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6 N W21(ā, α) W12(ā, α) 谢琏造謝璉造

7 β β β β N = 3 β β p 3

23 p q 0 q < p 1

24 a i > 0 i = r i = c b i < 0 ρ 0 < ρ < 1 ρa i + δa i 0 < δ < 1 ρ ρb i 0 pa r (1 p)b r p(ρa r + δa r ) (1 p)ρb r qa c (1 q)b c q(ρa c + δa c ) (1 q)ρb c δ = 1 1+r (1 ρ) r s {0, ρ, 1} s = 1 pa r (1) (1 p)b r (1) s = ρ p[a r (ρ) r a r(1 ρ)] (1 p)b r (ρ) s = 0 0 a r (s) a c (s) b r (s) b c (s) 0 s = 0

25 (1 p)(1 ρ)b r p p(1 ρ δ)a r p A r B r C r A r = (1 ρ)b r (1 ρ)a r δa r + (1 ρ)b r, B r = b r a r + b r, C r = ρb r ρa r + δa r + ρb r. A r B r C r A r > B r > C r A c B c C c p > A r p > B r p > C r

26 0 q < C c p q < p 1 C c < q < A c 0 q < C c C c < q 1 A c < q 1 (p, q) p q 0 q < p 1 p q

27 0 q < C c C c < q < A c Reformer s Belief, p 1 Big Bang Big Bang/ Experiment A r B r Doing Nothing Experiment C r 0 0 C c B c A c 1 Conservative s Belief, q a r = a c = b r = b c = 2 ρ = 0.25 δ = 0.5 A r = A c = 0.75 B r = B c = 0.5 C r = C c = 0.25 p B r q B c A r < p 1 B c < q 1

28 e d d > 0 e > 0 β [0, ] B r < p 1 0 q < B c f(p, q)e f(p, q)d f(p, q) B r < p 1 0 q < B c

29 pa r (1 p)b r p[ρa r + δa r + βf(p, q)e] (1 p) [ρb r + βf(p, q)d] qa c (1 q)b c q[ρa c + δa c βf(p, q)d] (1 q) [ρb c βf(p, q)e] ( ] [ f(p, q) = 1 p br b a r +b r, 1 q 0, c a c +b c ) f(p, q) = 0 D E D = ρb c βe ρa c + δa c + ρb c β(e + d), E = ρb r + βd ρa r + δa r + ρb r + β(e + d). p q

30 B r } ρ(ac+bc)+δa c e+d 0 q < {D, B c } {B r, E} ρ(ac+bc)+δa c, ρb c e+d e ρb c + βe > ρa c + δa c βd ρb c + βe > 0 0 q < {D, B c } B r < p < E 0 q < {D, B c } {B r, E} < p 1 D < q < B c B r < p < E p

31 B r q B c Reformer s Belief, p 1 A r E B r Experiment Doing Nothing Doing Nothing Exp Big Bang Big Bang/ Experiment Exp C r 0 0 C c D B c A c 1 Conservative s Belief, q a r = a c = b r = b c = 2 e = 1 d = 2 ρ = 0.25 δ = 0.50 β = 10 A r = A c = 0.75 B r = B c = 0.5 C r = C c = 0.25 D = 0.34 E = 0.64 β q E < p 1 q p C c < q < D p (C r, B r )

32 N { } q 0 q < {D, C c } β β > ρ(ac +b c )+δa c, ρbc e+d e 0 p < C r 0 q < {D, C c } C r < p < 1 0 q < {D, C c } 0 p < B r 0 q < {D, C c } B r < p < E 0 q < {D, C c }

33 {B r, E} ρ(ac+bc)+δa c, ρb c D e+d e e E e D E e e d d d d e β ρ D ρ E ρ ρ D > B r E < B r

34 e d D E e+d e+d (p, q) e d e d e d β } { β < ρ(ac +b c )+δa c e+d β { β < ρ(ac+bc)+δa c e+d, ρb c e }, ρb c e Reformer s Belief, p 1 A r E B r Doing Nothing Doing Nothing Exp Exp Big Bang/ Experiment Exp Big Bang C r 0 0 C c D B A c c 1 Conservative s Belief, q a r = a c = 1.1 b r = b c = 1 e = 2.4 d = 8 ρ = 0.29 δ = 0.50 β = 0.1 A r = A c = 0.76 B r = B c = 0.48 C r = C c = 0.25 D = 0.42 E = 0.50 β

35 ρ(a c +b c )+δa c e+d < β < ρb c ρb c < β < ρ(a c+b c )+δa c ρb e e e+d c + βe > ρa c + δa c βd ρb c + βe < 0 Reformer s Belief, p 1 A r E B r Doing Nothing Doing Nothing Exp Big Bang Big Bang/ Experiment Exp C r 0 0 C c B c A c 1 Conservative s Belief, q a r = a c = b r = b c = 2 e = 1 d = 5 ρ = 0.25 δ = 0.50 β = 0.4 A r = A c = 0.75 B r = B c = 0.5 C r = C c = 0.25 D = 0.25 E = 0.57 β ρb c + βe < ρa c + δa c βd ρb c + βe > 0 q E > B r B r < p < E

36 Reformer s Belief, p 1 A r Experiment Big Bang/ Experiment Exp Big Bang E B r Doing Nothing Exp Doing Nothing C r 0 0 D C c B c A c 1 Conservative s Belief, q a r = a c = 1.1 b r = b c = 1 e = 1 d = 2.6 ρ = 0.33 δ = 0.50 β = 0.34 A r = A c = 0.78 B r = B c = 0.48 C r = C c = 0.27 D = 0.53 E = 0.51 β a r = a c a b r = b c b p q π p+q 2 p q

37 π p + q 2 > A (1 ρ)b (1 ρ)a δa + (1 ρ)b. π p + q 2 > B b a + b. π p + q 2 > C ρb ρa + δa + ρb. C A C < π < A π < C Reformer s Belief, p 1 Big Bang A r Exp Exp B r C r Doing Nothing Exp 0 0 C B A c c c 1 Conservative s Belief, q a r = a c a = b r = b c b = 2 ρ = 0.25 δ = 0.50 A r = A c A = 0.75 B r = B c B = 0.5 C r = C c C = 0.25

38 p q 1 0 p B q B B = 2C = 2A 1 C < B < A

39 s f(p, q)h(s) f(p, q)g(s) f(p, q)g(s) f(p, q)h(s) s = 1 s = ρ (0, 1) s = 0 f(p, q) f(p, q) = 1 B r 0 d > 0 θ > 0 θ > 0

