博弈论 复旦大学 王永钦PPT学习教案

1、会计学1博弈论博弈论 复旦大学复旦大学 王永钦王永钦Fall, 2007, Fudan University 2第1页/共96页Fall, 2007, Fudan University 3第2页/共96页Fall, 2007, Fudan University 4第3页/共96页Fall, 2007, Fudan University 5第4页/共96页Fall, 2007, Fudan University 6-1 , -1-9 , 0 0 , -9-6 , -6Prisoner 1Prisoner 2ConfessMumConfessMum第5页/共96页Fall, 2007, Fudan

2、 University 7第6页/共96页Fall, 2007, Fudan University 8 2 , 1 0 , 0 0 , 0 1 , 2ChrisPatPrize FightOperaPrize FightOpera第7页/共96页Fall, 2007, Fudan University 9-1 , 1 1 , -1 1 , -1-1 , 1Player 1Player 2TailHeadTailHead第8页/共96页Fall, 2007, Fudan University 10A static (or simultaneous-move) game consists of:第

3、9页/共96页Fall, 2007, Fudan University 11第10页/共96页Fall, 2007, Fudan University 12第11页/共96页Fall, 2007, Fudan University 13第12页/共96页Fall, 2007, Fudan University 14Player 2s21s22Player 1s11u1(s11,s21), u2(s11,s21)u1(s11,s22), u2(s11,s22)s12u1(s12,s21), u2(s12,s21)u1(s12,s22), u2(s12,s22)s13u1(s13,s21), u2

4、(s13,s21)u1(s13,s22), u2(s13,s22)第13页/共96页Fall, 2007, Fudan University 15-1 , -1-9 , 0 0 , -9-6 , -6Prisoner 1Prisoner 2ConfessMumConfessMumPlayersStrategiesPayoffs第14页/共96页Fall, 2007, Fudan University 16 2 , 1 0 , 0 0 , 0 1 , 2ChrisPatPrize FightOperaPrize FightOpera第15页/共96页Fall, 2007, Fudan Unive

5、rsity 17-1 , 1 1 , -1 1 , -1-1 , 1Player 1Player 2TailHeadTailHead第16页/共96页Fall, 2007, Fudan University 18第17页/共96页Fall, 2007, Fudan University 19第18页/共96页Fall, 2007, Fudan University 20第19页/共96页Fall, 2007, Fudan University 21-1 , -1-9 , 0 0 , -9-6 , -6Prisoner 1Prisoner 2ConfessMumConfessMumPlayers

6、StrategiesPayoffs第20页/共96页Fall, 2007, Fudan University 22-1 , -1-9 , 0 0 , -9-6 , -6Prisoner 1Prisoner 2ConfessMumConfessMumregardless of other players choicessi” is strictly better than si第21页/共96页Fall, 2007, Fudan University 23PhilipNo AdAdReynoldsNo Ad60 , 6030 , 70Ad70 , 3040 , 40第22页/共96页Fall,

7、2007, Fudan University 24Player 2s21s22Player 1s11u1(s11,s21), u2(s11,s21)u1(s11,s22), u2(s11,s22)s12u1(s12,s21), u2(s12,s21)u1(s12,s22), u2(s12,s22)s13u1(s13,s21), u2(s13,s21)u1(s13,s22), u2(s13,s22)第23页/共96页Fall, 2007, Fudan University 25 1 , 1 2 , 0 0 , 2 2 , 2Player 1Player 2RUBLregardless of ot

8、her players choicessi” is at least as good as si第24页/共96页Fall, 2007, Fudan University 26第25页/共96页Fall, 2007, Fudan University 27第26页/共96页Fall, 2007, Fudan University 28 1 , 0 1 , 2 0 , 1 0 , 3 0 , 1 2 , 0Player 1Player 2MiddleUpDownLeft 1 , 0 1 , 2 0 , 3 0 , 1Player 1Player 2MiddleUpDownLeftRight第27

