cooperation_diversity_reputation.nlogo

;;------------------------------------------------------------------------------------
;; patches atributes
;;------------------------------------------------------------------------------------
patches-own [
  contribution ;; player's contribution: 1 - contributor, green, 0 - free-rider, black
  income ;; income from the last round
  neighborhood ;; group of players used for playng the game
  reputation ;; reputation - used to calculate the prestige (Good or Bad) of the player
  prestige ;; Good (1) or Bad (0)
]

;;------------------------------------------------------------------------------------
;; global variables
;;------------------------------------------------------------------------------------
globals [
  cooperators1k
  inv-noise-factor
  inv-reputation-updating-p-i

  cooperator
  freerider
  good
  bad

]

;;------------------------------------------------------------------------------------
;; setup the world
;;------------------------------------------------------------------------------------
to setup
  ;; initial cleanup
  clear-all

  ;; strategy
  set cooperator 1
  set freerider 0

  ;; prestige
  set good 1
  set bad 0

  ;; other constants
  set inv-noise-factor 1 / noise-factor
  set inv-reputation-updating-p-i floor ( 1 / reputation-updating-p )

  ;; data collected during the game
  set cooperators1k []

  ;; main setup
  setup-world
  setup-patches
  reset-ticks
end

;;------------------------------------------------------------------------------------
;; main subroutine
;;------------------------------------------------------------------------------------
to go
  ;; check if the neighborhoods should be chooes each round
  if random-float 1.0 < p-rev   [
    ask patches [
      choose-random-neighborhood
    ]
  ]

  ;; play the public goods game for all patches
  ask patches [
    play-pgg
  ]

  ;; if we are using reputation
  ;; update the reputation
  if utilize-reputation [
    ask patches [
      ;; update the prestige with some probability
      if random-float 1.0 < reputation-updating-p [
        update-prestige
        update-reputation
      ]
    ]
  ]

  ;; imitate the strategy using the selecedt policy
  (ifelse imitation-policy = "linear" [
    ask patches [
      imitate-strategy-linear
    ]
  ] imitation-policy = "fermi-dirac" [
    ask patches [
      imitate-strategy-fermi-dirac
    ]
  ] utilize-reputation [
    ask patches [
      imitate-strategy-reputation
    ]
    ]
  )

  ;; udate the strategy using the cumulative income from the round
  ask patches [
    ifelse utilize-reputation [
      ;; update the prestige
      if random-float 1.0 < reputation-updating-p [
        update-prestige
        update-reputation
      ]
      ;; calculate new strategy
      imitate-strategy-reputation
    ][
      ;; no prestige/reputation update, only strategy
      ifelse imitation-policy = "linear" [
        imitate-strategy-linear
      ] [
        imitate-strategy-fermi-dirac
      ]
    ]

    ;; update colors of the visual representation - NOTE: this should be commented out by default
    update-colors
    ;; reset the income for the next round
    set income 0
  ]

  ;; update the list with cooperators-fraction
  update-cooperators1k

  ;; finish the round
  tick

end

;;------------------------------------------------------------------------------------
;; world initialization
;;------------------------------------------------------------------------------------
to setup-world
  ;; make the world with custom size
  resize-world 0 (world-size - 1) 0 (world-size - 1)
  ;; heuristic scaling of the patch size
  set-patch-size floor ( 64 / (sqrt world-size) )

  ask patches [
    ;; make all patches white
    set pcolor white
    ;; add one turtle to each patch
    ;;sprout 1
  ]
end

;;------------------------------------------------------------------------------------
;; setup routine
;; contains
;; - selection of the initial strategies,
;; - initial neighborhood,
;; - initial reputation
;;------------------------------------------------------------------------------------
to setup-patches
  ask patches [
    ;; initail assignement of the neighborhood
    choose-random-neighborhood

    ;; initialize the income
    set income 0
    ;; randomly assign initial strategies
    ifelse random-float 1.0 < 0.5 [
      set contribution 1 ;; cooperator
    ] [
      set contribution 0 ;; no contribution, free-rider
    ]

    ;; initialize the reputation and the prestige
    set reputation random 100

    ifelse random-float 1.0 < 0.5 [
      set prestige 1 ;; Good
    ] [
      set prestige 0 ;; bad
    ]

    update-colors
  ]
end

;;------------------------------------------------------------------------------------
;; select random patches as neighbors
;;------------------------------------------------------------------------------------
to choose-random-neighborhood
  set neighborhood n-of 4 patches
end

;;------------------------------------------------------------------------------------
;; select near patches of some type
;;-----------------------------------------------------------------------------------
to choose-neighborhood
  ;; choose which neighborhood to use
  (ifelse neighborhood-type = "von Neumann" [
    set neighborhood neighbors4
  ] neighborhood-type = "Moore" [
    set neighborhood neighbors
  ] neighborhood-type = "random von Neumann" [
    set neighborhood n-of (1 + random 4 ) neighbors4
  ] neighborhood-type = "random Moore" [
    set neighborhood n-of (1 + random 8 ) neighbors
  ] neighborhood-type = "random von Neumann or Moore" [
    ifelse random 1 = 0 [
      set neighborhood n-of (1 + random 8 ) neighbors
    ][
      set neighborhood n-of (1 + random 4 ) neighbors4
    ]
  ] neighborhood-type = "von Neumann or Moore" [
    ifelse random 1 = 0 [
      set neighborhood neighbors
    ][
      set neighborhood neighbors4
    ]
  ])
end

