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1、會計學(xué)1競爭策略競爭策略 博弈論博弈論2個人簡介-中國人民大學(xué)經(jīng)濟(jì)學(xué)院院長助理 副教授 經(jīng)濟(jì)學(xué)博士-2008年北京奧運(yùn)會特許商品調(diào)查委員會首席專家-2008年北京奧運(yùn)會旅游紀(jì)念品調(diào)查研究首席專家-歐美同學(xué)會會員（1998年）-中國寶雞外國語學(xué)院客座教授(1999年)-新加坡華夏學(xué)院學(xué)術(shù)委員會委員(2001年)-歐洲維多利亞大學(xué)客座教授（2002年）-亞洲發(fā)展銀行青年組專家(Young Economist of ADB)（2002年）-清華大學(xué)繼續(xù)教育學(xué)院客座教授（2003年）-吉林電力高級經(jīng)濟(jì)顧問（2002年）-吉林白城市人民政府經(jīng)濟(jì)顧問（2003年）-國聯(lián)股份高級顧問（2003年）-中國人民

2、大學(xué)僑聯(lián)副主席（2004年）-中國井岡山干部學(xué)院兼職教授（2005年）第1頁/共43頁3博弈論和策略行為Game Theory&Strategic Behaviors第2頁/共43頁4Lecture Plan/本講計劃本講計劃n nGame Theory n nStrategy&Payoff Matrix Strategy&Payoff Matrix n nDominant&Dominated Dominant&Dominated Strategies Strategies n nNash EquilibriumNash Equilibriumn nMaximin Strategy&Mixed

3、 Maximin Strategy&Mixed Strategy Strategy n nStrategic Behavior 第3頁/共43頁5Elements of a GameGame has the following elements:PlayersPlayers:who is involved?:who is involved?RulesRules:who moves when?What do:who moves when?What do they know when they move?What they know when they move?What can they do?

4、can they do?Outcomes:Outcomes:for each possible set of for each possible set of actions by the layers,which is the actions by the layers,which is the outcome of the gameoutcome of the gamePayoffsPayoffs:what are the players:what are the players preferences over the possible preferences over the poss

5、ible outcome?outcome?第4頁/共43頁6Strategy&Payoffsn n博弈論把人間一切競爭活動看成是玩策略游戲博弈論把人間一切競爭活動看成是玩策略游戲。這種策略游戲是在一定的游戲規(guī)則之下進(jìn)行這種策略游戲是在一定的游戲規(guī)則之下進(jìn)行n n它的兩個最基本的概念是策略與支付矩陣它的兩個最基本的概念是策略與支付矩陣n n一種策略一種策略(Strategy)(Strategy)表示游戲參與者的一套運(yùn)作計劃表示游戲參與者的一套運(yùn)作計劃和手段。如和手段。如“降價降價15%”15%”就是一種策略就是一種策略n n收益矩陣收益矩陣(Payoff matrix)(Payoff matri

6、x)是表示游戲參與者在各種不是表示游戲參與者在各種不同策略下的利潤額的一套支付表格同策略下的利潤額的一套支付表格n n寡頭壟斷寡頭壟斷，尤其是雙寡頭壟斷競爭，特別適合使，尤其是雙寡頭壟斷競爭，特別適合使用用博弈論研究博弈論研究第5頁/共43頁7Strategy&Payoffsn nPrisoners Dilemma(囚犯兩難)n n兩個嫌犯被捕并受到指控，但除非兩個嫌犯被捕并受到指控，但除非至少一人招供犯罪，警方并無充分至少一人招供犯罪，警方并無充分證據(jù)將其按罪判刑證據(jù)將其按罪判刑n n警方將他們分開審訊（不能溝通），警方將他們分開審訊（不能溝通），并對他們說明不同行動帶來的后果。并對他們說明

7、不同行動帶來的后果。n n如果二人都不坦白，只能判簡單刑事罪，如果二人都不坦白，只能判簡單刑事罪，坐牢坐牢1 1個月個月n n如果二人都坦白，兩人都會定罪，判刑如果二人都坦白，兩人都會定罪，判刑六個月；六個月；n n如果其中一個坦白，另一個不坦白；那如果其中一個坦白，另一個不坦白；那么坦白者馬上釋放（從寬）、不坦白者么坦白者馬上釋放（從寬）、不坦白者將會判刑九個月。將會判刑九個月。n n請問兩個嫌犯該怎么辦？請問兩個嫌犯該怎么辦？第6頁/共43頁8Strategy&Payoffsn nPrisoners Dilemma(囚犯兩難)n n策略策略(Strategy):“(Strategy):“沉

