在 NetLogo 中实现时间延迟
Implementing a time lag in NetLogo
我正在尝试为 NetLogo 程序中的性能指标实现时间滞后。这就是我目前正在尝试编写的代码，但我不知道如何在以下公式中实现 (t-1) 因子：
performance(t) = θ × performance(t−1) + (1 − θ) π(t), 0 < θ < 1
现在我是这样离开的：
ask turtles [
set performance theta * performance + (1 - theta) * profit
]
但是我的模型没有给出合法的结果（据我所知，因为这个公式没有考虑时间滞后）。
完整代码：
globals [
N ; Number of firms
price ; Market price
totOutput ; Total production of firms
meanProd ; Average productivity of firms
maxProd ; Maximal productivity of firms
minProd ; Minimal productivity of firms
meanProf-innov ; Average profit of innovators
meanProf-imit ; Average profit of pure imitators
HK ; Concentration index over capital
HQ ; Concentration index over output
; Other parameters
rIn ; Innovative R&D calibration parameter
rIm ; Imitative R&D calibration parameter
aIn ; Innovative R&D calibration parameter
aIm ; Imitative R&D calibration parameter
avgRIn ; NEW -> Represents the Average Rate of R&D Investments by Innovators
avgRIm ; NEW -> Represents the Average Rate of R&D Investments by Imitators
avgCapitalProfit
CapitalProfit
Ae
Ue
Entrynumber
sumCapSq
totCapital
]
breed [Innovators Innovator]
breed [Imitators Imitator]
Innovators-own [
output ; output of the firm
prod ; productivity of the firm
capital ; capital stock of the firm
profit ; gross profit of the firm
rInF ; Each innovator's innovative R&D parameter will be the common rIn
rImF ; Each innovator's imitative R&D parameter will the common rIm
RDIn ; Innovative R&D investment of the firm
RDIM ; Imitative R&D investment of the firm
RInCapital ; NEW -> See below (Formula for new rates) , it is equal to rImF * capital for each innovator
RImCapital ; NEW -> See below (Formula for new rates) , it is equal to rImF * capital for each imitator
prodInnovate ; Productivity discovered thanks to the innovation
prodImitate ; Productivity discovered thanks to the imitation
performance ; NEW -> Performance Indicator
]
Imitators-own [
output ; output of the firm
prod ; productivity of the firm
capital ; capital stock of the firm
profit ; net profit of the firm
rImF ; Each imitator's imitative R&D parameter will be the common rIm
rInF ; Each imitator's innovative R&D parameter will be zero
RDIn ; Innovative R&D investment of the imitator will be 0
RDIM ; Imitative R&D investment of the firm
RInCapital ; NEW -> See below (Formula for new rates) , it is equal to rImF * capital for each innovator
RImCapital ; NEW -> See below (Formula for new rates) , it is equal to rImF * capital for each imitator
prodInnovate ; Productivity discovered thanks to the innovation
prodImitate ; Productivity discovered thanks to the imitation
performance ; NEW -> Performance indicator
]
to setup
clear-all
create-Innovators nbInnov
create-Imitators nbImit
set N nbInnov + nbImit
; Initial capital stock of the firms in order to have zero desired net investment (investment just compensates the depreciation in the initial Cournot equilibrium)
let K0 ( (Dem * A0 * ( N * Eta - 1))/(N * Eta * c) ^ (1 / Eta )) / (N * A0)
; Innovation and imitation parameters
set aIn 0.125
set aIm 1.25
; Innovation and imitation parameters deducted from probabilities
; NEW Investment R&D Rates
set rIn probInnov / ( K0 * aIn)
set rIm probImitate / ( K0 * aIm)
; Setting these parameters at the firm level for each type of firm
ask Innovators [
set prod A0
set capital K0
set rInF random-float 0.004 + 0.005 ; NEW -> Gives a number following a Uniform distribution between 0.005 and 0.009
set rImF random-float 0.0004 + 0.0003 ; NEW -> Gives a number following a Uniform distribution between 0.0003 and 0.0007
]
ask Imitators [
set prod A0
set capital K0
set rInF 0
set rImF random-float 0.0004 + 0.0003 ; NEW -> Gives a number following a Uniform distribution between 0.0003 and 0.0007
]
ask Turtles [
set performance 0
]
reset-ticks
end
to go
if ticks > nbPeriods [stop]
ask turtles [ ; NEW
if capital < Kmin [ die ] ; NEW
if performance < performance-min [ die ] ; NEW
] ; NEW
; NEW
; Eventually, hereafter is the problem of decision that decides wheter a company should enter the industry or not
