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榆滏汤
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5 Microeconomics aims to model economic activity as an interaction of individual economic agents pursuing their private interests ---M-W-G (1995) Game theory strategic interaction 5

6 2/3 n x i TA TA x1 + x xn x = n 100 x 2 x / 3 i 6

7 Game theory strategic interaction 7

8 A B C A B C A 1 B 1 C B 2 C 2 A C 3 A 3 B 8

9 1 (A,B) (X,C) (A,B) (A,C) C A B C

10 1 (A,B) (X,C) (A,C) C; (B,C) B 1 B 3 1 A A B C

11 Microeconomics aims to model economic activity as an interaction of individual economic agents pursuing their private interests ---M-W-G (1995) Game theory strategic interaction 11

12 : X B u(x) ( ) x X x * B x B x * x Max x B u(x) 12

13 Common Knowledge M M M 13

14 M 14

15 AWell Well-known Fable

16 AWell Well-known Fable 16

17 n=2 i i j i=1,2; i j 2 > 1 17

18 n=3 i i j i=1,2,3; 123 i j 18

19 AWell Well-known Fable

20 i 20

21 21

22 Nobel Prize in Economics since John F. Nash Jr., John C. Harsanyi, Reinhard Selten 1996 James A. Mirrlees, William Vickrey 2001 George A. Akerlof, A. Michael Spence, Joseph E. Stiglitz 2005 Robert J. Aumann, Thomas C. Schelling 2007 Leonid Hurwicz, Eric S. Maskin, Roger B. Myerson 22

23 23

24 A Strategic g Game or Game in Strategic Form B (Dominated Strategy) 24

25 A

26 A. 1 2 (d) (c) (s 1, s 2 ) (c,c) c) (c,d), (d,c), (d,d) u 1 (c,c)= -1; u 1 (c,d)= -4; u 1 (d,c)= 0; u 1 (d,d)= -3; u 2 (c,c)= -1; u 2 (c,d)= 0; u 2 (d,c)= -4; u 2 (d,d)= -3; 26

27 G = ( S, u ) = A. ( ) N i i i 1 i=1,2,n I {1,2,N} i s i S i s=(s ( 1, s 2 2,,,s N ) S=S 1 S 2 S N u i (s) : S R i=1,2,n 27

28 I={1,2} S 1 {c d}; { S 2 {c d}; c: Quiet d:fink S S 1 S 2 {(c,c); (c,d); (d,c); (d,d) } u 1 (c,c)= -1; u 1 (c,d)= -4; u 1 (d,c)= 0; u 1 (d,d)= -3; u 2 (c,c)= c)= -1; u 2 (c,d)= 0; u 2 (d,c)= -4; u 2 (d,d)= d)= -3; (d,c) 1 (c,c) 1 (d,d) 1 (c, d) (c,d) 2 (c,c) c) 2 (d,d) d) 2 (d, c) 28

29 Suspect 1 Quiet (c) Fink (d) Suspect 2 Quiet t( (c) Fink (d) -1, -1-4, 0 0, -4-3, -3 29

30 Boxed Pig Game press Small pig wait Big pig press wait (5, 1 ) (4, 4) (9, -1) (0, 0) 30

31 Bach or Stravinsky Bach, Stravinsky Stravinsky. 1 Bach 2 Stravinsky Player 2 Player 1 Bach Stravinsky Bach Stravinsky 2, 1 0, 0 0, 0 1, 2 31

32 the Stag Hunt stag Hunter 2 hare Hunter 1 stag hare (2, 2) (0, 1) (1, 0) (1, 1) 32

33 Player 2 Player 1 Head Tail Head Tail -1, 1 1, -1 1, -1-1, 1 33

34 100 s i, s 1 + s s 1 + s 2 >100, 0 I={1,2} s i [0, 100], i=1,2 s=(s 1, s 2 ) s if s +s 100 = i = 12 0 if +s >100 1, ui () s s1 2 34

35 2/3 I={1,2,,N} x i [0, [, 100], i=1,2,n,, x=(x 1, x 2,,x N ) u ( x) = 100 x 2 x/ 3 i x 1+ x xn x = n i 35

36 : N I i, i=1,2,n U i =(1-t) F i + λ C i λ 0 C i S tf i I i α β F ( ) i = A ρi ki I α > 0, β > 0, α + β < 1 i Fi (1 t) = r kk i N N * k = K = k i i= 1 i= 1 i 36

37 1 u 1 (d,c)= 0 > u 1 (c,c)= -1; u 1 (d,d)= -3 > u 1 (c,d)= -4; 2 u 2 (c, d)= 0 > u 2 (c, c)= -1 u 2 2( (d, d)= ) -3 > u 2 2( (d, c)= ) -4; d, d Suspect 1 Quiet (c) Suspect 2 Fink (d) Quiet (c) -1, -1-4, 0 Fink (d) 0, -4-3, -3 37

