Strategic Behavior
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Elements of a Game
Game has the following elements:
Players: who is involved? Rules: who moves when? What do they know when they move? What can they do? Outcomes: for each possible set of actions by the layers, which is the outcome of the game Payoffs: what are the players’ preferences over the possible outcome?
Solution Concepts
Nash Equilibrium is the very first solution concept for non-cooperative games.
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Nash Equilibrium (纳什均衡)
Essence of Nash Equilibrium
A Nash Equilibrium is defined as a set of strategies such that non of the participants in the game can improve their payoff, given the strategies of the other participants.
Does the Prisoner’s Dilemma have any dominant strategy? How about the Coordination Game?
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Dominated Strategies (被支配策略)
A dominated strategy is an alternative that yields a lower payoff than some other strategy, no matter what the other players in the game do.
A rational player will never use a dominated strategy in the actual action of game playing. Hence it can be eliminated. It is clear that if the existence of a dominant strategy implies that all other choices are in fact the dominated strategies.
一男一女试图安排一个晚上的娱乐内容 选择（策略）：“歌剧”、“拳击”；不过男女有 别 收益矩阵(Payoff Matrix)如下：
男 (The Man) 女 (The Lady) 歌剧 拳击 歌剧 2， 1 0，0 拳击 0，0 1，2
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Strategy & Payoffs
Other Examples
No one has a strictly incentive to deviate from the strategies in a Nash Equilibrium.
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Nash Equilibrium (纳什均衡)
Example
Consider the following game. Is there any dominant or dominated strategy?
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A
M D
Nash Equilibrium (纳什均衡)
Even though using a dominant strategy or a dominated strategy is a powerful simple way of “solving” a game, this kind of game is usually an exception, instead of a norm. We must have a generic method of finding the solution(s) of a game.
Coordination games
Smith and Jones are trying to decide whether to design the computers they sell to use large or small floppy disks Both players will sell more compute compatible. Strategies: “Large” or “Small” Payoffs are as follows.
寡头垄断，尤其是双寡头垄断竞争，特别适合使 用博弈论研究
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Strategy & Payoffs
Prisoner’s Dilemma(囚犯两难)
两个嫌犯被捕并受到指控，但除非至少一人招供 犯罪，警方并无充分证据将其按罪判刑
警方将他们分开审讯（不能沟通），并对他们说明不 同行动带来的后果。
如果二人都不坦白，只能判简单刑事罪，坐牢1个月 如果二人都坦白，两人都会定罪，判刑六个月； 如果其中一个坦白，另一个不坦白；那么坦白者马上释放 （从宽）、不坦白者将会判刑九个月。
Player 2 L U Player1 M D 5, 3 4, 0 3, 5 C 0, 4 5, 5 0, 4 R 3, 5 4, 0 5, 3
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Nash Equilibrium (纳什均衡)
Problem of Nash Equilibrium:
Multiple solutions! Examples:
Problem of Nash Equilibrium:
Insensitive to extreme payoffs (risks)
Example: Dangerous Coordination Game
Smith
Large Small
Jones Large Small 2, 2 -1000, -1 1, 1 -1，-1
请问两个嫌犯该怎么办？
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Strategy & Payoffs
Prisoner’s Dilemma(囚犯两难)
策略(Strategy): “沉默” & “招认” 收益矩阵(Payoff Matrix)如下： 囚犯2 沉默 招认 沉默 -1， -1 0， -9 招认 -9， 0 -6， -6
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囚犯1
Strategy & Payoffs
职业经理人资格－－中国最具价值的三大证书之一
〖 CCMC与企业管理〗
企业管理中的竞争问题
董志勇
博士 副教授
中国人民大学经济学院
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个人简介 ----中国人民大学经济学院院长助理 副教授 经济学博士 ----2008年北京奥运会特许商品调查委员会首席专家 ----2008年北京奥运会旅游纪念品调查研究首席专家 ----欧美同学会会员（1998年） ----中国宝鸡外国语学院客座教授(1999年) ----新加坡华夏学院学术委员会委员(2001年) ----欧洲维多利亚大学客座教授（2002年） ----亚洲发展银行青年组专家(Young Economist of ADB)（2002 年） ----清华大学继续教育学院客座教授（2003年） ----吉林电力高级经济顾问（2002年） ----吉林白城市人民政府经济顾问（2003年） ----国联股份高级顾问（2003年） ----中国人民大学侨联副主席（2004年） ----中国井冈山干部学院兼职教授（2005年）
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Strategy & Payoffs
Other Examples
Coordination games: payoff matrix Jones Large Small Large 2, 2 -1，-1 Small -1, -1 1, 1
Smith
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Dominant Strategies (支配策略)
But it is possible that there are dominated strategies, while there is no dominant strategy
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Application: Iterative Eliminations
Example
B
L U 3, 0 1, -1 2, 4 C 0, -5 3, 3 4, 1 R 0, -4 -2, 4 -1, 8
No dominant strategy, no dominated strategy & no pure strategy Nash equilibrium as well!
B Head Tail Head 1, -1 -1，1 Tail -1, 1 1, -1
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A
Nash Equilibrium (纳什均衡)
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博弈论和策略行为 Game Theory & Strategic Behaviors
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Lecture Plan/本讲计划
Game Theory
Strategy & Payoff Matrix Dominant & Dominated Strategies Nash Equilibrium Maximin Strategy & Mixed Strategy
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In Practice, it is almost sure that Smith wants to “play safe” and never try “large”!
Nash Equilibrium (纳什均衡)
Problem of Nash Equilibrium: