Collusion between the government and the enterprise in pollution management

Transcription

1 JOURNAL OF SYSTEMS ENGINEERING Vol.30 No.5 Oct , (1., ;., :. Stackelberg,.,,,. : ; Stackelberg ; ; ; : F4 : A : ( doi: /j.cnki.jse Collusion between the government and the enterprise in pollution management Jiang Danlu 1, Cao Guohua (1. School of Business Administration, Chongqing University of Science & Technology, Chongqing , China;. School of Economics and Business Administration, Chongqing University, Chongqing , China Abstract: By the method of stocahastic differential game, this paper studies pollution reduction decision problems of the local government under the influence of river basin ecological compensation mechanism. Through the analysis of the Nash equilibrium of a Stackelberg game and a cooperation game between the upstream area local government and the enterprise, it is found that the collusion phenomenon is a kind of Nash equilibrium. Because the collusion phenomenon can seriously impact the local pollution control efficiency, the intrinsic reasons of collusion are analyzed. The result shows that such reasons lie in information asymmetry and benefit difference. Finally, some policy suggestions are put forward to overcome this collusion problem. Key words: stochastic differential game; Stackelberg game; cooperation game; government and enterprise collusion; river basin eco-compensation 1,.,,, [1].,, : ; : : (ck013136; (NCET

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3 ,,,. ; 5,,, [14].,,,,..,,,. x(t t, x(t. x(t, ( dx(t = αq (t β (u(t + I (t(x(t 1 δx(t dt + σ (x(tdz (t, x(t 0 = x 0, (1 α, u(t I(t, β, βu(t(x(t 1 βi(t(x(t 1, u(t I(t,, x(t,. δ. σ (x(t = σx(t,σx(tdz(t(z Wiener..3. t, p(t = a bq(t, p(t t,q(t t. a b. q(t [0,Q,Q,. a bq(t < 0, p(t = 0. t π(t = (a bq(tq(t c(q(t v(tq(t d(i(t, c, ; v(t t,. d,d > 0, d(i(t I(t. q(t I(t,,., 1 [ T ( E t0 (a bq(t q(t c(q(t v(tq(t d(i(t ] e r(t t0 dt k (x(t Ae r(t t0, ( t 0 A,,,,,. k (x(t A,k, k > 0, k < 0..4.,,,,,, (,. t v(tq(t d(u(t hx(t, d(u(t u(t, h,.

4 5 : 587 [ t 0,T ],.,. [ T ( ] E t0 v(tq(t d(u(t hx(t e r(t t0 dt g (x(t A e r(t t0. (3 t 0,,,,, [3]. (3, g. T,,, A,,,. g,.,, ,.,, (leader, (follower, (Stackelberg.,.,.,.,, ;,.,,. : v(t, q (t, I (t,., v (t, u (t,.,.,. T, :, (.,. v(t, v(t, q (t, I (t., q(t, I(t. V 1 (t,x, (4,q (t,i (t (, V 1 t (t,x 1 (( σ x V 1 xx (t,x = Max (a bq(tq(t c(q(t v(tq(t d(i(t q(,i( e r(t t0 + V 1 x (αq(t β (u(t + I(t x 1 δx, (4 V 1 (T,x = k(x Ae r(t t0. q (t,i (t, q (t,i (t, v (t,u (t. v(t, u(t. V (t,x (5,v (t,u (t (3, V t (t,x 1 (( σ x V xx (t,x = Max v(tq(t d(u(t hx(t e r(t t0 + u(,v( (αq(t β (u(t + I(tx 1 δx, (5 V (T,x = g(x Ae r(t t0. V x