ask turtles [ ; NEW
if (price * Ae - c > entry-barrier + ue) [ ; NEW
hatch entryNumber [ ; NEW
set performance 0.1 ; NEW
set capital random-normal (sumCapSq / totCapital) 5 ; NEW
set RDIm random-normal (RImCapital / totCapital) 0.01 ; NEW
set RDIn random-normal (RInCapital / totCapital) 0.01 ; NEW
]
]
]
; Fixing the output of each firm
ask turtles [
set output prod * capital
]
;Computing the total output and the intraperiod price
set totOutput sum [output] of turtles
set price invDemand totOutput
;Productivity indicators of the current period
set maxProd max [prod] of turtles
set meanProd mean [prod] of turtles
set minProd min [prod] of turtles
;Concentration indicators of the current period
set totCapital sum [capital] of turtles
set HK (totCapital) ^ 2 / sum [capital ^ 2] of turtles
set HQ (totOutput) ^ 2 / sum [output ^ 2] of turtles
; Moving towards the next period (new productivity and capital stock)
ask turtles [
; Compute net profits
set profit (price * prod - c) * capital - RDIn - RDIm
; NEW Formulas used to calculate new rates
set capitalProfit sum [capital * profit] of turtles ;NEW
set avgCapitalProfit capitalProfit / totCapital ;NEW
set RInCapital sum [(rInF * capital)] of turtles ;NEW
set RImCapital sum [(rImF * capital)] of turtles ;NEW
set avgRIn (RInCapital) / (totCapital) ;NEW
set avgRIm (RImCapital) / (totCapital) ;NEW
; Compute R&D investments
]
ask turtles [
set RDIn rInF * aIn * capital
set RDIm rImF * aIm * capital
; Below are the original commands of the original model, kept this way should an error arise
; OLD set RDIn (rInF * aIn * capital)
; OLD set RDIm (rImF * aIm * capital)
; Compute productivities discovered thanks to innovation and imitation
set prodInnovate innovation
set prodImitate imitation
; Set the new productivity of the firm
set prod max (list prod prodInnovate prodImitate)
; Compute the new capital stock of the firm
set capital investK
]
;profit indicators
set meanProf-innov mean [profit] of Innovators
set meanProf-imit mean [profit] of Imitators
; NEW
; Below we code the performance indicator
ask turtles [
set profit (price * prod - c) * capital - RDIn - RDIm
set performance theta * performance + (1 - theta) * profit
]
tick
; NEW
; The group of commands below represents the entry process of decision
set entryNumber round (entry-trials-rate * N) ; NEW
let prodCapital sum [prod * capital] of turtles ; NEW
let avgA prodCapital / totCapital ; NEW
set Ae random-normal avgA STD ; NEW
set ue random-normal 0 0.1 ; NEW
set sumCapSq sum [capital ^ 2] of turtles ; NEW
; NEW
; Below are is the command representing the exit process of decision
; NEW R&D RATES
; Hereafter we compute the new rates following the satisficing rule à la Simon
ask turtles [
if performance < avgCapitalProfit [
set rInF (1 - beta) * rInF + beta * avgRIn + random-normal 0 sigma-n
set rImF (1 - beta) * rImF + beta * avgRIm + random-normal 0 sigma-m
]
]
end ;INVESTK
; Imitation procedure
to-report imitation
; Draw a number between 0 and 1
let draw random-float 1.
; Compare it with the rescaled value of the R&D
ifelse draw <= RDIm [report maxProd][report 0.]
end
; Innovation procedure
to-report innovation
; Draw a number between 0 and 1
let draw random-float 1.
; Compare it with the rescaled value of the R&D
ifelse draw <= RDIn [report random-normal prod STD][report 0.]
end
;Investment procedure
to-report investK
; Compute the current market share of the firm
let marketShare output / totOutput
; Compute the current margin of the firm
let margin c / (prod * price)
; The target price
let target-price (margin * ETA) / (ETA - marketShare)
; Compute the desired investment of the firm
let desInvest (DEPREC + 1 - ( target-price / price) )
; Compute maximal possible investment (No external financing)
let maxInvest (DEPREC + profit)
; Possible investment
let posInvest min (list desInvest maxInvest)
; Compute the effective investment rate of the firm (it cannot be negative)
let investmentRate max (list posInvest 0.)