8、默沉默”&“&“招認(rèn)招認(rèn)”n n收益矩陣收益矩陣(Payoff Matrix)(Payoff Matrix)如下：如下：囚犯2沉默招認(rèn)囚犯1沉默-1，-1-9，0招認(rèn)0，-9-6，-6第7頁/共43頁9Strategy&Payoffsn nPrisoners Dilemma(囚犯兩難)n n囚犯兩難的問題在現(xiàn)實(shí)中常常出囚犯兩難的問題在現(xiàn)實(shí)中常常出現(xiàn)?，F(xiàn)。n n比如兩家企業(yè)的價格戰(zhàn)。比如兩家企業(yè)的價格戰(zhàn)。企業(yè)B遵守協(xié)議違約降價企業(yè)A遵守協(xié)議100，10030，130違約降價130，3070，70第8頁/共43頁10Strategy&Payoffsn n性別戰(zhàn)性別戰(zhàn)博弈博弈(The Battle

9、of Sex)(The Battle of Sex)n n一男一女試圖安排一個晚上的娛樂內(nèi)容一男一女試圖安排一個晚上的娛樂內(nèi)容n n選擇選擇（策略）：（策略）：“歌劇歌劇”、“拳擊拳擊”；不過男女；不過男女有別有別n n收益矩陣收益矩陣(Payoff Matrix)(Payoff Matrix)如下：如下：男(The Man)歌劇拳擊女(The Lady)歌劇2，10，0拳擊0，01，2第9頁/共43頁11第10頁/共43頁12Strategy&Payoffsn nOther Examples n nCoordination games Coordination games n nSmith

10、and Jones are trying to Smith and Jones are trying to decide whether to design the decide whether to design the computers they sell to use large or computers they sell to use large or small floppy disks small floppy disks n nBoth players will sell more Both players will sell more computers if their

11、disk drives are computers if their disk drives are patible.n nStrategies:“Large”or“Small”Strategies:“Large”or“Small”n nPayoffs are as follows.Payoffs are as follows.第11頁/共43頁13Strategy&Payoffsn nOther Examples n nCoordination games:payoff Coordination games:payoff matrixmatrixJonesLargeSmallSmithLar

12、ge2,2-1,-1Small-1，-11,1第12頁/共43頁14Dominant Strategies(支配策略支配策略)n nWe say a player has a We say a player has a dominant strategydominant strategy if it is if it is the strictly best response to the strictly best response to anyany strategies the strategies the other players might pick.other players m

13、ight pick.n nIn the analysis of any game,the first step is to In the analysis of any game,the first step is to determine if any player has a dominant strategy.determine if any player has a dominant strategy.n nIf such a strategy exists,then the outcome of the If such a strategy exists,then the outco

14、me of the game should be easily determined,since the player game should be easily determined,since the player will use the dominant strategy and other players will will use the dominant strategy and other players will subsequently adopt their best responses.subsequently adopt their best responses.n

15、nExamples:Examples:n nDoes the Prisoners Dilemma have any dominant Does the Prisoners Dilemma have any dominant strategy?strategy?n nHow about the Coordination Game?How about the Coordination Game?第13頁/共43頁15Dominated Strategies(Dominated Strategies(被支配策略被支配策略被支配策略被支配策略)n nA A dominated strategydomi

16、nated strategy is an alternative that is an alternative that yields a lower payoff than some other strategy,yields a lower payoff than some other strategy,no matter what the other players in the game do.no matter what the other players in the game do.n nA rational player will A rational player will

17、nevernever use a dominated strategy use a dominated strategy in the actual action of game playing.Hence it can be in the actual action of game playing.Hence it can be eliminatedeliminated.n nIt is clear that if the existence of a dominant strategy It is clear that if the existence of a dominant stra

18、tegy implies that all other choices are in fact the implies that all other choices are in fact the dominated strategies.dominated strategies.n nBut it is possible that there are dominated strategies,But it is possible that there are dominated strategies,while there is no dominant strategywhile there

