Nowak2000.nlogo

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

;; reproduction of the model presented in Nowak, 2000: Fairness versus reason in the ultimatum game.
;; http://www.ncbi.nlm.nih.gov/pubmed/10976075
;; most parameter values were given in caption of figure 2
;; parameters not reported in the paper: mutation rate (assuming 1), mutation amplitude, trembling hand values

;; see the effect of the assumption that p+q<= 1 by turning on the option "pqConstraint"

to setup
  clear-all
  ;;set seed new-seed ;; pick random number for seed
  
  random-seed seed  ;; set the seed of the random generator to seed
  
  create-turtles populationSize [ setxy random-xcor random-ycor ]
  ask turtles [
    set shape "person"
    set p pStart set q qStart
    set breed parent
  ]
  reset-ticks
end

to go
  if ticks = (numberOfGenerations + 1) 
  [ 
    stop 
  ]
  resetValues
  playUG
  
  update-plots
  reproduceAndDie
  tick-advance 1
end

to resetValues
  ask turtles [
    set cumulatedPayoff 0 ;; payoff since the beginning of life
    set numberOfOffsprings 1
    set breed parent
    set paired 0
    set reputationOthers n-values populationSize [-1]
  ]
  let myWho 0
  ask turtles [
    set myID myWho 
    set myWho (myWho + 1)
  ]
end

to playUG
  let numberOfGames 0 let offer -1 let request -1
  let proposer one-of turtles let responder one-of turtles let tremblingHand 0 let whoResponder -1
  while [numberOfGames < 2 * timesProposer * populationSize]
  [
    
    set proposer one-of turtles
    ask proposer [ set paired 1 ] ;; to avoid picking the same guy for second individual
    set responder one-of turtles with [paired = 0]
    ask proposer [ set paired 0 ]
    set offer [p] of proposer ;; important to have this, working on [p] or [q] directly increases the risk to make errors on whose p is it
    set whoResponder [myID] of responder
    
    if random-float 1 < probabilityTremblingHand ;; present in Nowak 2000, but probability and amplitude unknown
    [
      set tremblingHand random-float tremblingHandMagnitude 
      set offer offer - tremblingHand
    ]
    let minimumOfferAcceptedResponder item whoResponder ([reputationOthers] of proposer) 
    if minimumOfferAcceptedResponder != -1  
    [
        if minimumOfferAcceptedResponder < offer [set offer minimumOfferAcceptedResponder]
    ]

    set request [q] of responder 
    
    if offer >= request
    [
      ask proposer [set cumulatedPayoff (cumulatedPayoff + 1 - offer)]
      ask responder [set cumulatedPayoff (cumulatedPayoff + offer)]
      let selectedIndividuals n-of (round (w * populationSize)) turtles ;individuals who have access to the offer accepted
      ask selectedIndividuals [
        if (request < (item whoResponder reputationOthers)) OR ((item whoResponder reputationOthers) < 0)
        [
          set reputationOthers replace-item whoResponder reputationOthers request ;update list with what the responder has accepted
        ]
        
      ] 
    ]    
    
    set numberOfGames numberOfGames + 1
  ]  
  
  
  
end



to reproduceAndDie
  
  let averagePayoff mean [cumulatedPayoff] of turtles  
  let offspringTable []
  let offspringTableTurtle []
  if averagePayoff != 0 [
    ask turtles [ set numberOfOffsprings round (100 * cumulatedPayoff / averagePayoff)]
  ]
  
  ask turtles [
    set offspringTableTurtle n-values numberOfOffsprings [who] ;; create a table containing as many cases as offspring, with the who of the parent inside
    set offspringTable (sentence offspringTable offspringTableTurtle) ;; concatenate to the previous table
  ]
  
  ;print offspringTable
  
  let newGeneration n-values populationSize [one-of offspringTable]   ;; random drawing with replacement
                                                                      
  
  
  (foreach newGeneration
    [
      ask turtle ? [hatch-offspring 1] ;; parents make offsprings in the breed offspring
    ]) 
  ask turtles with [breed = parent] [die]
  
  let newP -1 let newQ -1
  
  ask turtles [ 
    setxy random-xcor random-ycor ;; to be able to right click on a turtle
    
    set newP applyMutation p
    ifelse pqConstraint = True [if newP + q <= 1 [set p newP]][set p newP] ;; mutation takes place only if it doesn't break p + q <= 1
    set newQ applyMutation q
    ifelse pqConstraint = True [if newQ + p <= 1 [set q newQ]][set q newQ]
  ]
  
end


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

to-report mutatedValue [gene]
  ;; mutation happens
  let mutationSize (random-float mutationStd) ;; mutations are always uniform in Nowak 2000
  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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INPUTBOX
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SWITCH
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pqConstraint
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@#$#@#$#@
## WHAT IS IT?

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

Nowak, M. a., K. M. Page, and K. Sigmund, 2000. Fairness versus reason in the ultimatum
game. Science 289:1773-5. http://www.ncbi.nlm.nih.gov/pubmed/10976075 

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.

At the end of the generations, the model prints a txt file with the results in the current folder. The file contains the average p value in the population at each generation.

## HOW TO USE IT

Non explicit parameters in the interface:

**seed**: displays the random seed used to initialize the model: write it down for replication purposes.
**pStart and qStart**: initial values for p and q
**w**: fraction of the population that learns about each accepted offer
**probabilityTremblingHand**: probability to make a smaller offer than p
**tremblingHandMagnitude**: magnitude of this smaller offer
**timesProposer**: average number of times each individual will play proposer in his life (same number applies for number of times responder)
**updatePlotsEvery**: number of generations between two updates of the plots, or between two records of p in the result txt file.

## THINGS TO TRY

See the effect of the assumption p+q<= 1 by turning on and off the option "pqConstraint"

## CREDITS AND REFERENCES

Find other Netlogo models of the evolution of human fairness and learn more about the review at http://stephanedebove.net/?p=239
@#$#@#$#@
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@#$#@#$#@
NetLogo 5.1.0
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