;;------------------------------------------------------------------------------------
;; helper function to update visual aspects of turtles
;;------------------------------------------------------------------------------------
to update-colors
  ifelse contribution = 1 [
    set pcolor green
  ][
    set pcolor black
  ]
end

;;------------------------------------------------------------------------------------
;; evolution routine
;;------------------------------------------------------------------------------------
to play-pgg

  ;; calculate the payoff
  let game-gain ( synergy-factor * (contribution + sum [ contribution ] of neighborhood) / (1 + count neighborhood) )

  set income income + game-gain - contribution

  ask neighborhood [
    set income income + game-gain - contribution
  ]

end

;;------------------------------------------------------------------------------------
;; strategy update policies
;;------------------------------------------------------------------------------------

;;------------------------------------------------------------------------------------
;; version with F-D function, without reputation
;;------------------------------------------------------------------------------------
to imitate-strategy-fermi-dirac
  ;; select one of the neighbors
  let my-neighbor one-of neighborhood
  let my-neighbor-income [ income ] of my-neighbor

  ;; select new strategy using Fermi-Dirac function
  if ( random-float 1.0 ) * (1 + exp ( ( income - my-neighbor-income  ) * inv-noise-factor  ) ) < 1 [
    set contribution [ contribution ] of my-neighbor
  ]
end

;;------------------------------------------------------------------------------------
;; version with linear imitation, without reputation
;;------------------------------------------------------------------------------------
to imitate-strategy-linear
  ;; select one of the neighbors
  let my-neighbor one-of neighborhood
  let my-neighbor-income [ income ] of my-neighbor

  ;; select new strategy using linear imitation
  if income < my-neighbor-income [
    if random-float 1.0 < ( my-neighbor-income - income ) / (1 + synergy-factor ) [
      set contribution [ contribution ] of my-neighbor
    ]
  ]
end

;;------------------------------------------------------------------------------------
;; version based on the reputation and F-D function
;;------------------------------------------------------------------------------------
to imitate-strategy-reputation

  ;; select one of the neighbors
  let my-neighbor one-of neighborhood

  ;; check its income and strategy
  let my-neighbor-income [ income ] of my-neighbor
  let my-neighbor-contribution [ contribution ] of my-neighbor

  ;; check its prestige
  let my-neighbor-prestige [ prestige ] of my-neighbor
    let imitation-susceptibility 1
  if my-neighbor-prestige = 0 [
    set imitation-susceptibility 0.01
  ]

  ;; select new strategy using Fermi-Dirac function with prestige-based susceptibility
  if ( random-float 1.0 ) * (1 + exp ( ( income - my-neighbor-income  ) * inv-noise-factor  ) )  < imitation-susceptibility [
    set contribution [ contribution ] of my-neighbor
  ]

end

;;------------------------------------------------------------------------------------
;; reputation and prestige update
;;------------------------------------------------------------------------------------

;;------------------------------------------------------------------------------------
;; prestige
;;------------------------------------------------------------------------------------
to update-prestige

  ;; update the prestige accordig to the erned reputation
  ifelse reputation >= reputation-threshold [
    set prestige 1
  ] [
    set prestige 0
  ]

end

;;------------------------------------------------------------------------------------
;; adaptive reputation update
;;------------------------------------------------------------------------------------
to update-reputation
  (ifelse
    prestige = good and contribution = cooperator
    [
      ;; increase reputation
      set reputation reputation + reputation-update
    ]
    prestige = good and contribution = freerider
    [
      ;; loose reputation
      set reputation reputation - 2 * inv-reputation-updating-p-i * reputation-update
    ]
    prestige = bad and contribution = cooperator
    [
      ;; no update
    ]
    prestige = bad and contribution = freerider
    [
      ;; loose reputation
      set reputation reputation + reputation-update
    ]
  )

  (ifelse reputation > 100 [
    set reputation 100
  ] reputation < 0 [
    set reputation 0
  ])

end

;;------------------------------------------------------------------------------------
;; reporters
;;------------------------------------------------------------------------------------

to-report cooperators-fraction
  report count patches with [ contribution = 1 ] / count patches
end

;; cooperators fraction in last 1000 steps
to update-cooperators1k
  ;; add current vale of cooperators-fraction to the list cooperators1k
  set cooperators1k fput cooperators-fraction cooperators1k
end

to-report mean-cooperators1k
  ifelse ticks >= 1000 [
    report mean ( sublist cooperators1k 0 1000 )
  ][
    report 0
  ]
end
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@#$#@#$#@
## WHAT IS IT?

Public Goods Game with some modifications.

## HOW IT WORKS

(what rules the agents use to create the overall behavior of the model)

Interaction diversity - different number of neighbours to interact with and to learn from.

## HOW TO USE IT

(how to use the model, including a description of each of the items in the Interface tab)

## THINGS TO NOTICE

(suggested things for the user to notice while running the model)

## THINGS TO TRY

(suggested things for the user to try to do (move sliders, switches, etc.) with the model)

## EXTENDING THE MODEL

(suggested things to add or change in the Code tab to make the model more complicated, detailed, accurate, etc.)

## NETLOGO FEATURES

(interesting or unusual features of NetLogo that the model uses, particularly in the Code tab; or where workarounds were needed for missing features)

## RELATED MODELS

(models in the NetLogo Models Library and elsewhere which are of related interest)

## CREDITS AND REFERENCES

Lihui Shang, Sihao Sun, Jun Ai, and Zhan Su. Cooperation enhanced by the interaction diversity for the spatial public goods game on regular lattices. Physica A: Statistical Mechanics and its Applications, 593:126999 DOI:10.1016/j.physa.2022.126999
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