40 p[a r + βh(1)] (1 p)[b r + βg(1)] p[ρa r + δa r + βh(ρ)] (1 p) [ρb r + βg(ρ)] q[a c βg(1)] (1 q)[b c βh(1)] q[ρa c + δa c βg(ρ)] (1 q) [ρb c βh(ρ)] ( ] [ f(p, q) = 1 p br b a r +b r, 1 q 0, c a c +b c ) D = ρb c βh(ρ) ρa c + δa c + ρb c β(h(ρ) + g(ρ)), E = ρb r + βg(ρ) ρa r + δa r + ρb r + β(h(ρ) + g(ρ)). B r ρ(ac+bc)+δa c, ρb c e h(ρ)+g(ρ) h(ρ) 0 q < {D, B c } {B r, E } < p 1 D < q < B c B r < p < E θ < 1 p q

41 { } β > ρ(ac+bc)+δa c, ρb c h(ρ)+g(ρ) h(ρ) q = 0 θ < 1 h(s) = es θ g(s) = ds θ h(s) g(s)

43 q

65 ā α a 0 > 0 {a 0, ā} w 0 [0, {a 0, ā}] s 0 {a 0, ā} w 0 s 0 ā e 1 [e, ē] e > 0 a 0 a 1 e 1 + (1 d)s 0, d {a 1, ā} 0 w 1 {a 1, ā} w t t {0, 1} B(w t, α) Period 0 Period 1 Wet season: Dry season: Stochastic water Water storage: availability: a0 > 0 s0î[0,min{ a0, a}] Water catchment: Water release: min{ a0, a} w º min{ a, a} -s Benefit: B( w, a) Wet season: Stochastic inflow: e Î[ e, e ] 1 Water availability: a º (1- d) s + e Water catchment: min{ a, a} 1 Dry season: Water release: w º min{ a, a} 1 1 Benefit: B( w, a) 1

66 B(w t, α) B(αw t ) α α [0, 1] B ( ) < 0 B ( ) 0 < B ( ) < B(, )

67 B 1 (w t, α) αb (αw t ) a 0 e 1 W (ā, α) [V (ā, a 0, α)], V (ā, a 0, α) w 0,s 0 {B(w 0, α) + ρ 0 [B(w 1, α)]} s 0 0, w 0 = {a 0, ā} s 0 0, a 1 = (1 d)s 0 + e 1, w 1 = {a 1, ā}, ρ V (ā, a 0, α) {B({a 0, ā} s 0, α) + ρ 0 [B({(1 d)s 0 + e 1, ā}, α)]} s 0 s 0 0, {a 0, ā} s 0 0. α a 0 e 1 W (ā, α) C(ā) ā ā 0 W (ā, α) C(ā). B(w, α) w x w α c = B 1 (w, α) B(x, α) cx a 0 e 0 a 0

68 C ( ) > 0 C ( ) > 0 W 1 (ā, α) = C (ā). ā = ā α W1 (ā, α) w 0 = 0 s 0 = {a 0, ā} w 0 = {a 0, ā} s 0 (0, {a 0, ā}) w 0 = {a 0, ā} > 0 s 0 = 0

69 a 0 V (ā, a 0, α) = B({a 0, ā} s 0, α) + ρ 0 [B({(1 d)s 0 + e 1, ā}, α)] B 1 ({a 0, ā} s 0, α) = ρ(1 d) 0 [ I(1 d)s 0 +e 1 ā B 1 ((1 d)s 0 + e 1, α) ]. s 0 s 0(ā, a 0, α) a 0 V (ā, a 0, α) = B({a 0, ā}, α) + ρ 0 [B({e 1, ā}, α)] B 1 ({a 0, ā}, α) ρ(1 d) 0 [I e1 ā B 1 (e 1, α)], B 1 (0, α) ρ(1 d) 0 [ I(1 d) {a0,ā}+e 1 ā B 1 ((1 d) {a 0, ā} + e 1, α) ] ρ(1 d) 0 [ I(1 d) {a0,ā}+e 1 ā B 1 ((1 d) {a 0, ā} + e 1, α) ] B 1 ({e, ā}, α) < B 1 (0, α)

70 W 1 (ā, α) = [V 1 (ā, a 0, α)] = [I a0 >ā B 1 (ā s 0, α) + ρb 1 (ā, α) [(1 d)s 0 + e 1 > ā a 0 ]] = B 1 (ā s, α) [a 0 > ā] + ρb 1 (ā, α) [ [(1 d)s 0 + e 1 > ā a 0 ]], s s 0(ā, a 0, α) a 0 ā a 0 > ā (1 d)s 0 + e 1 > ā B 1 (ā s, α) B 1 (ā, α) B 1 (ā s, α) B 1 (ā s, α) [a 0 > ā] [ [(1 d)s 0 + e 1 > ā a 0 ]]

71 Marginal-water-benefit channel Full-dam-probability channel Marginal benefit of dam capacities Marginal benefit of the dryseason water release if the dam was full in the former wet season Probability that the dam will be full in wet seasons Storage-release decision (Inverse) Demand for water Water-use efficiency B 1 (ā s, α) B 1 (ā s, α) α B 1 (, α) B 1 (ā s, α) B 1 (ā s, α) α B 1 (ā s, α) s ā s αwb (αw) B (αw) [ [(1 d)s 0 + e 1 > ā a 0 ] ] α

72 s 0 αwb (αw) B (αw) α W 1 (ā, α) ( ) W12(ā, s(ā, α) α) = B 12 (ā s, α) B 11 (ā s, α) [a 0 > ā] α + ρb 12 (ā, α) [ [e 1 > ā (1 d)s 0 a 0 ]] [ ] ρ(1 d)b 1 (ā, α) f e1 (ā (1 d)s 0) s 0(ā, a 0, α), α s 0 s 0(ā, a 0, α) F e1 ( ) f e1 ( ) B 12 (w, α) w [(1 d) s + e, ā] s s 0(ā, a 0, α) a 0 ā

73 B 12 (w, α) = d2 B(αw) dαdw = B (αw) + αwb (αw). B 12 (w, α) 0 αwb (αw) B (αw) 1, dw db 1 = (w,α) B1(w,α) B (αw) w αwb (αw)

74 B 12 (w, α) 0 B 121 (w, α) 0 B 111 (w, α) 0 B 1211 (w, α) 0 w [e, (1 d) s + ē] s s 0(ā, a 0, α) a 0 ā a 0 B 1 ({a 0, ā} s 0, α) = ρ(1 d) 0 [ I(1 d)s 0 +e 1 ā B 1 ((1 d)s 0 + e 1, α) ].