19、 is no dominant strategy第14頁/共43頁16Application:Iterative EliminationsApplication:Iterative Eliminationsn nExample第15頁/共43頁17Nash Equilibrium(納什均衡納什均衡)n nEven 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,

20、instead of a norm.n nWe must have a generic method of finding the solution(s)of a game.n nSolution ConceptsSolution Conceptsn nNash Equilibrium is the very first Nash Equilibrium is the very first solution concept for non-solution concept for non-cooperative games.cooperative games.第16頁/共43頁18Nash E

21、quilibrium(納什均衡納什均衡)n nEssence of Nash Equilibriumn nA A Nash EquilibriumNash Equilibrium is defined as is defined as a set of strategies such that non a set of strategies such that non of the participants in the game of the participants in the game can improve their payoff,given can improve their p

22、ayoff,given the strategies of the other the strategies of the other participants.participants.n nNo one has a strictly incentive to No one has a strictly incentive to deviatedeviate from the strategies in a from the strategies in a Nash Equilibrium.Nash Equilibrium.第17頁/共43頁19Nash Equilibrium(納什均衡納什

23、均衡)n nExample Example n nConsider the following game.Is there any Consider the following game.Is there any dominant or dominated strategy?dominant or dominated strategy?第18頁/共43頁20Nash Equilibrium(納什均衡納什均衡)n nProblem of Nash Equilibrium:n nMultiple solutions!Multiple solutions!n nExamples:Examples:n

24、 nBattle of SexBattle of Sex n nCoordination GameCoordination Game男(The Man)歌劇拳擊女(The Lady)歌劇2，10，0拳擊0，01，2JonesLargeSmallSmithLarge2,2-1,-1Small-1，-11,1第19頁/共43頁21Nash Equilibrium(納什均衡納什均衡)n nProblem of Nash Equilibrium:n nInsensitive to extreme payoffs Insensitive to extreme payoffs(risks)(risks)n

25、 nExample:Dangerous Coordination Example:Dangerous Coordination GameGameJonesLargeSmallSmithLarge2,2-1000,-1Small-1，-11,1In Practice,it is almost sure that Smith wants to“play safe”and never try“l(fā)arge”!第20頁/共43頁22Nash Equilibrium(納什均衡納什均衡)n nProblem of Nash Equilibrium:n nNon-existence of Non-existe

26、nce of pure strategy Nash Equilibriumpure strategy Nash Equilibriumn nExample:Match the PenniesExample:Match the Penniesn nNo dominant strategy,no dominated strategy&no pure No dominant strategy,no dominated strategy&no pure strategy Nash equilibrium as well!strategy Nash equilibrium as well!BHeadTa

27、ilAHead1,-1-1,1Tail-1，11,-1第21頁/共43頁23Nash Equilibrium(納什均衡納什均衡)n nMixed Strategies（混合策略）n nA mixed strategy is a profile that A mixed strategy is a profile that specifies the probability of each specifies the probability of each pure strategy that is to be played.pure strategy that is to be played.

28、n nNash Theorem:Nash Theorem:n nFor any game with finite number of For any game with finite number of pure strategies,there always exists pure strategies,there always exists a Nash Equilibrium in mixed a Nash Equilibrium in mixed strategy form.strategy form.第22頁/共43頁24Nash Equilibrium(納什均衡納什均衡)n nMi

29、xed Strategies Mixed Strategies（混合策略）混合策略）:Examples:Examplesn nCoordination GameCoordination Gamen nJones plays(Large,Small)according to(p,1-p)Jones plays(Large,Small)according to(p,1-p)n nSmiths expected payoffs are:Smiths expected payoffs are:n n“Large”:“Large”:2p+(-1)(1-p)=U2p+(-1)(1-p)=US S(L|(p

30、,1-p)(L|(p,1-p)n n“Small”:(-1)p+1(1-p)=U“Small”:(-1)p+1(1-p)=US S(S|(p,1-p)(S|(p,1-p)n nSmith should be“indifferent”between the two choices Smith should be“indifferent”between the two choices n nU US S(L|(p,1-p)=U(L|(p,1-p)=US S(S|(p,1-p)(S|(p,1-p)p=2/5 p=2/5 n nHence Jones optimal mixed strategy mu

