An interprovincial cooperative game model for air pollution control in China

Figures & data

Table 1. Definitions of variables and parameters

Variables and parameters	Definitions	Unit
	Annual air pollutant reduction quantity for province i	10^4 ton
	Annual air pollutant quantity produced by province i	10^4 ton
	Annual air pollutant quantity produced by industry in province i	10^4 ton
	Annual air pollutant emission quota set by the government for province i	10^4 ton
	The transfer cost/benefit for abating the pollutant quantity transferred out/into province i during 1 year	K USD
	Environment cost, including pollution reduction cost and the transfer cost for province i	K USD
EC	Total environment cost for the region	K USD
	Cost of air pollutant reduction for province i	K USD
αi	The lower bound of pollutant reduction capacity for province i	Dimensionless
βi	The upper bound of pollutant reduction capacity for province i	Dimensionless
γi	The multiplier of pollution emission quota assigned to province i	Dimensionless

Figure 1. The Beijing–Tianjin–Hebei region of China.

Table 2. Data for the years 2003–2009

	Beijing			Tianjin			Hebei
Year	Volume of exhaust gas emission (bil m^3) Wi	SO2 reduction quantity (10^4 ton)	Cost of air pollutant reduction (K USD)	Volume of exhaust gas emission (bil m^3) Wi	SO2 reduction quantity (10^4 ton)	Cost of air pollutant reduction (K USD)	Volume of exhaust gas emission (bil m^3) Wi	SO2 reduction quantity (10^4 ton)	Cost of air pollutant reduction (K USD)
2003	300.5	2.4	72,826.5	436.0	4.4	36,462.5	1,576.8	21.2	152,806.3
2004	319.8	3.6	73,846.2	305.8	5.0	70,769.2	2,169.6	51.3	246,153.8
2005	353.2	4.7	87,692.3	460.2	10.8	152,307.7	2,651.8	70.3	363,076.9
2006	464.1	6.8	75,998.9	651.2	17.7	94,743.2	3,925.4	72.3	731,046.5
2007	514.6	12.5	175,505.2	550.6	16.5	14,883.4	4,803.6	133.5	655,525.5
2008	431.6	11.2	116,072.3	600.5	22.1	220,773.4	3,755.8	92.8	819,449.8
2009	440.8	11.3	138,648.8	598.3	25.7	258,830.8	5,077.9	123.8	1171,050.6

Table 3. A comparison of SO₂ reductions between cooperative and noncooperative models for 2009

	SO2 reduction in NCRM (10^4 ton)	Optimal SO2 reduction in CRM (10^4 ton)	SO2 reduction cost in NCRM (K USD)	Optimal SO2 reduction cost in CRM (K USD)
Beijing	11.3	6.9	13,111.11	12,180.95
Tianjin	25.7	17.5	71,904.76	31,893.65
Hebei	123.8	136.4	282,936.51	306,000.00
Total	160.8	160.8	367,952.38	350,074.60

Figure 2. SO₂ pollution reduction quantities for each province (expressed as percentage of the total regional pollutant reduction quantity) under the NCRM and the CRM approaches in 2009.

Table 4. The calculation of benefit allocation to Beijing in 2009

S	Beijing	Beijing, Tianjin	Beijing, Hebei	Beijing, Tianjin, Hebei
V(S)	0	7900	95.24	17877.78
V(S-{Beijing})	0	0	0	17793.65
V(S)-V(S-{Beijing})	0	7900	95.24	84.13
|S|	1	2	2	3
W(|S|)	1/3	1/6	1/6	1/3
W(|S|)[V(S)-V(S-{Beijing})]	0	1316.67	15.87	28.05

Table 5. Pollution reduction benefit allocation (K USD)

	Beijing	Tianjin	Hebei	Total
SO2 reduction cost in NCRM (A)	13,111.11	71,904.76	282,936.51	367,952.38
Benefit allocation by sharply method (B)	1,360.59	10,209.79	6,307.41	17,877.78
SO2 reduction cost in CRM (before benefit allocation) (C)	12,180.95	31,893.65	306,000.00	350,074.60
SO2 reduction cost in CRM (after benefit allocation) (D)=(A)-(B)	11,750.52	61,694.97	276,629.05	350,074.60
Money pay to (receive from) other provinces (E)=(D)-(C)	–430.43	29,801.32	–2,9370.95	0

Table 6. Pollution reduction cost saving in CRM in 2003–2009 (K USD)

	Pollution reduction cost in CRM
Year	Beijing	Tianjin	Hebei	Total	Pollution reduction cost in NCRM	Saving
2003	21,896.17	93,058.73	456,149.42	547,404.34	617,071.74	11.29%
2004	20,117.83	69,294.74	357,650.25	447,062.81	498,009.15	10.23%
2005	3,861.99	13,130.77	146,314.26	187,582.39	201,376.69	6.85%
2006	14,767.43	41,841.05	189,515.33	246,123.81	257,937.34	4.58%
2007	43,600	116,266.67	566,800.00	726,666.67	770,181.95	5.65%
2008	21,817.46	69,815.87	344,715.87	436,349.2	484,240.59	9.89%
2009	11,750.52	61,694.97	276,629.05	350,074.6	367,952.38	4.86%

Table 7. The sensitivity result for CRM (K USD)

		[α, β, γ]	Beijing	Tianjin	Hebei	Total	Saving
Base		[0,4,0.9,1.3]	12,180.95	31,893.65	306,000.00	350,074.60	4.86%
Change α	Reduce to 0.3	[0.3,0.9,1.3]	10,764.60	31,893.65	307,380.95	350,031.75	4.87%
	Increase to 0.5	[0.5,0.9,1.3]	18,247.62	51,450.79	288,666.67	358,365.08	2.61%
	Increase to 0.6	[0.6,0.9,1.3]	1,993.65	33,933.33	317,841.27	353,761.90	0%
Change β	Reduce to 0.8	[0.4,0.8,1.3]	12,180.95	31,893.65	306,000.00	350,074.60	4.86%
	Reduce to 0.7	[0.4,0.7,1.3]	12,180.95	31,893.65	306,000.00	350,074.60	4.86%
	Reduce to 0.6	[0.4,0.6,1.3]	12,180.95	31,893.65	306,000.00	350,074.60	4.86%
Change γ	Reduce to 1.2	[0.4,0.9,1.2]	12,180.95	42,990.48	298,682.54	353,853.97	3.83%
	Increase to 1.4	[0.4,0.9,1.4]	12,180.95	30,638.10	306,920.63	349,746.03	4.95%
	Increase to 1.5	[0.4,0.9,1.5]	12,180.95	30,638.10	306,920.63	349,746.03	4.95%