5 [1], Bellman q (t, I (t,v (t,u (t, (4 (5,. 1 (i = 1, i = V i (t,x = (A i(tx(t + C i(t e r(t t0, (6 (6 ( Ȧ 1 (t = β β 4d A 1(t + d A (t + δ + r A 1 (t,a 1 (T = k ( Ȧ (t = β β 4d A (t + d A 1(t + δ + r A (t + h,a (T = g, (7., α (a + α (A 1 (t + A (t E[x(t] = ( β + 4(b + c d (A 1(t + A (t δ x 0 + (8 (11, : q (t = a + α(a 1(t + A (t, (8 4(b + c I (t = β A d (x(t1 1 (t, (9 v (t = a + α (A 1(t A (t, (10 u (t = β A d (x(t1 (t, (11 (( α (a + α(a 1 (t + A (t ( β β 4(b + c d (A exp 1(t + A (t δ d (A 1(t + A (t δ 1 (A 1 (t + A (t, (A 1 (t + A (t, A 1 (t,a (t,,,. 3.,.,,..,,.,.,,.,,., UI, [ T (( E t0 (a bq(tq(t c(q(t d(ui(t hx(t ] e r(t t0 r(t t0 dt (g + k(x(t Ae, (1 t 0 t.

6 5 : 589 dx(t = ( αq (t βui(x(t 1 δx(t dt + σ (x(tdz (t, x(t 0 = x 0 W (t,x (13, q 0 (t UI (t (1, W t (t,x 1 σ x W xx (t,x = Max q(,ui( q 0 (t UI (t (13, (14,. ( (a bq(tq(t c(q(t d(ui(t hx(t e r(t t0 + W x ( αq(t βuix 1 δx, (13 W (T,x = (g + k (x(t Ae r(t t0, (14 W (t,x = (A 0 (tx(t + C 0 (te r(t t0, (15 (0 Ȧ 0 (t = β 4d A 0 (t + (δ + r A 0(t + h, Ċ 0 (t = rc 0 (t (a + αa 0(t, 4(b + c A 0 (T = k g, (16 C 0 (T = (k + ga. q 0(t = a + αa 0(t (b + c, UI (t = β d (x(t 1 A 0, aα + α A 0 (t E[x(t] = aα + α A 0 (t + (b + c (β A 0 (t/(d δ + ( (( aα + α A 0 (t β x 0 + exp aα + α A 0 (t + (b + c (β A 0 (t/(d δ d A 0(t δ t.,,. W 1 (t 0,x, W (t 0,x, W 1 (t 0,x = V 1 (t 0,x V 1 (t 0,x + V (t 0,x W(t 0,x, W (t 0,x = V (t 0,x V 1 (t 0,x + V (t 0,x W(t 0,x. 4,,,,

7 590 30,.,,, t 0 = , :., x (.,., A 1 (t t. τ = T t, A 1 (τ = Ȧ1(t. (7 ( Ȧ 1 (τ = Ȧ1(t = β β 4d A 1 (τ + d A (τ δ r A 1 (τ. τ = 0,,A 1 (τ = k,a (τ = g, A 1 (τ > 0, A 1 (τ τ (0,T. A 1 (τ = 0,Ȧ 1 (τ = 0,A 1 (τ, τ = T., t = 0, A 1 (t = 0, t, A 1 (t A (t, t., A ( (t (. 1 h < β β 4d g +g d k + δ + r, [0,T]. A (T = g. ( h β β 4d g + g d k + δ + r, [0,T], t = 0,t = T. h, h (,,,,.,,,.,,,.,,,,. [1], 1. Table 1 1 Parameters value in numerical simulation k g r a b c d h α β δ ,, h = 0.1 h = 4, A (t 1. h = 4, A (t, h = 0.1, A (t, h = 4 A (t , A 0 (t, A 0 (t. 1..

8 t 4 5 t A 0 t 5 : 591, A 0 (t h > h 0 = β 4d (g + k + (g + k(δ + r,a 0 (t,..,,,,.,,,,, g k., h 0 h,. 1,,,. 4 6 h = 4. 0 h = A A 0 A * Fig. 1 Alliance shadow price and government shadow price Fig. Government shadow price under diffrent environmental degradation cost 4. 3,,,,.,,. 6 x Fig. 3 Payments in stacklberg game and cooperation game 4.3,,.,,,

9 q t x t 59 30,.,,. 4, Fig. 4 Outputs comparation in stacklberg game and cooperation game Fig. 5 Pullution comparation in stacklberg game and cooperation game 5 5.1,,.,.,. 1 :,,., h. :,,,. 5., : 1,,,,,,,,,,.,,.,,,,,. 6,,,

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