Page2000.nlogo

turtles-own [p q cumulatedPayoff numberOfOffsprings paired myID myNeighbours]
globals []
breed [offspring offsprings]
breed [parent parents]

;; SEE "INFO" TAB FOR MORE INFORMATION ON THIS MODEL

to setup
  clear-all
  ;;set seed new-seed ;; pick random number for seed, comment this line to always run with the same seed (for debug for example)
  
  random-seed seed  ;; set the seed of the random generator to seed
  
  create-turtles populationSize [ setxy random-xcor random-ycor ]
  let myWho 1
  ask turtles [
    set myID myWho ;myID represents the position of the turtle on the ring
    set myWho (myWho + 1)
    set shape "person"
    set p random-float 1 set q random-float 1
    set breed parent
  ]
  reset-ticks
end

to go
  if ticks = (numberOfGenerations + 1) 
  [ 
    stop 
  ]
  resetValues ;; reset turtle variables
  playUG  ;; turtles play ultimatum games
  
  update-plots
  reproduceAndDie ;; turtles reproduce and die
  tick-advance 1
end

to resetValues
  let x -1 let increment -1
  ask turtles [
    set cumulatedPayoff 0 ;; payoff since the beginning of life
    set numberOfOffsprings 1
    set breed parent
    set paired 0
    
    set myNeighbours [] ;; represents list of myID of neighbours
    
    set x 0 set increment 1
    while [x < (neighbourhoodSize / 2)] ;;creates list of neighbours on the right
    [
      set myNeighbours lput (myID + increment) myNeighbours
      set increment increment + 1
      set x (x + 1)
    ]
    
    set x 0 set increment -1
    while [x < (neighbourhoodSize / 2)] ;;creates list of neighbours on the left
    [
      set myNeighbours fput (myID + increment) myNeighbours
      set increment increment - 1
      set x (x + 1)
    ]    
    let indexList n-values (length myNeighbours) [?]
    (foreach myNeighbours indexList ;;if neighbours are 0, -1, -2, etc... we must go back to the other side of the ring
    [
      if (?1 < 1) [set myNeighbours (replace-item ?2 myNeighbours (?1 + populationSize))] 
      if (?1 > populationSize) [set myNeighbours (replace-item ?2 myNeighbours (?1 - populationSize))]     
    ])
  ]
end

to playUG
  let myWho -1 let offer -1 let request -1 let neighbourWho -1
  
  foreach [who] of turtles ;; each turtle plays an UG as proposer against its neighbours
    [
      set myWho ?
      set offer [p] of turtle myWho
      foreach [myNeighbours] of turtle myWho ;; for each neighour turtle
      [
        set neighbourWho [who] of turtles with [myID = ?] ; neighbourWho is a list of one element
        set neighbourWho item 0 neighbourWho ; now neighbourWho is a number
        set request [q] of turtle neighbourWho
        if offer >= request
        [
          ask turtle myWho [set cumulatedPayoff (cumulatedPayoff + 1 - offer)]
          ask turtle neighbourWho [set cumulatedPayoff (cumulatedPayoff + offer)]
        ]            
      ]
    ]
end



to reproduceAndDie
  
  let totalScore 0 let myWho -1
  let offspringTable []
  let offspringTableTurtle []
  foreach [who] of turtles               ;;might be a more elegant way to code reproduction !!
  [
     set myWho ?
     set totalScore [cumulatedPayoff] of turtle myWho
     foreach [myNeighbours] of turtle myWho ;; to compute totalScore of all neighbours
     [
       ask turtles with [myID = ?][set totalScore totalScore + cumulatedPayoff]
     ]
     if totalScore != 0
     [
       ask turtle myWho [set numberOfOffsprings round (500 * cumulatedPayoff / totalScore)] ;; computes number of offspring 
       foreach [myNeighbours] of turtle myWho 
       [
         ask turtles with [myID = ?][set numberOfOffsprings round (500 * cumulatedPayoff / totalScore)]
       ]
     ]
     set offspringTable []       
     ask turtle myWho [
       set offspringTableTurtle n-values numberOfOffsprings [who] ;; creates a table containing as many cells as offspring, each cell containing the "who" of the parent
       set offspringTable (sentence offspringTable offspringTableTurtle) ;; concatenates to the previous table
     ]
     foreach [myNeighbours] of turtle myWho 
     [
       ask turtles with [myId = ?]
       [
         set offspringTableTurtle n-values numberOfOffsprings [who]
         set offspringTable (sentence offspringTable offspringTableTurtle)
       ]
     ]      
     let newGeneration one-of offspringTable   ;; select the only offspring for this cell of the ring
     ask turtle newGeneration [hatch-offspring 1 [set myID [myID] of turtle myWho]] ;; parent produces offspring (in the breed offspring)
     
    
  ]
  
  ask turtles with [breed = parent] [die] ;; parents die
  
  ask turtles [ ;; mutations on offspring
    setxy random-xcor random-ycor ;; to be able to right click on a turtle
    set p applyMutation p
    set q applyMutation q
  ]
end



to-report applyMutation [gene]
  ifelse random-float 1 <= mutationRate [ report mutatedValue gene ][ report gene ]
end

to-report mutatedValue [gene]
  let mutationSize (random-float mutationAmplitude) 
  ifelse random-float 1 <= 0.5
    [ set gene gene + mutationSize ]
    [  set gene gene - mutationSize ]
  if gene > 1 [set gene 1] ;; if we go outside the bounds
  if gene < 0 [set gene 0]  ;; if we go outside the bounds
  
  report gene
end
@#$#@#$#@
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BUTTON
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OBSERVER
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BUTTON
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PLOT
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Average offer p
generations
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PLOT
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BUTTON
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go one
go
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OBSERVER
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MONITOR
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Average offer
mean [p] of turtles
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MONITOR
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mean [q] of turtles
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INPUTBOX
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neighbourhoodSize
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Number

@#$#@#$#@
## WHAT IS IT?

This model is a replication of the model of the evolution of human fairness presented in the following paper:

Page, K. M., M. a. Nowak, and K. Sigmund, 2000. The spatial ultimatum game. Proceedings Biological sciences / The Royal Society 267:2177-82. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1690799/

This replication is provided for comparison purposes as part of the review paper:

 Debove, S., et al., Models of the evolution of fairness in the ultimatum game: a review and classification, Evolution and Human Behavior (2015), http://www.ehbonline.org/article/S1090-5138%2816%2900003-9/abstract 

The present Netlogo replication of the original model has thus NOT been created, reviewed or endorsed by any authors of the original paper. No guarantee is provided that the original model has been replicated with 100% accuracy.

For any question about the Netlogo code in this replication, please contact the first author of the review at email address     sd ((AT)) stephanedebove ((dot)) net     or on the following website : http://stephanedebove.net/contact

Download all models of the review at http://stephanedebove.net/?p=239 , or fork them on https://github.com/BigNoob/fairness-netlogo/


## HOW IT WORKS

See methods in the above mentioned original paper or in the supplementary information of the review.


## HOW TO USE IT

Default parameter values when you download the model correspond to the values used in the original paper. Individuals are arranged on a ring (and not a grid).

Non explicit parameters in the interface:

**seed**: displays the random seed used to initialize the model: write it down for replication purposes.
**neighbourhoodSize**: number of neighbours with which each individual plays ultimatum games - must be an even number.
@#$#@#$#@
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@#$#@#$#@
NetLogo 5.1.0
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