75 s 0 = s 0 $ 50 Marginal benefit of water storage, low α Marginal cost of water storage, low α Marginal benefit of water storage, high α Marginal cost of water storage, high α m s * 0, low α s* 0, high α s 0 /acre foot B 12 (w, α) 0 B 121 (w, α) 0 B 111 (w, α) 0 B 1211 (w, α) 0 s 0 [(1 d)s 0 + e 1 ā a 0 ] a 0 { } B(w, α) = αx (αx) x w, α α = 0.6 α = 0.8 ā = a 0 = 0.8ā d = 0.04 ρ = e 1 = e 1 = [B 1 ((1 d)s 0 + e 1, α)] B 1 ((1 d)s [e 1 ], α) B 1 ({a 0, ā} s 0, α) B 1 ((1 d)s [e 1 ], α).

76 {a 0, ā} s 0 (1 d)s 0 + [e 1 ] B 111 (w, α) 0 B 1211 (w, α) 0 ρ(1 d) B 121 (w, α) 0 B 121 (w, α) = 2αB (αw) + α 2 wb (αw). B 121 (w, α) 0 αwb (αw) B (αw) 2,

78 W12 (ā, α) B 12 (w, α) 0 w [(1 d) s + e, ā] B 12 (w, α) 0 B 121 (w, α) 0 B 111 (w, α) 0 B 1211 (w, α) 0 w [e, (1 d) s + ē]

79 B ( ) = 0 W12 (ā, α) ā ŵ ŵ αŵb (αŵ) B (αŵ) = 1 e ŵ

81 B(x)

82 ā α [0,1] W (ā, α) G(α), W (ā, α) G(α) α W 2 (ā, α) = G (α). α W21(ā, α) W (ā, α) W21(ā, α) W12(ā, α)

84 T +1 T 0 V T (ā, a 0, α) W T (ā, α) [ V T (ā, a 0, α) ], [ T 0 ρ t B(w t, α) {w t} T t=0,{st}t t=0 t=0 s t 0, w t 0, w t + s t = {a t, ā} t 0; ] a 0 = e 0 ; a t = (1 d)s t 1 + e t t 1; w T = {ā, a T }

85 e t [e, ē] e T W 1 (ā, α) = [V 1 (ā, a 0, α)] = B 1 (ā s, α) ρ t [ [a t > ā a 0 ]], t=0 s a t t

86 B(w, α) = (αw) µ = 1.21 B(w, α) = (αw) µ = 0.79 B(w, α) = αx (αx) 2 µ = x { } w, α µ T = e t d = 0.04 ρ = B(w, α) = (αw) B(w, α) = (αw) B(w, α) = αx (αx) 2 2 x { } w, α α = ā = α W 1 (ā, α) ā W 2 (ā, α)

87 α ā 0.17 B 1 (ā s, α) 0.00 t=0 ρt [ [a t > ā a 0 ]] W1 (ā, α) ā (0, 0.01] W2 (ā, α) α (0, 0.01] 0.26 B 1 (ā s, α) 0.00 t=0 ρt [ [a t > ā a 0 ]] W1 (ā, α) ā [ 0.02, 0) W2 (ā, α) α [ 0.01, 0) 3.02 B 1 (ā s, α) 4.13 t=0 ρt [ [a t > ā a 0 ]] W1 (ā, α) ā (0, 0.17] W2 (ā, a 0, α) α (0, 0.03] ā = α = s

88 0.17/( 20.27) dā dα α ā ϵ W 1 α (ā,α) ϵ W 1 (ā,α) ā W11(ā, α)dā + W12(ā, α)dα = C (ā)dā 0 < ( ) dā dα = W 12 (ā,α) W11 (ā,α)+c (ā) < W 12 (ā,α) W11 dā (ā,α) 0 < dα α ā < W 12 (ā,α) W11 (ā,α) α ā = αw 12 (ā,α) V1 (ā,α) ā W 1 11 (ā,α) W1 (ā,α) / ϵ W 1 α (ā,α) ϵ W 1 (ā,α) ā

89 0.79

90 α ā 0.85 B 1 (ā s, α) 0.00 t=0 ρt [ [a t > ā a 0 ]] W1 (ā, α) ā (0, 0.10] W2 (ā, α) α (0, 0.04] 1.29 B 1 (ā s, α) 0.00 t=0 ρt [ [a t > ā a 0 ]] W1 (ā, α) ā [ 0.14, 0) W2 (ā, α) α [ 0.05, 0) 7.07 B 1 (ā s, α) t=0 ρt [ [a t > ā a 0 ]] W1 (ā, α) ā (0, 0.97] W2 (ā, α) α (0, 0.18] ā = α = s

100

101 +a a c d

102 EU EU = EP + α k E IND (A) + β k E INT (A), EP E IND (A) A E INT (A) A α k β k k = I, C I C β C > β I α I > α C q [0, 1] σ [0, 1] 0 EU R = q(a + β k c) + (1 q)( a + β k c) = 2qa + β k c a.

103 q 1 q σ 1 σ 1 a a a a α k 0 0 b b σ k c c c d EU I = σ(2a + β k (e + d)) a + α k b β k d. q k = 1 2 β kc 2a, σ k = a α kb + β k d 2a + β k (c + d), q k q σ k σ q k β k σ k α k q k β k α k σ k α k β k σ k β k σ k β k d a α kb c a α kb a+α k b a+α k 1 b d c α k > 0

104 q = σ σ < 1 α C 0 b > 0 β I 0 β k c + 2qa a σ(2a + β k (c + d)) a β k d + α k b, (1 σ)β k (c + d) + (q σ)2a α k b. q = σ 0 α C 0 σ < 1 0 β I 0 b > 0 b q > σ

105 q γq γ < 1 EU R = q(a + β k c) + (1 q)( a + β k c) = 2qa + β k c a. 2γqa + β k c a 2γqa a β k c 2γqa a > 0 γ

