Policy and Complex Systems
a production decision x i and a decision on whether to adopt an abatement technology
a i
, ( ∂PE i
( x i , a i
))/( ∂x i )> 0 , ( ∂PE i
( x i , a i
))/( ∂a i )< 0 , indicating lower production and the adoption of the technology are associated with lower private earnings through PEi ( x i
, a i
). The environmental damage generated by each farm is Di ( x i
, a i )= αβ i
x i
a i
+ β i
x i
( 1-a i ), where ( ∂PE i
( x i , a i
))/( ∂x i )> 0 , ( ∂PE i
( x i , a i
))/( ∂a i )< 0 , and β i depends on the location of the farm relative to the sensor and α denotes the effect of the technology . We assume that the total environmental damage is TD = ∑ 1N
D i
( x i , a i
). Without any regulation , a profit-maximizing farm will produce at their capacity level and not adopt the technology . The social planner ’ s problem is to maximize social benefits ( denoted as SP ), where SP = ∑ i = 1N
PE i
( x i , a i
) -∑ i = 1N
D i
( x i , a i
). Suppose the regulator hopes to achieve a pollution standard D and imposes a tax / subsidy policy , where the tax / subsidy equals to the environmental damage minus the target level of pollution , t ( TD )= . Following the literature , suppose PE i
( x i , a i
) takes a quadratic form γ 0 - γ 1
( γ 2i - x i
) 2 -τγ 2i
a i
, where τγ 2i
a i takes into account whether the firm adopted the technology . Now the individual payoff function under the tax / subsidy scheme becomes : π i
= PE i
( x i
, a i )-
. We find the Nash strategy by backward induction . Consider firm i , given the pollution level of others in the group D -i
, its profit function from producing x i and adopting the technology is :
Treatments
We consider two dimensions of treatments . On the within-subject level , we varied whether the tax / subsidy policy is in place and the complexity of heterogeneity that is in the experiment . For each of the policy treatment , we conducted four heterogeneity treatments , namely ,
1 . A homogeneous treatment where the locational impact on water quality and size of each farm is the same ( Homo );
2 . A first heterogeneous treatment where the locational impact on water quality vary , but the size of each farm is the same ( Hetero1 );
3 . A second heterogeneous treatment where the size of the farms vary , but locational impact on water quality is the same ( Hetero2 );
4 . A third heterogeneous treatment where both size and locational impact on water quality of farms vary ( Hetero3 ).
To control for potential order effects , we randomly varied the order of the within-subject treatments that are presented . On the between-subject level , we provided participants with three information treatments . No Info serves as the baseline . In the Info1 treatment , we provide testimonial information on what production and technology adoption decisions people “ like them ” have made in the past . The information comes from the “ no information ” treatments . We find true decisions participants made that are closest to the Nash optimal strategies conditioning on their size and location . Therefore , this information differs by the location and the size of the firm and approximates the actual Nash optimal strategies . This resembles some policy recommendation on what people should consider doing based on their location and size . In
169