report ((1 - DEPREC) + investmentRate) * capital
end
; The constant-elasticity inverse demand function
to-report invDemand [totQuant]
report Dem / (totQuant ^ Eta)
end
您的代码已经执行了 (t-1)。您可以通过执行以下操作来查看：
ask turtles
[ print performance
set performance theta * performance + (1 - theta) * profit
print performance
]
我们可能需要更多代码和错误示例
我正在尝试为 NetLogo 程序中的性能指标实现时间滞后。这就是我目前正在尝试编写的代码，但我不知道如何在以下公式中实现 (t-1) 因子：
performance(t) = θ × performance(t−1) + (1 − θ) π(t), 0 < θ < 1
现在我是这样离开的：
ask turtles [
set performance theta * performance + (1 - theta) * profit
]
但是我的模型没有给出合法的结果（据我所知，因为这个公式没有考虑时间滞后）。
完整代码：
globals [
N ; Number of firms
price ; Market price
totOutput ; Total production of firms
meanProd ; Average productivity of firms
maxProd ; Maximal productivity of firms
minProd ; Minimal productivity of firms
meanProf-innov ; Average profit of innovators
meanProf-imit ; Average profit of pure imitators
HK ; Concentration index over capital
HQ ; Concentration index over output
; Other parameters
rIn ; Innovative R&D calibration parameter
rIm ; Imitative R&D calibration parameter
aIn ; Innovative R&D calibration parameter
aIm ; Imitative R&D calibration parameter
avgRIn ; NEW -> Represents the Average Rate of R&D Investments by Innovators
avgRIm ; NEW -> Represents the Average Rate of R&D Investments by Imitators
avgCapitalProfit
CapitalProfit
Ae
Ue
Entrynumber
sumCapSq
totCapital
]
breed [Innovators Innovator]
breed [Imitators Imitator]
Innovators-own [
output ; output of the firm
prod ; productivity of the firm
capital ; capital stock of the firm
profit ; gross profit of the firm
rInF ; Each innovator's innovative R&D parameter will be the common rIn
rImF ; Each innovator's imitative R&D parameter will the common rIm
RDIn ; Innovative R&D investment of the firm
RDIM ; Imitative R&D investment of the firm
RInCapital ; NEW -> See below (Formula for new rates) , it is equal to rImF * capital for each innovator
RImCapital ; NEW -> See below (Formula for new rates) , it is equal to rImF * capital for each imitator
prodInnovate ; Productivity discovered thanks to the innovation
prodImitate ; Productivity discovered thanks to the imitation
performance ; NEW -> Performance Indicator
]
Imitators-own [
output ; output of the firm
prod ; productivity of the firm
capital ; capital stock of the firm
profit ; net profit of the firm
rImF ; Each imitator's imitative R&D parameter will be the common rIm
rInF ; Each imitator's innovative R&D parameter will be zero
RDIn ; Innovative R&D investment of the imitator will be 0
RDIM ; Imitative R&D investment of the firm
RInCapital ; NEW -> See below (Formula for new rates) , it is equal to rImF * capital for each innovator
RImCapital ; NEW -> See below (Formula for new rates) , it is equal to rImF * capital for each imitator
prodInnovate ; Productivity discovered thanks to the innovation
prodImitate ; Productivity discovered thanks to the imitation
performance ; NEW -> Performance indicator
]
to setup
clear-all
create-Innovators nbInnov
create-Imitators nbImit
set N nbInnov + nbImit
; Initial capital stock of the firms in order to have zero desired net investment (investment just compensates the depreciation in the initial Cournot equilibrium)
let K0 ( (Dem * A0 * ( N * Eta - 1))/(N * Eta * c) ^ (1 / Eta )) / (N * A0)
; Innovation and imitation parameters
set aIn 0.125
set aIm 1.25
; Innovation and imitation parameters deducted from probabilities
; NEW Investment R&D Rates
set rIn probInnov / ( K0 * aIn)
set rIm probImitate / ( K0 * aIm)
; Setting these parameters at the firm level for each type of firm
ask Innovators [
set prod A0
set capital K0
set rInF random-float 0.004 + 0.005 ; NEW -> Gives a number following a Uniform distribution between 0.005 and 0.009
set rImF random-float 0.0004 + 0.0003 ; NEW -> Gives a number following a Uniform distribution between 0.0003 and 0.0007
]
ask Imitators [
set prod A0
set capital K0
set rInF 0
set rImF random-float 0.0004 + 0.0003 ; NEW -> Gives a number following a Uniform distribution between 0.0003 and 0.0007
]
ask Turtles [
set performance 0
]
reset-ticks
end
to go
if ticks > nbPeriods [stop]
ask turtles [ ; NEW
if capital < Kmin [ die ] ; NEW
if performance < performance-min [ die ] ; NEW
] ; NEW
; NEW
; Eventually, hereafter is the problem of decision that decides wheter a company should enter the industry or not