106 2γqa a < 0 2γqa+β k c a > 0 2qa + β k c a, 2qa + β k c a 2γqa a + β k c, 2γqa a 2γqa a, 2γqa a + β k c 0, 0 q q k = 1 β kc 2 2a γ γ 2γqa a + β k c > 0 γ γ > γ kr = q k q 1 β k c γ > γ kr = q k q 1 γ kr q γ kr β k c γ kr 2γqa a + β k c q γq β k c β k c γ 1 2 q 1 γ kr ( 1 ) β kc 2 2a q 1 β k c β k c γ kr 1 2 q 1 γ kr γ kr β k q k β k β C > β I γ kr

107 (2a + β k (c + d))σ a + α k b β k d, (2a + β k (c + d))γσ a + α k b β k d, (2a + β k (c + d))σ a + α k b β k d 2γσa a 2γσa a, 0, (2a + β k (c + d))γσ a + α k b β k d 0 σ σ k = a α kb+β k d 2a+β k (c+d) (2a + β k (c + d))σ a + α k b β k d > 0 γ > γ ki = σ k σ 1 γ ki γ ki α k γ ki β k d c γ ki d c γ γ kr γ ki γ kr γ ki γ kr γ ki q q q i i = 1, 2 q i = q + ϵ i ϵ i N(0, δ 2 ) q ϵ 1 ϵ 2

108 q 1 q 2 q 1 N(q 1, 2δ 2 ) q 1 = q + ϵ 1 (q q 1 ) = q 1 ϵ 1 N(q, δ 2 ) q 2 = q + ϵ 2 (q 2 q 1 ) = q 1 ϵ 1 + ϵ 2 N(q 1, 2δ 2 ). ( x q x P (q 2 x q 1 ) = Φ 2δ 1 ) q 2 q 2 [( ( )) ( ) ] q2 q 1 q2 q 1 1 Φ (2qa a + βc) + Φ (2γqa a + βc) q 1 2δ 2δ ( )) q2 q 1 = 2aq 1 (1 (1 γ)φ a + β k c f(q 1, q 2δ 2 ). [( ( )) ( ) ] q2 q 1 q2 q 1 1 Φ (2γqa a) + Φ 0 q 1 2δ 2δ ( ( )) q2 q 1 = 1 Φ (2γq 1 a a) g(q 1, q 2δ 2 ). f(q 1, q 2 ) g(q 1, q 2 ) > 0 f(q 1, q 2 ) g(q 1, q 2 ) ( ( )) ( )] q2 q 1 q2 q 1 = a [2(1 γ)q 1 1 Φ + (2γq 1 1)Φ + β k c 2δ 2δ q 1 γ < 1 2q 1 γ kr < 1 2 γ γ kr q 2 q 1 f(q 1, q 2 ) g(q 1, q 2 ) = 0 (q, 1 q ) 2 f(q 1, q 2 ) g(q 1, q 2 ) = 0, f(q 2, q 1 ) g(q 2, q 1 ) = 0.

109 q = 1 q = 2 q = 1 β kc 2 a q β k β k = 0 q f(σ 1, σ 2 ) g(σ 1, σ 2 ) ( ( )) ( )] σ2 σ 1 σ2 σ = a [2(1 γ)σ 1 1 Φ 1 + (2γσ 1 1)Φ 2δ 2δ ( )] σ2 σ 1 + β k (c + d)σ 1 [1 (1 γ)φ + α k b β k d. 2δ σ 1 γ < 1 2σ 1

110 σ 2 ) σ 1 f(σ 1, σ 2 ) g(σ 1, σ 2 ) = 0 (σ 1, σ 2) f(σ 1, σ 2) g(σ 1, σ 2) = 0, f(σ 2, σ 1) g(σ 2, σ 1) = 0. a 2α kb+2β k d σ 1 = σ 2 = σ = α 2a+(1+γ)β k (c+d) k β k d (1+γ)a 2α kb(1+γ) (3 γ)a+2α k d c b(1+γ) q σ γ q = 1 β kc σ = a 2α kb+2β k d 2 a 2a+(1+γ)β k (c+d) β k β k 0 q > σ α k 0 σ a 2β kc+2β k (c+d) > a 2β kc 2a+(1+γ)β k (c+d) 2a = q q β k 0 σ = a α kb+β k d 2a+β k (c+d) a α kb 2a σ = a 2α kb+2β k d a 2α kb 2a < a α kb 2a σ < σ a 2α kb 2a+(1+γ)β k (c+d) 2a b

111 α k 0 σ = a α kb + β k d 2a + β k (c + d) a + β kd 2a + β k (c + d) σ = a 2α kb + 2β k d 2a + (1 + γ)β k (c + d) a + 2β k d 2a + (1 + γ)β k (c + d). σ > σ d c d 0 σ < σ q > σ σ > q

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143 2 (pa r (1 p)b r, qa c (1 q)b c ) 1 2 (0, 0) (p[ρa r + δa r + βf(p, q)e] (1 p)[ρb r + βf(p, q)d], q[ρa c + δa c βf(p, q)d] (1 q)[ρb c βf(p, q)e]) (0, 0) (0, 0) ( ] [ f(p, q) = 1 p br b a r +b r, 1 q 0, c a c +b c ) f(p, q) = 0 A r > B r > C r A r ρ(ac+bc)+δac e+d ( b r a r +b r, 1 ] q [ 0, b c a c +b c )

144 p(ρa r + δa r + βe) (1 p) (ρb r + βd) > 0 q(ρa c + δa c βd) (1 q) (ρb c βe) > 0. N N N 2 N = 2 N p i i = 1, 2,..., N N A i B i C i B i < p i 1 0 p i < B i N f(p 1, p 2,..., p N )e (1 ρ)b i A i = (1 ρ)a i δa i +(1 ρ)b i B i = a i +b i C i = p i = B i b i ρb i ρa i +δa i +ρb i

145 f(p 1, p 2,..., p N )d d > 0 e > 0 f(p 1, p 2,..., p N )d f(p 1, p 2,..., p N )e f(p 1, p 2,..., p N ) f(p 1, p 2,..., p N ) = 1 f(p 1, p 2,..., p N ) = 0 β 0 β + N D i E j ϕ {i : B i < p i 1, i = 1, 2,..., N} φ {j : 0 p j < B j, j = 1, 2,..., N} ϕ φ = {1, 2,..., N} ϕ D i = ρb i βe ρa i+δa i+ρb i β(e+d) E j = ρb j+βd ρa j+δa j+ρb j+β(e+d)

146 φ f(p 1, p 2,..., p N ) = 1 β > j φ { ρ(aj +b j )+δa j e+d }, ρb j e 0 p j < {D j, B j } j φ {B i, E i } , ρb j j φ e i ϕ, B i < p i < E i

