innovative-simulator_simulating-innovation/2_VV/ProbitModel.nlogo
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; Probit Model of diffusion of innovations
; This version (C) Christopher J Watts, 2014
; See Info tab for terms and conditions of use.
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globals [
  price
  num-adopted
  prev-num-adopted
  
  threshold-scalar ; used for displaying information by agents' locations on screen
  adoption-time-scalar
  max-a-threshold
  mean-a-threshold
  median-a-threshold
  min-a-threshold
]

breed [agents agent]

agents-own [
  a-threshold
  tech
  adoption-time
]

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to setup
  clear-all
  reset-ticks
  
  setup-pop
  update-positions
  setup-environment
  ;my-update-plots
  update-histogram
  
end

to setup-pop
  create-agents Population-Size [
    if Threshold-Method = "Normal" [
      set a-threshold random-normal mu sigma
      while [(a-threshold < 0) or (a-threshold > max-pxcor)] [set a-threshold random-normal mu sigma]
    ]
    if Threshold-Method = "Log Normal" [ set a-threshold exp ( random-normal mu_ln sigma_ln )
      while [(a-threshold < 0) or (a-threshold > max-pxcor)] [set a-threshold exp ( random-normal mu_ln sigma_ln )]
    ]
    set tech 0
  ]
  
end

to setup-environment
  if Tech-Dynamics-Method = "Exponential Decay" [
    set price max-pxcor * exp (- Expon-Rate * ticks)
  ]
  if Tech-Dynamics-Method = "Linear Decay" [ 
    set price (linear-slope * max-a-threshold) - ticks
  ]
  
  set num-adopted 0
  set prev-num-adopted 0
end

to update-histogram
  set-current-plot "Thresholds-Histogram"
  set-plot-x-range 0 int (0.5 + max [a-threshold] of agents)
  histogram [a-threshold] of agents
end

to update-positions
  set max-a-threshold (max [a-threshold] of agents)
  set min-a-threshold (min [a-threshold] of agents)
  set mean-a-threshold (mean [a-threshold] of agents)
  set median-a-threshold (median [a-threshold] of agents)
  
  set threshold-scalar 
   (max-pycor - min-pycor)
   / (max-a-threshold
    - min-a-threshold)
   
   set adoption-time-scalar
    (max-pxcor - min-pxcor)
    / ((max [adoption-time] of agents) 
     + 1)
   
  ask agents [
    ifelse tech = 0 [
      setxy new-xcor 0
    ]
    [
      setxy new-xcor new-ycor
    ]
  ]
end

to-report new-ycor
  report (a-threshold - min-a-threshold) * threshold-scalar
end

to-report new-xcor
  report adoption-time * adoption-time-scalar
end

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to go
  
  if Tech-Dynamics-Method = "Exponential Decay" [
    set price max-pxcor * exp (- Expon-Rate * ticks)
  ]
  if Tech-Dynamics-Method = "Linear Decay" [ 
    set price (linear-slope * max-a-threshold) - ticks
  ]
  
  make-decisions
  
  tick
  update-positions
  my-update-plots
  
  if ((num-adopted = Population-Size) and (num-adopted = prev-num-adopted)) [stop]
  
end

to make-decisions
  ask agents [
    if-else price > a-threshold [
      set tech 0
      set color red
    ]
    [ 
      if tech = 0 [
        set adoption-time ticks
        set tech 1
        set color green
      ]
    ]
  ]
  set num-adopted count agents with [tech = 1]
end


to my-update-plots
  set-current-plot "Environment"
  plotxy ticks price
  
  set-current-plot "Adoption"
  plotxy ticks num-adopted
  
  if ticks mod Output-Every-n-Ticks = 0 [
    set-current-plot "Adoption-Rate"
    plotxy ticks ((num-adopted - prev-num-adopted) / Output-Every-n-Ticks)
    set prev-num-adopted num-adopted
  ]
  
end
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Probit Model of Technological Diffusion
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Environment
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Linear only
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TEXTBOX
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Xcor represents Adoption Time
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Ycor represents Adoption Threshold
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MONITOR
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INPUTBOX
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INPUTBOX
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Sigma_LN
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TEXTBOX
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Parameters for Normal distribution:
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TEXTBOX
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Parameters for Log-Normal distribution:
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@#$#@#$#@
## A "PROBIT" OR "RANK" MODEL OF DIFFUSION OF A INNOVATION OR NEW TECHNOLOGY
(C) Christopher Watts, 2014. See below for terms and conditions of use.

Unlike an epidemic model of diffusion, in the Probit model agents are all aware of the innovative technology at the start, but differ in their adoption because of differences in their own attributes. E.g. firms differ in size, and larger firms may learn how to use a technology earlier.

Agents make decisions concerning whether or not to adopt the technology. The technology starts off expensive, but over time its price falls. Each agent has its own threshold value for the technology's cost below which the agent will decide to adopt the technology.

## HOW IT WORKS

Agents are initialised with threshold values sampled at random from a given distribution. Each time tick all agents renew their decision to adopt or not. Each time tick the cost of the technology changes according to some given function.

On the World screen, agents' x-coordinates are used to represent their adoption threshold.

## HOW TO USE IT

Select the methods for threshold setting and technology dynamics, and choose suitable parameters.

## THINGS TO NOTICE

For some combinations of threshold distribution and technology dynamics the number of adopters over time may form an s-shaped curve, and the rate of adoption may form a bell-shaped curve.

## THINGS TO TRY

In particular, try "Normal" for thresholds and "Linear" for technology dynamics. Then try "Log Normal" and "Exponential". (Note: the different methods take different parameters.) What happens if you have log normal thresholds, but linear change?

## EXTENDING THE MODEL

This model considered only one changing factor - price. What about the benefits of adopting technology? i.e. Agents adopt if the technology is profitable - i.e. benefits > costs. What methods should we use for benefits as opposed to costs?

## RELATED MODELS

Compare with diffusion models based on the notion of diffusion as an epidemic, or adoption because of word-of-mouth advertising.

## CREDITS AND REFERENCES

For more on Probit models, and other models of technological diffusion, see chapter 3 in:  
Stoneman, Paul (2002) "The Economics of Technological Diffusion" Blackwell Publishers: Oxford.

Also see:
Davies, S. (1979). "The Diffusion of Process Innovations". Cambridge University Press: Cambridge.

## OUR TERMS AND CONDITIONS OF USE

This program was developed for the book:

Watts, Christopher and Gilbert, Nigel (2014) “Simulating Innovation: Computer- based Tools for Rethinking Innovation”. Cheltenham, UK and Northampton, MA, USA: Edward Elgar.

If you use this program in your work, please cite the book, as well as giving the URL for the website from which you downloaded the program and the date on which you downloaded it. A suitable form of citation for the program is:

Watts, Christopher (2014) “Name-of-file”. Retrieved 31 January 2014 from http://www.simian.ac.uk/resources/models/simulating-innovation.

This program is free software: you can redistribute it and/or modify it under the terms of version 3 of the GNU General Public License as published by the Free Software Foundation. See http://www.gnu.org/licenses/ for more details. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 

Those wishing to make commercial use of the program should contact the book’s authors to discuss terms.

This program has been designed to be run using NetLogo version 5, which can be obtained from http://ccl.northwestern.edu/netlogo/
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