競(jìng)爭(zhēng)策略博弈論-new課件

1、企業(yè)管理中的競(jìng)爭(zhēng)和合作問題董志勇 博士 副教授北京大學(xué)經(jīng)濟(jì)學(xué)院博弈論1個(gè)人簡(jiǎn)介-原中國(guó)人民大學(xué)經(jīng)濟(jì)學(xué)院院長(zhǎng)助理 副教授 經(jīng)濟(jì)學(xué)博士-2008年北京奧運(yùn)會(huì)特許商品委員會(huì)首席專家-中國(guó)旅游紀(jì)念品委員會(huì)首席專家-歐美同學(xué)會(huì)會(huì)員（1998年）-中國(guó)寶雞外國(guó)語(yǔ)學(xué)院客座教授(1999年)-新加坡華夏學(xué)院學(xué)術(shù)委員會(huì)委員(2001年)-歐洲維多利亞大學(xué)客座教授（2002年）-北京應(yīng)用技術(shù)大學(xué)客座教授-吉林電力高級(jí)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(guó)聯(lián)股份高級(jí)顧問（2003年）-中國(guó)人民大學(xué)僑聯(lián)副主席（2004年）-中國(guó)井岡山干部學(xué)院兼職教授（2005年）2博弈論和策略行為Gam

2、e Theory & Strategic Behaviors3智豬博弈石頭、剪刀、布田忌賽馬麻將4Lecture Plan/本講計(jì)劃Game Theory Strategy & Payoff Matrix Dominant & Dominated Strategies Nash EquilibriumMaximin Strategy & Mixed Strategy Strategic Behavior 5Elements of a GameGame has the following elements:Players: who is involved?Rules: who moves whe

3、n? 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 gamePayoffs: what are the players preferences over the possible outcome?6Strategy & Payoffs博弈論把人間一切競(jìng)爭(zhēng)活動(dòng)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)行它的兩個(gè)最基本的概念是策略與支付矩陣一種策略(Strate

4、gy)表示游戲參與者的一套運(yùn)作計(jì)劃和手段。如“降價(jià)15%”就是一種策略收益矩陣(Payoff matrix)是表示游戲參與者在各種不同策略下的利潤(rùn)額的一套支付表格寡頭壟斷，尤其是雙寡頭壟斷競(jìng)爭(zhēng)，特別適合使用博弈論研究7Strategy & PayoffsPrisoners Dilemma(囚犯兩難)兩個(gè)嫌犯被捕并受到指控，但除非至少一人招供犯罪，警方并無充分證據(jù)將其按罪判刑警方將他們分開審訊（不能溝通），并對(duì)他們說明不同行動(dòng)帶來的后果。如果二人都不坦白，只能判簡(jiǎn)單刑事罪，坐牢1個(gè)月如果二人都坦白，兩人都會(huì)定罪，判刑六個(gè)月；如果其中一個(gè)坦白，另一個(gè)不坦白；那么坦白者馬上釋放（從寬）、不坦白者將會(huì)

5、判刑九個(gè)月。請(qǐng)問兩個(gè)嫌犯該怎么辦？8Strategy & PayoffsPrisoners Dilemma(囚犯兩難)策略(Strategy): “沉默” & “招認(rèn)”收益矩陣(Payoff Matrix)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， -69Strategy & PayoffsPrisoners Dilemma(囚犯兩難)囚犯兩難的問題在現(xiàn)實(shí)中常常出現(xiàn)。比如兩家企業(yè)的價(jià)格戰(zhàn)。蘇寧遵守協(xié)議違約降價(jià)國(guó)美遵守協(xié)議100，10030， 130違約降價(jià)130， 3070， 7010Strategy & Payoffs性別戰(zhàn)博弈 (The Battle of S

6、ex)一男一女試圖安排一個(gè)晚上的娛樂內(nèi)容選擇（策略）：“歌劇”、“拳擊”；不過男女有別收益矩陣(Payoff Matrix)如下：男 (The Man)歌劇拳擊女 (The Lady)歌劇2， 10.5，0.5拳擊0，01，21112Strategy & PayoffsOther Examples 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

7、 sell more computers if their disk drives are compatible. Strategies: “Large” or “Small” Payoffs are as follows. 13Strategy & PayoffsOther Examples Coordination games: payoff matrix瓊公司大光驅(qū)小光驅(qū)施密斯公司大光盤2, 2-1, -1小光盤-1，-11, 114Nash Equilibrium (納什均衡)Problem of Nash Equilibrium:Insensitive to extreme payo

8、ffs (risks) Example: Dangerous Coordination Game瓊公司大光驅(qū)小光驅(qū)施密斯公司大光盤2, 2-1000, -1小光盤-1，-11, 1In Practice, it is almost sure that Smith wants to “play safe” and never try “l(fā)arge”!15Nash Equilibrium (納什均衡)Problem of Nash Equilibrium:Non-existence of pure strategy Nash EquilibriumExample: Match the Pennie

9、sNo dominant strategy, no dominated strategy & no pure strategy Nash equilibrium as well! B正面反面A正面1, -1-1, 1反面-1，11, -116Dominant Strategies (支配策略)We say a player has a dominant strategy if it is the strictly best response to any strategies the other players might pick.In the analysis of any game, t

10、he first step is to determine if any player has a dominant strategy. If such a strategy exists, then the outcome of the game should be easily determined, since the player will use the dominant strategy and other players will subsequently adopt their best responses. Examples: Does the Prisoners Dilem