147 N N = 3 (0, 0, 0) (1, 1, 1) p > q β 3 (0, 0, 1) (0, 1, 0) (1, 0, 0) (0, 1, 1) (1, 0, 1) (1, 1, 0) ϕ φ

148 Experiment Big Bang /Experiment Big Bang Experiment Big Bang /Experiment Big Bang /Experiment Experiment Experiment a i = b i = 2 i = 1, 2, 3 e = 1 d = 2 ρ = 0.25 δ = 0.50 β = 10 A i = 0.75 B i = 0.5 C i = 0.25 D i = 0.34 E i = 0.64 N = 3 β

149 1 0.8 Exp BigBang/Exp BigBang 0.6 Exp BigBang/Exp Player Exp 0.2 Exp Player 1 a 1 = a 2 = b 1 = b 2 = 2 e = 1 d = 2 ρ = 0.25 δ = 0.50 β = 10 A 1 = A 2 = 0.75 B 1 = B 2 = 0.5 C 1 = C 2 = 0.25 D = 0.34 E = 0.64 β 3 (p 3 < 0.34) (0.34 0.64 p 2 > 0.64 p 3 < 0.34

150 Exp Exp 0.8 Exp Exp Player Player Exp 0.2 Exp 0.2 Exp Player 1 p 3 = Player 1 p 3 = BigBang/Exp BigBang/Exp Player Exp Player Exp BigBang/Exp Player 1 p 3 = Player 1 p 3 = Exp BigBang/Exp BigBang/Exp 0.8 Exp BigBang/Exp BigBang Player Exp BigBang/Exp Player BigBang/Exp BigBang/Exp 0.2 Exp Exp 0.2 Exp Exp Player 1 p 3 = Player 1 p 3 = 0.9 a i = b i = 2 i = 1, 2, 3 e = 1 d = 2 ρ = 0.25 δ = 0.50 β = 10 A i = 0.75 B i = 0.5 C i = 0.25 D i = 0.34 E i = 0.64 p 3

151 3 3 p 3 (p 3 > 0.64) 1 2 q[a c βg(1)] (1 q)[b c βh(1)] < 0, q[a c + b c β(g(1) + h(1))] 0 b a c +b c β(h(1)+g(1)) < 0 a c +b c β(h(1)+g(1)) > 0 c βh(1) a c+b c β(g(1)+h(1)) > bc a c+b c 3

152 β < bc h(1) a c +b c β(h(1)+g(1)) < 0 b c βh(1) > 0 { } β > ρ(ac+bc)+δa c, ρb c h(ρ)+g(ρ) h(ρ) { } β ρ(ac +b c )+δa c, ρbc ρbc < β < h(1) h(ρ)+g(ρ) h(ρ) h(ρ) θ < 1 a c + b c β(h(1) + g(1)) < 0 b c βh(1) > 0 a c b c b c < d e b c βh(1) > 0 a c +b c β(h(1)+g(1)) > 0 h(1) b c h(1) a c +b c < β < h(1)+g(1) b c h(1) b c βh(1) a c +b c β(g(1)+h(1)) > a c +b c β ρ(ac +b c )+δa c, ρb c h(ρ)+g(ρ) h(ρ) { } β < bc β > ρ(ac+bc)+δa c, ρbc ρbc < β < bc h(1) h(ρ)+g(ρ) h(ρ) h(ρ) h(1) θ < 1 a c + b c β(h(1) + g(1)) > 0 b c βh(1) > 0 b c βh(1) a c + b c β(g(1) + h(1)) > b c a c + b c a c b c < d e. [ ) b q 0, c a c +b c β 0 a c b c < d a e c + b c β(h(1) + g(1)) < 0 [ b q 0, c a c +b c ) b c βh(1) > 0 q[a c + b c β(g(1) + h(1))] < b c βh(1) q = 0 a c + b c β(h(1) + g(1)) < 0 q[a c + b c β(g(1) [ + h(1))] q q[a c + b c β(g(1) + b h(1))] < b c βh(1) q 0, c a c +b c )

153 b c βh(1) > 0 a c b c < d a e c + b c β(h(1) + g(1)) > 0 [ b q 0, c a c +b c ) a c + b c β(h(1) + g(1)) > 0 q[a c + b c β(g(1) + h(1))] q q = b c a c +b c q[a c +b c β(g(1)+h(1))] = b c a c +b c [a c + b c β(g(1) + h(1))] a c b c < d b c e a c +b c [a c + b c β(g(1) + h(1))] < b c βh(1) [ b q[a c + b c β(g(1) + h(1))] < b c βh(1) q 0, c a c+b c )

154 ( ) B 12 (ā s, α) B 11 (ā s, α) s(ā,α) [a α 0 > ā] [a 0 > ā] = 0 [a 0 > ā] > 0 B 12 (ā s, α) B 11 (ā s, α) s(ā,α) a α 0 a 0 B 12 (ā s, α) B 11 (ā s, α) s(ā,α) α B 12 (ā s, α) 0 = B 12 (ā s, α) a 0 s 0 (ā,a 0,α) α B 1 ({a 0, ā} s 0, α) = ρ(1 d) 0 [ I(1 d)s 0 +e 1 ā B 1 ((1 d)s 0 + e 1, α) ] = ρ(1 d) ā (1 d)s 0 f e1 (x)b 1 ((1 d)s 0 + x, α)dx,