ask turtles [ ; NEW
if (price * Ae - c > entry-barrier + ue) [ ; NEW
hatch entryNumber [ ; NEW
set performance 0.1 ; NEW
set capital random-normal (sumCapSq / totCapital) 5 ; NEW
set RDIm random-normal (RImCapital / totCapital) 0.01 ; NEW
set RDIn random-normal (RInCapital / totCapital) 0.01 ; NEW
]
]
]
; Fixing the output of each firm
ask turtles [
set output prod * capital
]
;Computing the total output and the intraperiod price
set totOutput sum [output] of turtles
set price invDemand totOutput
;Productivity indicators of the current period
set maxProd max [prod] of turtles
set meanProd mean [prod] of turtles
set minProd min [prod] of turtles
;Concentration indicators of the current period
set totCapital sum [capital] of turtles
set HK (totCapital) ^ 2 / sum [capital ^ 2] of turtles
set HQ (totOutput) ^ 2 / sum [output ^ 2] of turtles
; Moving towards the next period (new productivity and capital stock)
ask turtles [
; Compute net profits
set profit (price * prod - c) * capital - RDIn - RDIm
; NEW Formulas used to calculate new rates
set capitalProfit sum [capital * profit] of turtles ;NEW
set avgCapitalProfit capitalProfit / totCapital ;NEW
set RInCapital sum [(rInF * capital)] of turtles ;NEW
set RImCapital sum [(rImF * capital)] of turtles ;NEW
set avgRIn (RInCapital) / (totCapital) ;NEW
set avgRIm (RImCapital) / (totCapital) ;NEW
; Compute R&D investments
]
ask turtles [
set RDIn rInF * aIn * capital
set RDIm rImF * aIm * capital
; Below are the original commands of the original model, kept this way should an error arise
; OLD set RDIn (rInF * aIn * capital)
; OLD set RDIm (rImF * aIm * capital)
; Compute productivities discovered thanks to innovation and imitation
set prodInnovate innovation
set prodImitate imitation
; Set the new productivity of the firm
set prod max (list prod prodInnovate prodImitate)
; Compute the new capital stock of the firm
set capital investK
]
;profit indicators
set meanProf-innov mean [profit] of Innovators
set meanProf-imit mean [profit] of Imitators
; NEW
; Below we code the performance indicator
ask turtles [
set profit (price * prod - c) * capital - RDIn - RDIm
set performance theta * performance + (1 - theta) * profit
]
tick
; NEW
; The group of commands below represents the entry process of decision
set entryNumber round (entry-trials-rate * N) ; NEW
let prodCapital sum [prod * capital] of turtles ; NEW
let avgA prodCapital / totCapital ; NEW
set Ae random-normal avgA STD ; NEW
set ue random-normal 0 0.1 ; NEW
set sumCapSq sum [capital ^ 2] of turtles ; NEW
; NEW
; Below are is the command representing the exit process of decision
; NEW R&D RATES
; Hereafter we compute the new rates following the satisficing rule à la Simon
ask turtles [
if performance < avgCapitalProfit [
set rInF (1 - beta) * rInF + beta * avgRIn + random-normal 0 sigma-n
set rImF (1 - beta) * rImF + beta * avgRIm + random-normal 0 sigma-m
]
]
end ;INVESTK
; Imitation procedure
to-report imitation
; Draw a number between 0 and 1
let draw random-float 1.
; Compare it with the rescaled value of the R&D
ifelse draw <= RDIm [report maxProd][report 0.]
end
; Innovation procedure
to-report innovation
; Draw a number between 0 and 1
let draw random-float 1.
; Compare it with the rescaled value of the R&D
ifelse draw <= RDIn [report random-normal prod STD][report 0.]
end
;Investment procedure
to-report investK
; Compute the current market share of the firm
let marketShare output / totOutput
; Compute the current margin of the firm
let margin c / (prod * price)
; The target price
let target-price (margin * ETA) / (ETA - marketShare)
; Compute the desired investment of the firm
let desInvest (DEPREC + 1 - ( target-price / price) )
; Compute maximal possible investment (No external financing)
let maxInvest (DEPREC + profit)
; Possible investment
let posInvest min (list desInvest maxInvest)
; Compute the effective investment rate of the firm (it cannot be negative)
let investmentRate max (list posInvest 0.)
report ((1 - DEPREC) + investmentRate) * capital
end
; The constant-elasticity inverse demand function
to-report invDemand [totQuant]
report Dem / (totQuant ^ Eta)
end
您的代码已经执行了 (t-1)。您可以通过执行以下操作来查看：
ask turtles
[ print performance
set performance theta * performance + (1 - theta) * profit
print performance
]
我们可能需要更多代码和错误示例