9、页/共96页Fall, 2007, Fudan University 29第28页/共96页Fall, 2007, Fudan University 30Bar 2$2$4$5Bar 1$210 , 1014 , 1214 , 15$412 , 1420 , 2028 , 15$515 , 1415 , 2825 , 25Payoffs are in thousands of dollarsBar 2$4$5Bar 1$420 , 2028 , 15$515 , 2825 , 25第29页/共96页Fall, 2007, Fudan University 31第30页/共96页Fall, 20

10、07, Fudan University 32第31页/共96页Fall, 2007, Fudan University 33第32页/共96页Fall, 2007, Fudan University 34Player 2LCRPlayer 1T0 , 44 , 05 , 3M4 , 00 , 45 , 3B3 , 53 , 56 , 6The combination of strategies (B, R) has the following property:Player 1 CANNOT do better by choosing a strategy different from B,

11、 given that player 2 chooses R.Player 2 CANNOT do better by choosing a strategy different from R, given that player 1 chooses B.第33页/共96页Fall, 2007, Fudan University 35Player 2LCRPlayer 1T0 , 44 , 03 , 3M4 , 00 , 43 , 3B3 , 33 , 33.5 , 3.6The combination of strategies (B, R) has the following proper

12、ty:Player 1 CANNOT do better by choosing a strategy different from B, given that player 2 chooses R.Player 2 CANNOT do better by choosing a strategy different from R, given that player 1 chooses B.第34页/共96页Fall, 2007, Fudan University 36第35页/共96页Fall, 2007, Fudan University 37Given others choices, p

13、layer i cannot be better-off if she deviates from si* (cf: dominated strategy)Prisoner 2MumConfessPrisoner 1Mum-1 , -1-9 , 0Confess 0 , -9-6 , -6第36页/共96页Fall, 2007, Fudan University 38Player 2s21s22Player 1s11u1(s11,s21), u2(s11,s21)u1(s11,s22), u2(s11,s22)s12u1(s12,s21), u2(s12,s21)u1(s12,s22), u2

14、(s12,s22)s13u1(s13,s21), u2(s13,s21)u1(s13,s22), u2(s13,s22)第37页/共96页Fall, 2007, Fudan University 39 1 , 0 1 , 2 0 , 1 0 , 3 0 , 1 2 , 0Player 1Player 2MiddleUpDownLeft 1 , 0 1 , 2 0 , 3 0 , 1Player 1Player 2MiddleUpDownLeftRight第38页/共96页Fall, 2007, Fudan University 40Bar 2$2$4$5Bar 1$210 , 1014 , 1

15、214 , 15$412 , 1420 , 2028 , 15$515 , 1415 , 2825 , 25Payoffs are in thousands of dollarsBar 2$4$5Bar 1$420 , 2028 , 15$515 , 2825 , 25第39页/共96页Fall, 2007, Fudan University 41第40页/共96页Fall, 2007, Fudan University 42Player 2LCRPlayer 1T0 , 44 , 03 , 3M4 , 00 , 43 , 3B3 , 33 , 33.5 , 3.6第41页/共96页Fall,

16、 2007, Fudan University 43Bar 2$2$4$5Bar 1$210 , 1014 , 1214 , 15$412 , 1420 , 2028 , 15$515 , 1415 , 2825 , 25Payoffs are in thousands of dollars第42页/共96页Fall, 2007, Fudan University 44Player 2s21s22Player 1s11u1(s11,s21), u2(s11,s21)u1(s11,s22), u2(s11,s22)s12u1(s12,s21), u2(s12,s21)u1(s12,s22), u

17、2(s12,s22)s13u1(s13,s21), u2(s13,s21)u1(s13,s22), u2(s13,s22)第43页/共96页Fall, 2007, Fudan University 45-1 , -1-9 , 0 0 , -9-6 , -6Prisoner 1Prisoner 2ConfessMumConfessMum第44页/共96页Fall, 2007, Fudan University 46Player 2LCRPlayer 1T0 , 44 , 03 , 3M4 , 00 , 43 , 3B3 , 33 , 33.5 , 3.6第45页/共96页Fall, 2007,

18、Fudan University 47Bar 2$2$4$5Bar 1$210 , 1014 , 1214 , 15$412 , 1420 , 2028 , 15$515 , 1415 , 2825 , 25Payoffs are in thousands of dollarsUse best response function to find the Nash equilibrium. 第46页/共96页Fall, 2007, Fudan University 48 2 , 1 0 , 0 0 , 0 1 , 2ChrisPatPrize FightOperaPrize FightOpera

19、第47页/共96页Fall, 2007, Fudan University 49第48页/共96页Fall, 2007, Fudan University 50-1 , 1 1 , -1 1 , -1-1 , 1Player 1Player 2TailHeadTailHead第49页/共96页Fall, 2007, Fudan University 51Player is best responseGiven the strategies chosen by other players第50页/共96页Fall, 2007, Fudan University 52Player is best

20、response to other players strategies is an optimal solution to第51页/共96页Fall, 2007, Fudan University 53第52页/共96页Fall, 2007, Fudan University 54第53页/共96页Fall, 2007, Fudan University 55.nThe cost to firm i of producing quantity qi is Ci(qi)=cqi.第54页/共96页Fall, 2007, Fudan University 56第55页/共96页Fall, 200

21、7, Fudan University 57subject to 0 q2 +第56页/共96页Fall, 2007, Fudan University 58第57页/共96页Fall, 2007, Fudan University 59第58页/共96页Fall, 2007, Fudan University 60第59页/共96页Fall, 2007, Fudan University 61q1q2(a c)/2(a c)/2a ca cNash equilibrium第60页/共96页Fall, 2007, Fudan University 62nquantity qi is Ci(qi

22、)=cqi.第61页/共96页Fall, 2007, Fudan University 63第62页/共96页Fall, 2007, Fudan University 64第63页/共96页Fall, 2007, Fudan University 65第64页/共96页Fall, 2007, Fudan University 66第65页/共96页Fall, 2007, Fudan University 67第66页/共96页Fall, 2007, Fudan University 68Max u2(p1*, p2) = (a p2 + bp1* )(p2 c)subject to 0 p2

23、+第67页/共96页Fall, 2007, Fudan University 69第68页/共96页Fall, 2007, Fudan University 70第69页/共96页Fall, 2007, Fudan University 71第70页/共96页Fall, 2007, Fudan University 72第71页/共96页Fall, 2007, Fudan University 7312212212222122121112111211 if0 if2/ )( if)() ,( if0 if2/ )( if)() ,(pppppacppppacpppupppppacppppacp

24、ppu第72页/共96页Fall, 2007, Fudan University 74111122112212222211221121 if if if : if :)( if if if : if :)(pppppccppppcpppppBpppppccppppcpppppBmmmmmm第73页/共96页Fall, 2007, Fudan University 75p1p2ccpmpmp1p2ccpmpmFirm 1s best response to Firm 2s p2Firm 2s best response to Firm 1s p1第74页/共96页Fall, 2007, Fuda

25、n University 76p1p2ccpmpmNash Equilibrium( c, c )第75页/共96页Fall, 2007, Fudan University 77第76页/共96页Fall, 2007, Fudan University 78第77页/共96页Fall, 2007, Fudan University 79第78页/共96页Fall, 2007, Fudan University 80and c2* solvesMax u2(c1*, c2) = v2(c1*+ c2) + w2 c2subject to 0 c2 w2第79页/共96页Fall, 2007, F

26、udan University 8111112112110 somefor , 1)( :Assume1*)( 01*)( :FOCwrrvccvccv第80页/共96页Fall, 2007, Fudan University 8222222122120 somefor , 1)( :Assume1)*( 01)*( :FOCwrrvccvccv第81页/共96页Fall, 2007, Fudan University 83222211112122110 somefor , 1)( 0 somefor , 1)( :Assume1*)*( 1*)*( wrrvwrrvccvccv第82页/共96页Fall, 2007, Fudan University 84c1c2r2r1r2r1(r1, 0)is a NESuppose that r1