155 B 11 ({a 0, ā} s 0, α)ds 0 + B 12 ({a 0, ā} s 0, α)dα [ = ρ(1 d) 2 0 I(1 d)s 0 +e 1 ā B 11 ((1 d)s 0 + e 1, α) ] ds 0 ρ(1 d) 2 f e1 (ā (1 d)s 0)B 1 (ā, α)ds 0 [ + ρ(1 d) 0 I(1 d)s 0 +e 1 ā B 12 ((1 d)s 0 + e 1, α) ] dα, s 0(ā, a 0, α) α = ( [ B 12 ({a 0, ā} s 0, α) ρ(1 d) 0 I(1 d)s 0 +e 1 ā B 12 ((1 d)s 0 + e 1, α) ]) [B 11 ({a 0, ā} s 0, [ α) + ρ(1 d) 2 0 I(1 d)s 0 +e1 ā B 11 ((1 d)s 0 + e 1, α) ] ρ(1 d) 2 f e1 (ā (1 d)s 0)B 1 (ā, α)] 1. B 12 (ā s 0, α) B 11 (ā s 0, α) s 0(ā, a 0, α) α = B 12 (ā s 0, α) B 11 (ā s 0, α) (B [ 12 (ā s 0, α) ρ(1 d) 0 I(1 d)s 0 +e 1 ā B 12 ((1 d)s 0 + e 1, α) ]) [B 11 (ā s 0, [ α) + ρ(1 d) 2 0 I(1 d)s 0 +e1 ā B 11 ((1 d)s 0 + e 1, α) ] ρ(1 d) 2 f e1 (ā (1 d)s 0)B 1 (ā, α) = [ρ(1 d) 2 B 12 (ā s 0, [ α) 0 I(1 d)s 0 +e1 ā B 11 ((1 d)s 0 + e 1, α) ] ρ(1 d) 2 B 12 (ā s 0, α)f e1 (ā (1 d)s 0)B 1 (ā, α) [ + ρ(1 d)b 11 (ā s 0, α) 0 I(1 d)s 0 +e 1 ā B 12 ((1 d)s 0 + e 1, α) ] ] [B 11 (ā s 0, [ α) + ρ(1 d) 2 0 I(1 d)s 0 +e1 ā B 11 ((1 d)s 0 + e 1, α) ] ] 1 ρ(1 d) 2 f e1 (ā (1 d)s 0)B 1 (ā, α)] 1.

156 s 0(ā, a 0, α) s(ā, α) s a 0 ā B 12 (ā s 0, α) B 11 (ā s 0, α) s 0(ā, a 0, α) α [ = [ρ(1 d) 2 B 12 (ā s, α) 0 I(1 d) s+e1 ā B 11 ((1 d) s + e 1, α) ] ρ(1 d) 2 B 12 (ā s, α)f e1 (ā (1 d) s)b 1 (ā, α) [ + ρ(1 d)b 11 (ā s, α) 0 I(1 d) s+e1 ā B 12 ((1 d) s + e 1, α) ] ] [ [B 11 (ā s, α) + ρ(1 d) 2 0 I(1 d) s+e1 ā B 11 ((1 d) s + e 1, α) ] ρ(1 d) 2 f e1 (ā (1 d) s)b 1 (ā, α)] 1. B 1 (ā s, α) = ρ(1 d) 0 [ I(1 d) s+e1 ā B 1 ((1 d) s + e 1, α) ] B 1 ((1 d) s + e, α), ā s (1 d) s + e B 1 (w, α) > 0 B 1 (w, α) < 0 B ( ) > 0 B ( ) < 0 s(ā, α) B 12 (ā s, α) B 11 (ā s, α) α B 12 (w, α) 0 w [(1 d) s + e, ā] s(ā, α) B 12 (ā s, α) B 11 (ā s, α) α B 12 (w, α) 0 w [(1 d) s + e, ā] 0 0 a 0 B 12 (ā s, α) B 11 (ā s, α) s(ā,α) α B 12 (w, α) w [(1 d) s + e, ā] [a 0 > ā] = 0 B 12 (w, α) w [(1 d) s + e, ā] ρb 12 (ā, α) [ [e 1 > ā (1 d)s 0 a 0 ]] [ [e 1 > ā (1 d)s 0 a 0 ]] = 0 [ [e 1 > ā (1 d)s 0 a 0 ]] > 0 ρb 12 (ā, α) [ [e 1 > ā (1 d)s 0 a 0 ]] 0 B 12 (ā, α) 0 [ [e 1 > ā (1 d)s 0 a 0 ]] = 0 B 12 (ā, α)

157 [ ρ(1 d)b 1 (ā, α) f e1 (ā (1 d)s 0) s 0 (ā,a 0,α) α f e1 (ā (1 d)s 0) a 0 a 0 f e1 (ā (1 d)s 0) s 0 (ā,a 0,α) α a 0 f e1 (ā (1 d)s 0) = 0 a 0 f e1 (ā (1 d)s 0) s 0 (ā,a 0,α) α f e1 (ā (1 d)s 0) > 0 a 0 s 0 (ā,a 0,α) s 0 (ā,a 0,α) B α α 12 (w, α) 0 w [e, (1 d) s + ē] B 12 ({a 0, ā} s 0, α) ρ(1 d) 0 [ I(1 d)s 0 +e 1 ā B 12 ((1 d)s 0 + e 1, α) ] B 12 ({a 0, ā} s 0, α) 0 [B 12 ((1 d)s 0 + e 1, α)]. ] B 12 (w, α) 0 B 1211 (w, α) 0 w [e, (1 d) s + ē] B 12 ({a 0, ā} s 0, α) ρ(1 d) 0 [ I(1 d)s 0 +e 1 ā B 12 ((1 d)s 0 + e 1, α) ] B 12 ({a 0, ā} s 0, α) 0 [B 12 ((1 d)s 0 + e 1, α)] B 12 ({a 0, ā} s 0, α) B 12 ((1 d)s [e 1 ], α). B 111 (w, α) 0 w [e, (1 d) s + ē] B 1 ({a 0, ā} s 0, α) = ρ(1 d) 0 [ I(1 d)s 0 +e 1 ā B 1 ((1 d)s 0 + e 1, α) ] 0 [ I(1 d)s 0 +e 1 ā B 1 ((1 d)s 0 + e 1, α) ] 0 [B 1 ((1 d)s 0 + e 1, α)] B 1 ((1 d)s [e 1 ], α), {a 0, ā} s 0 (1 d)s [e 1 ] B 12 (w, α) 0 B 1211 (w, α) 0 B 111 (w, α) 0 w [e, (1 d) s+ē] B 121 (w, α) 0 [(1 d)s 0+ 0 [e 1 ], {a 0, ā}