11、ma have any dominant strategy? How about the Coordination Game? 17Dominated 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 actu

12、al 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. But it is possible that there are dominated strategies, while there is no dominant strategy18Application: Iterative Eli

13、minationsExample19Nash Equilibrium (納什均衡)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. Solution ConceptsNash

14、 Equilibrium is the very first solution concept for non-cooperative games. 20Nash Equilibrium (納什均衡)Essence of Nash EquilibriumA 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.N

15、o one has a strictly incentive to deviate from the strategies in a Nash Equilibrium. 21Nash Equilibrium (納什均衡)Example Consider the following game. Is there any dominant or dominated strategy? 22Nash Equilibrium (納什均衡)Problem of Nash Equilibrium: Multiple solutions! Examples: Battle of Sex Coordinati

16、on 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, 123Nash Equilibrium (納什均衡)Mixed Strategies （混合策略）A mixed strategy is a profile that specifies the probability of each pure strategy that is to be played. Nash Theorem: For any game with finite number o

17、f pure strategies, there always exists a Nash Equilibrium in mixed strategy form. 24Nash Equilibrium (納什均衡)Mixed Strategies （混合策略）: ExamplesCoordination GameJones plays (Large, Small) according to (p, 1-p)Smiths expected payoffs are: “Large”: 2p+(-1)(1-p) = US(L |(p, 1-p)“Small”: (-1)p+1(1-p) = US(S

18、 |(p, 1-p) Smith should be “indifferent” between the two choices US(L |(p, 1-p) = US(S |(p, 1-p) p = 2/5 Hence Jones optimal mixed strategy must be (0.4, 0.6)Exercise: find the optimal mixed strategy for Smith.Matching the Pennies Find the Nash equilibrium in mixed strategies 252627Nash Equilibrium

19、(納什均衡)Nash Equilibrium 不一定有效率The Centipede Game (蜈蚣蟲游戲):In this finite game of perfect information, there are two players, 1 and 2. The players each start with 1 dollar in front of them. They alternate saying stop or continue, starting with player 1. When a player says continue, 1 dollar is taken by

20、 a referee from her pile and 2 dollars are put in her opponents pile. As soon as either player says stop, ply is terminated, and each player receives the money currently in her pile. Alternatively, play stops if both players piles reach 100 dollars.28Player 1Player 2Player 1Player 2Player 1Player 2S

21、CCCCCCSSSSS11032297100999998101100,10029Maxmin Strategies (最大最小策略)When 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. This may happen in situations when the market is highly c

22、ompetitive and decision makers are risk averse. So this is a useful case for managerial decision making. 30 31迄今為止，對(duì)市場(chǎng)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(jìng)爭(zhēng)十分激烈的場(chǎng)合，決策者可能采取一種風(fēng)險(xiǎn)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(gè)博弈者將在可能最少的利潤(rùn)方案中選擇利潤(rùn)最大的方案。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(gè)例子中，Nash 不是

23、小中取大解！33Maxmin Strategies (最大最小策略)Another example: 34Sequential Game (順序性博弈)順序性博弈：先下弈的優(yōu)勢(shì) (First-mover Advantage)迄今為止，我們都隱含假定雙方下弈者都是同時(shí)實(shí)施。在順序(Sequential game)中，就是有先有后了。進(jìn)入新的市場(chǎng)就是一個(gè)順序博弈的例子。35博弈論與企業(yè)管理中的權(quán)力游戲者票數(shù)權(quán)力指數(shù)權(quán)力指數(shù)(%)A101233.3B91233.3C71233.3D300E100F100總票數(shù)為31，16票通過36班扎夫權(quán)力指數(shù)（1965年）：把一個(gè)決策者作為“關(guān)鍵加入者”的個(gè)數(shù)稱為

24、“權(quán)力指數(shù)”權(quán)力支持和票數(shù)不是一回事，票數(shù)只是一個(gè)虛數(shù)的指標(biāo)！在設(shè)計(jì)具體的投票制度時(shí)，票數(shù)的分配要考慮權(quán)力支持，合適的選舉制度應(yīng)該是：票數(shù)的安排要使得權(quán)力指數(shù)與人數(shù)成大體一致相同的比例！游戲者票數(shù)權(quán)力指數(shù)權(quán)力指數(shù)(%)A101433.3B91433.3C71433.3D300E100F100cabdea bdfa befa bda bea Bfacda cea cfacacdea cdfa cefa37企業(yè)管理中的權(quán)力票數(shù)權(quán)力指數(shù)權(quán)力指數(shù)(%)A121834.615B91426.923C71426.923D323.846E123.846F123.846總票數(shù)為33，17票通過多給A兩票！看D: BCD AEFD 38聯(lián)盟博弈：三人的財(cái)產(chǎn)分配假定財(cái)產(chǎn)100萬A擁有50的票力B擁有40的票力C擁有10的票力規(guī)則，當(dāng)超過50的票任課了某種方案時(shí)，才能分配，否則三人將一無所得。在這個(gè)例子里，任何人的權(quán)力都不是“決定性”的，也沒有一個(gè)人的權(quán)力為039此時(shí)，財(cái)產(chǎn)分配是按照5：4：1分配嗎？如果是的話，C可以提出這樣的方案：A7，B0，C3。這個(gè)方案AC可以接受，因?yàn)閷?duì)他們是一個(gè)改進(jìn)方案。但是，B也會(huì)向A提出這樣的方案，A8B2C040夏普里值(Sharpley Value)：在各種可能的聯(lián)盟次序下，