文档介绍：序贯博弈内容提要 Outline
Games with Sequential
描述博弈:博弈树 Game trees
Moves 求解博弈:反转 Rollback
扩展
第3章
增加参与者 Adding more players
Chapter 3
增加行动 Adding more moves
证据 Evidences
Slide 2
序贯博弈序贯博弈
Sequential-move Games Sequential-move Games
序贯博弈要求一个有严格博弈顺序的策略环无论何时采取行动,参与者都需要考虑他们当
境。前的行动会如何影响未来的行动,包括对手和
Sequential-move games entail strategic 自己的行动。
situations in which there is a strict order Whenever actions are taken, players
of play. need to think about how their current
参与者按顺序出招,并且知道在他们之前的那 actions will influence future actions,
些参与者都干了什么。 both for their rivals and for themselves.
Players take turns making their moves, 参与者在计算未来后果的基础上,决定现在如何出
and they know what players who have 招。
Players thus decide their current moves on
gone before them have done. the basis of calculations of future
consequences.
Slide 3 Slide 4
博弈树决策树与博弈树
Game Trees Decision Trees vs. Game Trees
博弈树,或博弈的扩展型,是用来表示和分析决策树表示在一个中立的环境下,单个决策者
序贯博弈的图形方法。所有的连续决策点。
A game tree, or the extensive form of a A decision tree show all the essive
game is a graphical technique for decision points, or nodes, for a single
displaying and analyzing sequential-
decision maker in a neutral environment.
move games.
它表明了所有参与者能够采取的所有可能的行博弈树就是一个博弈当中所有参与者共用的决
动,指出了博弈的所有可能结果。策树。
It illustrate all of the possible actions Game trees are just joint decision trees
that can be taken by all of the players for all of the players in a game.
and indicate all of the possible
es from the game. Slide 5 Slide 6
1
博弈树:一个例子博弈树
Game Trees: An Example Game Trees
节点
Up (2,7,4,1) node
ANN
branch分支
Down (1,-2,3,0) 博弈树由节点和分支组成。节点之间由
Branches 1 High (,2,-11,3)
DEB 分支相连。
Low (0,-,0,0) Game trees consist of nodes and
BOB 2
are connected to
Stop Terminal nodes
3 (10,7,1,1) one another by branches.
ANN Good 50% (6,3,4,0)
NATURE
Risky
Go Bad 50% (2,8,-1,2)
Root
CHRIS
(Initial node) Safe Go back to the table
(3,5,3,1