158 s 0] B 12 ({a 0, ā} s 0, α) ρ(1 d) 0 [ I(1 d)s 0 +e 1 ā B 12 ((1 d)s 0 + e 1, α) ] B 12 ({a 0, ā} s 0, α) B 12 ((1 d)s [e 1 ], α) 0. {a 0, ā} s 0 (1 d) s + ē (1 d)s [e 1 ] e B 12 (w, α) 0 B 121 (w, α) 0 B 1211 (w, α) 0 B 111 (w, α) 0 w [e, (1 d) s + ē] B 12 ({a 0, ā} s 0, α) ρ(1 d) 0 [ I(1 d)s 0 +e 1 ā B 12 ((1 d)s 0 + e 1, α) ] 0, s 0 (ā,a 0,α) 0 a α 0 B 12 (w, α) 0 B 121 (w, α) 0 B 1211 (w, α) 0 B 111 (w, α) [ 0 w [e, (1 d) s ] + ē] ρ(1 d)b 1 (ā, α) f e1 (ā (1 d)s 0) s 0 (ā,a 0,α) α W 21(ā, α) W 12(ā, α) W21(ā, α) = [V31(ā, a 0, α)] W12(ā, α) = [V13(ā, a 0, α)] V13(ā, a 0, α) V31(ā, a 0, α) a 0 ( ) V13(ā, a 0, α) = I a0 >ā B 12 (ā s 0, α) B 11 (ā s 0, α) s 0(ā, a 0, α) α V + ρb 12 (ā, α) [1 F e1 (ā (1 d)s 0)] + ρ(1 d)b 1 (ā, α)f e1 (ā (1 d)s 0) s 0(ā, a 0, α) α 31(ā, a 0, α) = I a0 >ā B 21 (ā s 0, α) + ρb 21 (ā, α) [1 F e1 (ā (1 d)s 0)] s 0(ā, a 0, α) [ B 21 ({a 0, ā} s ā 0, α) ρ(1 d) 0 [ I(1 d)s 0 +e 1 ā B 21 ((1 d)s 0 + e 1, α) ] ]. V13(ā, a 0, α) V31(ā, a 0, α) V13(ā, a 0, α) = V31(ā, a 0, α) W21(ā, α) = W12(ā, α)

159 ā α ā 0, α 0 W (ā + ā, α + α) pā ā + p α α b, pā C (ā)+d (ā) p α G (α) b ā > 0 α > 0 ā = 0 α = 0 W (ā + ā, α + α) = v pā ā + p α α = b ā > 0 α > 0 ā α ā W 1 (ā+ ā,α+ α) W2 (ā+ ā,α+ α) ā d ( ) W 1 (ā+ ā,α+ α) W2 (ā+ ā,α+ α) d ā = W 11(ā + ā, α + α) W 2 (ā + ā, α + α) } {{ } (+) + W 1 (ā + ā, α + α) W 2 (ā + ā, α + α) 2 }{{} (+) W 12(ā + ā, α + α) > 0. W 12(ā + ā, α + α) > 0 W 12(ā + ā, α + α) 0

160 B 1 (w T 0, α) ρ(1 d) 0 [ V T 1 2 (ā, (1 d)s T 0 + e t+1, α) ] s T 0 = 0 B 1 (w T 0, α) = ρ(1 d) 0 [ V T 1 2 (ā, (1 d)s T 0 + e t+1, α) ] s T 0 > 0 w T 0 > 0 w0 T s T 0 a 0 w0 T + s T 0 {a 0, ā} 0 T 0 T = B 12 (w, α) 0 w [e, ā] B 12 (w, α) 0 B 121 (w, α) 0 B 111 (w, α) 0 B 1211 (w, α) 0 w [e, (1 d)ā + ē] V T (ā, a 0, α) s 0 { B({a0, ā} s 0, α) + ρ 0 [ V T 1 (ā, (1 d)s 0 + e 1, α) ]}

161 s 0 0, {a 0, ā} s 0 0, a 0. a 0 V1 T (ā, a 0, α) = I a0 >ā B 1 (ā s T 0, α) B 1 ({a 0, ā} s T 0, α) st 0 (ā, a 0, α) ā [ + ρ 0 V T 1 1 (ā, (1 d)s T 0 + e 1, α) ] [ + ρ(1 d) 0 V T 1 2 (ā, (1 d)s T 0 + e 1, α) ] s T 0 (ā, a 0, α) ā s T 0 = {a 0, ā} B 1 (0, α) ρ(1 d) 0 [ V T 1 2 (ā, (1 d) {a 0, ā} + e 1, α) ] = ρ(1 d) 0 [ I(1 d) {a0,ā}+e 1 ā B 1 (w T 1, α) ], B 1 (0, α) ρ(1 d) 0 [ I(1 d) {a0,ā}+e 1 ā B 1 (w T 1, α) ] ā B 1 (ā, α) + ρ 0 [ V T 1 1 (ā, e 1, α) ]. s T 0 (0, {a 0, ā}) B 1 ({a 0, ā} s T 0, α) = ρ(1 d) 0 [ V T 1 2 (ā, (1 d)s T 0 + e 1, α) ], V T 1 (ā, a 0, α) = I a0 >ā B 1 (ā s T 0, α) + ρ 0 [ V T 1 1 (ā, (1 d)s T 0 + e 1, α) ]. s T 0 [0, {a 0, ā}) a 0 V T 1 (ā, a 0, α) = I a0 >ā B 1 (ā s T 0, α) + ρ 0 [ V T 1 1 (ā, (1 d)s T 0 + e 1, α) ] I a0 >ā B 1 (ā s T, α) + ρ 0 [ V T 1 1 (ā, (1 d)s T 0 + e 1, α) ],

162 s T (ā, α) s T V T 1 (ā, a 0, α) = I a0 >ā B 1 (ā s T, α) + ρ 0 [ V T 1 1 (ā, (1 d)s T 0 + e 1, α) ] = I a0 >ā B 1 (ā s T, α) + = B 1 (ā s T, α) I a0 >ā + = B 1 (ā s T, α) I a0 >ā + T [ ρ t 0 Ia t >ā B 1 (ā s T t, α) ] t=1 T t=1 T t=1 W T 1 (ā, α) = [ V T 1 (ā, a 0, α) ] = T t=0 a 0 = e 0 T B 1 (ā s T t, α)ρ t 0 [I a T t >ā ) B 1 (ā s T t, α)ρ (1 t F a T t ā,a 0,α(ā; ā, a 0, α). ] ( B1 (ā s T t, α) ρ t [ [ a T t > ā a 0 ]]), W 1 (ā, α) = [V 1 (ā, a 0, α)] = B 1 (ā s, α) ρ t [ [a t > ā a 0 ]]. t=0 W T 12 (ā, α) = T [ db1 (ā s T t, α) t=0 T t=0 dα ( B 1 (ā s T t, α) ρ t ρ t [ [ a T t > ā a 0 ]] ] [ Fa T t ā,a 0,α(ā; ā, a 0, α) α ]). B 12 (w, α) 0 w [e, ā] db 1(ā s T t,α) db 1 (ā s T t,α) dα dα 0 t {0, 1, 2,..., T } B 12 (w, α) 0 w [e, ā] 0 t {0, 1, 2,..., T } B 12 (w, α) 0 w [e, ā] db 1 (w T t 0 (ā,a 0,α),α) 0 a dα 0 t {0, 1, 2,..., T } B 12 (w, α) 0

163 w [e, ā] db 1(w T t 0 (ā,a 0,α),α) 0 a dα 0 t {0, 1, 2,..., T } t = T db 1(w T t 0 (ā,a 0,α),α) = db 1({a 0,ā} s 0 0 (ā,a 0,α),α) s 0 dα dα 0 (ā, a 0, α) = 0 = B 12 ({a 0, ā}, α) t = T t = T k t = T k 1 db 1(w T t 0 (ā,a 0,α),α) db 1 (w T t 0 (ā,a 0,α),α) dα db 1 ({a 0,ā} s k+1 0 (ā,a 0,α),α) dα dα = s k+1 0 (ā, a 0, α) = 0 s k+1 0 (ā, a 0, α) > 0 s k+1 0 (ā, a 0, α) db 1(w T t 0 (ā,a 0,α),α) dα B 1 ({a 0, ā} s k+1 0 (ā, a 0, α), α) = ρ(1 d) 0 [ V k 2 (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α) ] = ρ(1 d) 0 [ I(1 d)s k+1 0 (ā,a 0,α)+e 1 <ā B 1 (w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α), α) ]. α s k+1 0 (ā, a 0, α) B 12 (w, α) w [e, ā] t = T k α s k+1 0 (ā, a 0, α) B 12 (w, α) w [e, ā] = B 1 ({a 0, ā} db 1 (w T t 0 (ā,a 0,α),α) dα s k+1 0 (ā, a 0, α), α) α B 12 (w, α) w [e, ā] s k+1 0 (ā, a 0, α) = 0 s k+1 0 (ā, a 0, α) > 0 t = T k 1 t {0, 1, 2,..., T } a 0 ā B 12 (w, α) 0 B 121 (w, α) 0 B 111 (w, α) 0 B 1211 (w, α) 0 w [e, (1 d)ā + ē] F a T t ā,a 0,α (ā;ā,a 0,α) 0 α t {0, 1, 2,..., T } B 12 (w, α) 0 B 121 (w, α) 0 B 111 (w, α) 0 B 1211 (w, α) 0 w [e, (1 d)ā + ē] st t 0 (ā,a 0,α) α 0 a 0 t {0, 1, 2,..., T } T = t s T 0 t (ā, a 0, α) = s 0 0 (ā, a 0, α) = 0 t = T k t = T k 1 s k+1 0 (ā, a 0, α) = 0 s k+1 0 (ā, a 0, α) > 0 s k+1 0 (ā, a 0, α)

164 db 1 (w T t 0 (ā,a 0,α),α) dα B 1 ({a 0, ā} s k+1 0 (ā, a 0, α), α) = ρ(1 d) 0 [ V k 2 (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α) ] = ρ(1 d) 0 [ I(1 d)s k+1 0 (ā,a 0,α)+e 1 <ā B 1 (w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α), α) ]. s k+1 0 (ā, a 0, α) α B 12 ({a 0, ā} s k+1 0 (ā, a 0, α), α) [ ρ(1 d) 0 I(1 d)s k+1 0 (ā,a 0,α)+e 1 <ā (B 12 (w k (ā, (1 d)s k+1 0 (ā, a 0, α)+e 1, α), α) B 11 (w k (ā, (1 d)s k+1 0 (ā, a 0, α)+e 1, α), α) sk 0 (ā,(1 d)sk+1 0 (ā,a 0,α)+e 1,α))] α B 12 ({a 0, ā} s k+1 0 (ā, a 0, α), α) ρ(1 d) 0 [ I(1 d)s k+1 0 (ā,a 0,α)+e 1 <ā (B 12 (w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α), α) B 11 (w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α), α) sk 0 (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α) α B 12 ({a 0, ā} s k+1 0 (ā, a 0, α), α) [ ρ(1 d) 0 I(1 d)s k+1 0 (ā,a 0,α)+e 1 <ā B 12(w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α), α) ] [ B 12 ({a 0, ā} s k+1 0 (ā, a 0, α), α) 0 B12 (w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α), α) ] B 12 ({a 0, ā} s k+1 0 (ā, a 0, α), α) B 12 ( 0 [ w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α) ], α) [ B 1 ({a 0, ā} s k+1 0 (ā, a 0, α), α) = ρ(1 d) 0 I(1 d)s k+1 0 (ā,a 0,α)+e 1 <ā B 1 (w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α), α) ] 0 [ B1 (w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α), α) ] )] B 1 ( 0 [ w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α) ], α). {a 0, ā} s k+1 0 (ā, a 0, α) 0 [ w k (ā, (1 d)s k+1 0 (ā, a 0, α)+e 1, α) ]

165 B 12 ({a 0, ā} s k+1 0 (ā, a 0, α), α) [ ρ(1 d) 0 I(1 d)s k+1 0 (ā,a 0,α)+e 1 <ā (B 12 (w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α), α) B 11 (w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α), α) sk 0 (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α) )] α [ B 12 ({a 0, ā} s k+1 0 (ā, a 0, α), α) B 12 ( 0 w k (ā, (1 d)s k+1 0 (ā, a 0, α) + e 1, α) ], α) 0. s k+1 0 (ā, a 0, α) α s k+1 0 (ā, a 0, α) = 0 s k+1 0 (ā, a 0, α) > 0 t = T k 1 t = 0 F a T t ā,a 0,α(ā; ā, a 0, α) = I a0 <ā α t k t = k + 1 a T t (1 d)s T 0 k (ā, a T, α) + e k+1 = (1 d)s T 0 k (ā, (1 d)s T 0 k+1 (ā, a T k = a T k+1 = k 1, α) + e k, α) + e k+1 s0 T k (ā, a 0, α) a 0 α F a T t 0 t = k + 1 α ā,a 0,α (ā;ā,a 0,α) T < T

166 = = =

167 0.79

168 ( ) 1 =

169 谢琏造謝璉造

170 谢琏造謝璉造

171 谢琏造謝璉造

172 谢琏造謝璉造

173 谢琏造謝璉造

Synchronous Machine Modeling

Synchronous Machine Modeling ECE 53 Session ; Page / Fall 07 Synchronous Machine Moeling Reference θ Quarature Axis B C Direct Axis Q G F D A F G Q A D C B Transient Moel for a Synchronous Machine Generator Convention ECE 53 Session