38 Dominant strategy {S 1, S 2,..., S n, u 1, u 2,..., u n }, s * i* s -i S -i. s i S i. u i (s i *, s -i ) u i (s i, s -i ) 38

39 (Vickrey ) N N i v i v i (private value) i b b i 39

40 (Vickrey ) SPA(c, r) c r b i (v ) { No} [ r, ) v [0, 1] 0 0 v - z - c if b > z ub ( i, zi, c) = pb ( i)( vi zi) c if bi = zi - c if bi < zi z = Max {b -i } p(b i ) i i i i i Jijun Xia, Spring

41 (Vickrey ) 1 c=0, r=0, b(v)=v z z < v u(b=v)=v-z ) u(b v) ) z > v u(b=v)=0 u(b v) z = v u(b=v)=0 =u(b v) w 2 = v (2) v-z r z v b r v-z v z b Jijun Xia, Spring

42 (Vickrey ) 2 SPA(c=0, r>0) v-z r v if v r bv () = No if v < r z v b v-z v r z b SPA(r>0, c=0) i Jijun Xia, Spring

43 (Vickrey ) 3 SPA(c>0, SPA( 0 r 0) b(v)=v c+r 1 v 0 v 0 0 (v 0 -r) G(v 0 )-c=0 bv () v if v v0 ( r, c) = No if v < v0 ( r, c) Jijun Xia, Spring

44 ( ) ) button auction b i (v ) { No} [ r, ) v [0, 1] c=0, r=0, b(v)=v w E = v (2) =w 2 E[w E ]= E[w 2 ] Jijun Xia, Spring

45 ( ) ) 1 c=0, r=0, b(v)=v z z < v u(b=v)=v-z ) u(b v) ) z > v u(b=v)=0 u(b v) z = v u(b=v)=0 =u(b v) w E = v (2) v-z r z v b r v-z v z b Jijun Xia, Spring

46 u S (p,w)= 4 > u S (p, p)= 1; u S (w,w)= w)= 0 > u S (w,p)= -1; 1 Press wait 2 Press Press press Small pig wait Big pig press wait (5, 1 ) (4, 4) (9,-1) (0, 0) 1 r 46

47 2 u 2 (L,B)= 2 > u 2 (L, T)= 1; u 2 (R,B)= 1 > u 2 (R, T)= 0; Player 2 T M B 0, 1 2, 3 1, 2 Player 1 L R 3, 0 1, 0 0, 1 47

48 {S 1, S 2,..., S n, u 1, u 2,..., u n }, s i S i i s s i s -i S -i. s i u i (s i ', s -i ) < u i (s i, s -i ) Player 1 L R Player 2 T M B 0, 1 2, 3 1, 2 3, 0 1, 0 0, 1 48

49 T 2 T 2 2 T R 1 R Player 2 T M B 0, 1 2, 3 1, 2 Player 1 L R 2 r 3, 0 1, 0 0, 1 1 r 49

50 T 2 T 2 T R 1 R R 1 R B 2 B B : (L, M) Player 2 T M 0, 1 2, 3 1, 2 3, 0 1, 0 0, 1 2 Player 1 L R 2 r B 1 r 3r 50

51 51

52 : (press, wait) ) press Small pig wait Big pig press wait (5, 1 ) (4, 4) (9,-1) (0, 0) 2 r 1 r 52

53 (d, d) ) Suspect 2 Quiet (c) Fink (d) Suspect 1 Quiet (c) -1, -1-4, 0 1 r Fink (d) 0, -4-3, -3 1 r 53

54 2/3 2/3 ui( x) = 100 xi 2 x/ 3 x -i 2/3 200/3 x i = 200/3, 100>x i > 200/3 i, i 54

55 {S 1, S 2,..., S n, u 1, u 2,..., u n }, s i, s i " S i i s i ', s i u i (s i ', s -i ) u i (s i ", s -i ) for all s -i S -i. u i (s i ', s -i ) < u i (s i ", s -i ) for some s -i S -i Player 1 L R Player 2 T M B 0, 1 2, 3 1, 2 3, 1 1, 0 0, 1 55

56 56

57 Player 2 1 L M R Player 1 U 2, 1 1, 1 0, 0 C 1, 2 3, 1 2, 1 D 2, -2 1, -1-1, r 2 r 2 L M R U 2, 1 1, 1 0, 0 3 r 1 r Player 1 C 1, 2 3, 1 2, 1 D 2, -2 1, -1-1,-1 1 r 57

58 Player 2 no solution Bach Stravinsky Player 1 Bach Stravinsky 2, 1 0, 0 0, 0 1, 2 Hunter 2 stag hare Hunter 1 stag hare (2, 2) (0, 1) (1, 0) (1, 1) 58

课堂游戏 ( 一 ) n 纸币拍卖

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