Game Trees

决策树表示在一个中立的环境下，单个决策者所有的连续决策点。

A decision tree show all the successive decision points, or nodes, for a single decision maker in a neutral environment.博弈树其实就是一个博弈当中的所有参与者共用的决策树。

Game trees are just joint decision trees for all of the players in a game.

Slide 6

博弈树：一个例子

Game Trees: An Example

ANN

BOB CHRIS

ANN

DEB

NATURE Stop

Go

123

Risky

Safe

Up Down High Low (2,7,4,1)(1,-2,3,0)(1.3,2,-11,3)(0,-2.718,0,0)

(10,7,1,1)

(6,3,4,0)(2,8,-1,2)

(3,5,3,1)Good 50%

Bad 50%

(ANN,BOB,CHRIS,DEB)

node 节点branch 分支

Terminal nodes Root

(Initial node)Branches

Slide 7

博弈树由节点和分支组成。节点之间由分支相连。

Game trees consist of nodes and branches.Nodes are connected to one another by branches.

Slide 8

博弈树

Game Trees

节点有两类

Nodes come in two types:

每个决策点与在该节点采取某一行动的参与者相关联。

A decision node is associated with the

player who chooses an action at that node.

每一博弈树有一个决策点为该博弈的初始点。

Every tree has one decision node that is the

game ’s initial node, the starting point of the game.

每一终结点和参与者的一组结果（收益）相关联。A terminal node is associate with a set of outcomes (payoffs) for the players taking part in.

Slide 9分支代表从任一决策点出发的可能采取的行动。The branches represent the possible actions that can be taken from any decision node.每一分支都从博弈树上的一个决策点指向另一个决策点或终结点。

Each branch leads from a decision node on the tree either to another decision node, or to a terminal node.

在任何一个博弈中，从每一个决策点出发，至少要有一个分支；不过，仅允许有一个分支指向任何一个决策点。

In any game, there must be at least one branch leading from each decision node. However, every decision node can have only

one branch leading to it.

Slide 10不确定性与“自然之手”

Uncertainty and “Nature ’s Moves ”

将自然作为一个参与者，使得我们可以将不确定性引入博弈当中，提供了一个允许所发生的事情不在任何一个实际参与者掌控之中的机制。Use of the player Nature allows us to introduce uncertainty in a game and gives us a mechanism to allow things to happen that outside the control of any of the actual players.

引入自然的选择，意味着决策者需要确定预期收益。

The inclusion of a choice by Nature means players need to determine the

expected payoffs .