31、st be(0.4,0.6)Hence Jones optimal mixed strategy must be(0.4,0.6)n nExercise:find the optimal mixed strategy for Smith.Exercise:find the optimal mixed strategy for Smith.n nMatching the Pennies Matching the Pennies n nFind the Nash equilibrium in mixed strategies Find the Nash equilibrium in mixed s

32、trategies 第23頁/共43頁25第24頁/共43頁26第25頁/共43頁27Nash Equilibrium(納什均衡納什均衡)n nNash Equilibrium Nash Equilibrium 不一定有效率不一定有效率The Centipede Game(The Centipede Game(蜈蚣蟲游戲蜈蚣蟲游戲):):In this finite game of perfect information,there are two players,In this finite game of perfect information,there are two players,

33、1 and 2.The players each start with 1 dollar in front of them.1 and 2.The players each start with 1 dollar in front of them.They alternate saying stop or continue,starting with player 1.They alternate saying stop or continue,starting with player 1.When a player says continue,1 dollar is taken by a r

34、eferee When a player says continue,1 dollar is taken by a referee from her pile and 2 dollars are put in her opponents pile.As from her pile and 2 dollars are put in her opponents pile.As soon as either player says stop,ply is terminated,and each soon as either player says stop,ply is terminated,and

35、 each player receives the money currently in her pile.Alternatively,player receives the money currently in her pile.Alternatively,play stops if both players piles reach 100 dollars.play stops if both players piles reach 100 dollars.第26頁/共43頁28Player 1Player 2Player 1Player 2Player 1Player 2SCCCCCCSS

36、SSS11032297100999998101100,100第27頁/共43頁29Maxmin Strategies(Maxmin Strategies(最大最小策略最大最小策略最大最小策略最大最小策略)n nWhen each player in the game will select the option that maximizes the minimum possible profit(or other desirable outcome),we say that the decision rule is a maxmin strategy.n nThis may happen in

37、 situations This may happen in situations when the market is highly when the market is highly competitive and decision makers competitive and decision makers are risk averse.are risk averse.n nSo this is a useful case for So this is a useful case for managerial decision making.managerial decision ma

38、king.第28頁/共43頁30 第29頁/共43頁31迄今為止，對市場結(jié)構(gòu)分析都以假定管理決策的中心是謀求最大利益。但是在如壟斷寡頭那樣競爭十分激烈的場合，決策者可能采取一種風(fēng)險厭惡政策，即確保在可能的最壞結(jié)果中得到最好的結(jié)果。也就是每個博弈者將在可能最少的利潤方案中選擇利潤最大的方案。第30頁/共43頁32（續(xù)）Nash 均衡為（3，6）和（6，3）企業(yè)1 最小32企業(yè)2 最小 3 2結(jié)果：雙方都沒有新產(chǎn)品推出 在這個例子中，Nash 不是小中取大解！第31頁/共43頁33Maxmin Strategies(Maxmin Strategies(最大最小策略最大最小策略最大最小策略最大最小策

39、略)n nAnother example:第32頁/共43頁34Sequential Game(Sequential Game(順序性博弈順序性博弈順序性博弈順序性博弈)順序性博弈：先下弈的優(yōu)勢順序性博弈：先下弈的優(yōu)勢 (First-mover Advantage)(First-mover Advantage)迄今為止，我們都隱含假定雙方下弈者都是同時實(shí)施。迄今為止，我們都隱含假定雙方下弈者都是同時實(shí)施。在順序在順序(Sequential game)(Sequential game)中，就是有先有后了。中，就是有先有后了。進(jìn)入新的市場就是一個順序博弈的例子。進(jìn)入新的市場就是一個順序博弈的例子。

40、第33頁/共43頁35第34頁/共43頁36第35頁/共43頁37第36頁/共43頁38第37頁/共43頁39Strategic Behavior:Barriers of EntryStrategic Behavior:Barriers of Entryn nFour traditional barriers to entry(passive)n nEconomies of scale,product Economies of scale,product differentiation,control over scare differentiation,control over scare

