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博弈论和策略行为
GameTheory&StrategicBehaviors
LecturePlan/本讲计划
GameTheory
Strategy&PayoffMatrix
Dominant&DominatedStrategies
NashEquilibrium
MaximinStrategy&MixedStrategy
StrategicBehavior
ElementsofaGame
Gamehasthefollowingelements:
Players:whoisinvolved?
Rules:whomoveswhen?Whatdotheyknowwhentheymove?Whatcantheydo?
Outcomes:foreachpossiblesetofactionsbythelayerswhichistheoutcomeofthegame
Payoffs:whataretheplayers’preferencesoverthepossibleoutcome?
Strategy&Payoffs
博弈论把人间一切竞争活动看成是玩策略游戏这种策略游戏是在一定的游戏规则之下进行
它的两个最基本的概念是策略与支付矩阵
一种策略(Strategy)表示游戏参与者的一套运作计划和手段如“降价15%”就是一种策略
收益矩阵(Payoffmatrix)是表示游戏参与者在各种不同策略下的利润额的一套支付表格
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
Strategy&Payoffs
Prisoner’sDilemma(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
请问两个嫌犯该怎么办？
Strategy&Payoffs
Prisoner’sDilemma(囚犯两难)
策略(Strategy):“沉默”&“招认”
收益矩阵(PayoffMatrix)如下：
Strategy&Payoffs
Prisoner’sDilemma(囚犯两难)
囚犯两难的问题在现实中常常出现
比如两家企业的价格战
Strategy&Payoffs
性别战博弈(TheBattleofSex)
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(PayoffMatrix)如下：
Strategy&Payoffs
OtherExamples
Coordinationgames
SmithandJonesaretryingtodecidewhethertodesignthecomputerstheyselltouselargeorsmallfloppydisks
Bothplayerswillsellmorecomputersiftheirdiskdrivesarecompatible.
Strategies:“Large”or“Small”
Payoffsareasfollows.
Strategy&Payoffs
OtherExamples
Coordinationgames:payoffmatrix
DominantStrategies(支配策略)
Wesayaplayerhasadominantstrategyifitisthestrictlybestresponsetoanystrategiestheotherplayersmightpick.
Intheanalysisofanygamethefirststepistodetermineifanyplayerhasadominantstrategy.
Ifsuchastrategyexiststhentheoutcomeofthegameshouldbeeasilydeterminedsincetheplayerwillusethedominantstrategyandotherplayerswillsubsequentlyadopttheirbestresponses.
Examples:
DoesthePrisoner’sDilemmahaveanydominantstrategy?
HowabouttheCoordinationGame?
DominatedStrategies(被支配策略)
Adominatedstrategyisanalternativethatyieldsalowerpayoffthansomeotherstrategynomatterwhattheotherplayersinthegamedo.
Arationalplayerwillneveruseadominatedstrategyintheactualactionofgameplaying.Henceitcanbeeliminated.
Itisclearthatiftheexistenceofadominantstrategyimpliesthatallotherchoicesareinfactthedominatedstrategies.
Butitispossiblethattherearedominatedstrategieswhilethereisnodominantstrategy
Application:IterativeEliminations
Example
NashEquilibrium(纳什均衡)
Eventhoughusingadominantstrategyoradominatedstrategyisapowerfulsimplewayof“solving”agamethiskindofgameisusuallyanexceptioninsteadofanorm.
Wemusthaveagenericmethodoffindingthesolution(s)ofagame.
SolutionConcepts
NashEquilibriumistheveryfirstsolutionconceptfornon-cooperativegames.
NashEquilibrium(纳什均衡)
EssenceofNashEquilibrium
ANashEquilibriumisdefinedasasetofstrategiessuchthatnonoftheparticipantsinthegamecanimprovetheirpayoffgiventhestrategiesoftheotherparticipants.
NoonehasastrictlyincentivetodeviatefromthestrategiesinaNashEquilibrium.
NashEquilibrium(纳什均衡)
Example
Considerthefollowinggame.Isthereanydominantordominatedstrategy?
NashEquilibrium(纳什均衡)
ProblemofNashEquilibrium:
Multiplesolutions!
Examples:
BattleofSex
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