41、resources,and legal factors resources,and legal factors n nMarket Entry Decision(Entry Game)Market Entry Decision(Entry Game)(aggressive)(aggressive)n nPresent vs.Future Profits:Entry-Limiting PricingPresent vs.Future Profits:Entry-Limiting Pricingn nMain ideas:Main ideas:n nMotivation:short-run Mon

42、opoly pricing practice earns Motivation:short-run Monopoly pricing practice earns“too much profits”,hence attract new entrants that will eat“too much profits”,hence attract new entrants that will eat up the market share and drive down the prices in the up the market share and drive down the prices i

43、n the long run long run n nEntry-Limit Pricing:need to set a price below the short-Entry-Limit Pricing:need to set a price below the short-run monopoly price(Fig 11-1,p.293)run monopoly price(Fig 11-1,p.293)n nFigure 11-2:profit streams Figure 11-2:profit streams 第38頁/共43頁40Strategic Behavior:Barrie

44、rs of EntryStrategic Behavior:Barriers of Entryn nStiglers Open Oligopoly ModelStiglers Open Oligopoly Modeln nObjective:maximize the present value of profitObjective:maximize the present value of profitn nIn some cases,this may be achieved by setting a In some cases,this may be achieved by setting

45、a price designed to deter entry price designed to deter entry n nOptimal strategy depends on the discount rates used Optimal strategy depends on the discount rates used by the managers to determine the present value of by the managers to determine the present value of profitprofitn nA ComparisonA Co

46、mparisonn nEntry-Limiting Pricing:long-time horizon&a lower Entry-Limiting Pricing:long-time horizon&a lower discount rate discount rate n nOpen Oligopoly Model:short planning horizon&a Open Oligopoly Model:short planning horizon&a bigger discount rate bigger discount rate 第39頁/共43頁41Strategic Behav

47、ior:Barriers of EntryStrategic Behavior:Barriers of Entryn nPrice Retaliation（價格報復(fù)）n nIn contrast with Limit Pricing that In contrast with Limit Pricing that keeps the price low over a long keeps the price low over a long period of time,another strategic period of time,another strategic response to

48、the threat of entry is response to the threat of entry is to retaliate by reducing prices to retaliate by reducing prices when entry actually does occur or when entry actually does occur or it appears imminent.it appears imminent.n nWhen the perceive danger has When the perceive danger has diminishe

49、d,prices can be diminished,prices can be increased to whatever level increased to whatever level management views as management views as appropriate for market conditions.appropriate for market conditions.第40頁/共43頁42Strategic Behavior:Barriers of EntryStrategic Behavior:Barriers of Entryn nEstablish

50、ing Commitment:Capacity Expansion Establishing Commitment:Capacity Expansion（擴(kuò)大生產(chǎn)能力）擴(kuò)大生產(chǎn)能力）n nA strategic response by established firms to prevent A strategic response by established firms to prevent the new entrants from occurring would be to invest in the new entrants from occurring would be to in

51、vest in additional capacity.additional capacity.n nOnce this investment has been made,it becomes a Once this investment has been made,it becomes a sunk cost and places existing firms in a position to sunk cost and places existing firms in a position to expand their production as relatively low cost.

52、The expand their production as relatively low cost.The existence of excess capacity provides a strong signal existence of excess capacity provides a strong signal that the established firms can(and probably will)that the established firms can(and probably will)reduce prices as a strategic response t

53、o entry in their reduce prices as a strategic response to entry in their market.market.第41頁/共43頁43Strategic Behavior:Barriers of EntryStrategic Behavior:Barriers of Entryn nPreemptive Action:Market Saturation(Preemptive Action:Market Saturation(先發(fā)制人：先發(fā)制人：使市場飽和使市場飽和)n nOne entry-deterring strategy fo

54、r the existing firm One entry-deterring strategy for the existing firm would be to disperse its production facilities.By the would be to disperse its production facilities.By the existing firm spreading its plants throughout the existing firm spreading its plants throughout the market area(the analy

55、sis of geographic saturation market area(the analysis of geographic saturation can also be applied to product characteristics)the can also be applied to product characteristics)the opportunity for the new entrant to take advantage of opportunity for the new entrant to take advantage of high transportation costs is greatly reduced.high transportation costs is greatly reduced.n nExample:Example:Brand Proliferation in the Brand Proliferation in the Cereal IndustryCereal Industry第42頁/共43頁