nxn-games-on-networks.nlogo

extensions [nw rnd]

globals [
  payoff-matrix
  n-of-strategies
  n-of-players

  avg-nbrs-within-radius
  avg-clustering-coefficient
  size-of-largest-component

  max-payoff-difference-in-matrix
  max-payoff-difference
  max-n-of-nbrs-of-each-player
]

breed [players player]

players-own [
  strategy
  strategy-after-revision
  payoff

  my-nbrs-and-me
]

;;;;;;;;;;;;;
;;; SETUP ;;;
;;;;;;;;;;;;;

to setup
  clear-all
  setup-payoffs
  setup-players
  setup-graph
  reset-ticks
  update-graph
  compute-network-metrics
end

to setup-payoffs
  set payoff-matrix read-from-string payoffs
  set n-of-strategies length payoff-matrix

  set max-payoff-difference-in-matrix
     (max-of-matrix payoff-matrix) - (min-of-matrix payoff-matrix)
  if decision-rule = "imitative-positive-proportional-m"
     [ check-payoffs-are-non-negative ]
end

to setup-players
  let initial-distribution
      read-from-string n-of-players-for-each-strategy

  if length initial-distribution != length payoff-matrix [
    user-message (word "The number of items in\n"
      "n-of-players-for-each-strategy (i.e. "
      length initial-distribution "):\n"
      n-of-players-for-each-strategy
      "\nshould be equal to the number of rows\n"
      "in the payoff matrix (i.e. "
      length payoff-matrix "):\n"
      payoffs
    )
  ]

  set n-of-players sum initial-distribution
  ifelse n-of-players < 4
    [ user-message "There should be at least 4 players" ]
    [
      build-network

      ask players [set strategy -1]
      let i 0
      foreach initial-distribution [ j ->
        ask up-to-n-of j players with [strategy = -1] [
          set payoff 0
          set strategy i
          set strategy-after-revision strategy
          set my-nbrs-and-me
               (turtle-set link-neighbors self)
        ]
        set i (i + 1)
      ]

      set n-of-players count players
      update-players-color
    ]
end

;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; NETWORK CONSTRUCTION ;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;

to build-network
  set-default-shape players "circle"
  run (word "build-" network-model "-network")
  ask players [fd 15]
end

to build-Erdos-Renyi-network
  nw:generate-random players links n-of-players prob-link
end

to build-Watts-Strogatz-small-world-network
 nw:generate-watts-strogatz players links n-of-players (avg-degree-small-world / 2) prob-rewiring
end

to build-preferential-attachment-network
  nw:generate-preferential-attachment players links n-of-players min-degree
end

to build-ring-network
  nw:generate-ring players links n-of-players
end

to build-star-network
  nw:generate-star players links n-of-players
end

to build-grid-4-nbrs-network
  let players-per-line (floor sqrt n-of-players)
  nw:generate-lattice-2d players links players-per-line players-per-line false
end

to build-wheel-network
  nw:generate-wheel players links n-of-players
end

to build-path-network
  build-ring-network
  ask one-of links [die]
end

;;;;;;;;;;
;;; GO ;;;
;;;;;;;;;;

to go
  update-max-payoff-difference
  ask players [update-payoff]
  ask players [
    if (random-float 1 < prob-revision) [
      update-strategy-after-revision
    ]
  ]
  ask players [update-strategy]

  tick

  update-graph
  update-players-color
end

;;;;;;;;;;;;;;;;;;;;;;;;;
;;; UPDATE PROCEDURES ;;;
;;;;;;;;;;;;;;;;;;;;;;;;;

to update-payoff
  if any? link-neighbors [
    run (word "play-with-" play-with)
  ]
end

to play-with-one-random-nbr
    let mate one-of link-neighbors
    set payoff item ([strategy] of mate) (item strategy payoff-matrix)
end

to play-with-all-nbrs-TOTAL-payoff
  let n-of-coplayers-with-strategy-? n-values n-of-strategies [ i ->
    count link-neighbors with [strategy = i] ]
  let my-payoffs (item strategy payoff-matrix)
  set payoff sum (map * my-payoffs n-of-coplayers-with-strategy-?)
end

to play-with-all-nbrs-AVG-payoff
  play-with-all-nbrs-TOTAL-payoff
  set payoff (payoff / count link-neighbors)
end

to update-max-payoff-difference
  set max-payoff-difference
    max-payoff-difference-in-matrix *
      ifelse-value play-with = "all-nbrs-TOTAL-payoff"
        [max-n-of-nbrs-of-each-player][1]
end

to update-strategy-after-revision
  ifelse random-float 1 < noise
    [ set strategy-after-revision (random n-of-strategies) ]
    [ if any? link-neighbors [run (word decision-rule "-rule")] ]
end

to best-neighbor-rule
  set strategy-after-revision [strategy] of
      one-of my-nbrs-and-me with-max [payoff]
end

to imitate-if-better-rule
  let observed-player one-of link-neighbors

  if ([payoff] of observed-player) > payoff [
    set strategy-after-revision ([strategy] of observed-player)
  ]
end

to imitative-pairwise-difference-rule
  let observed-player one-of link-neighbors

  ;; compute difference in payoffs
  let payoff-diff ([payoff] of observed-player - payoff)

  set strategy-after-revision ifelse-value
    (random-float 1 < (payoff-diff / max-payoff-difference))
      [ [strategy] of observed-player ]
      [ strategy ]
    ;; If your strategy is the better, payoff-diff is negative,
    ;; so you are going to stick with it.
    ;; If it's not, you switch with probability
    ;; (payoff-diff / max-payoff-difference)
end

to imitative-positive-proportional-m-rule
  let chosen-nbr rnd:weighted-one-of my-nbrs-and-me [ payoff ^ m ]
  set strategy-after-revision [strategy] of chosen-nbr
end

to Fermi-m-rule
  let observed-player one-of link-neighbors

  ;; compute difference in payoffs
  let payoff-diff ([payoff] of observed-player - payoff)

  set strategy-after-revision ifelse-value
    (random-float 1 < (1 / (1 + exp (- m * payoff-diff))))
      [ [strategy] of observed-player ]
      [ strategy ]
end

to Santos-Pacheco-rule
  let observed-player one-of link-neighbors

  ;; compute difference in payoffs
  let payoff-diff ([payoff] of observed-player - (payoff))

  let degree count link-neighbors
  let degree-of-observed-player
      [count link-neighbors] of observed-player

  set strategy-after-revision ifelse-value
    (random-float 1 < (payoff-diff / (max-payoff-difference-in-matrix *
       max (list degree degree-of-observed-player))))
        [ [strategy] of observed-player ]
        [ strategy ]
end

to update-strategy
  set strategy strategy-after-revision
end



;;;;;;;;;;;;;
;;; PLOTS ;;;
;;;;;;;;;;;;;

to setup-graph
  set-current-plot "Strategy Distribution"
  foreach (range n-of-strategies) [ i ->
    create-temporary-plot-pen (word i)
    set-plot-pen-mode 1
    set-plot-pen-color 25 + 40 * i
  ]
end

to update-graph
  let strategy-numbers (range n-of-strategies)
  let strategy-frequencies map [ n ->
        count players with [strategy = n] / n-of-players
      ] strategy-numbers

  set-current-plot "Strategy Distribution"
  let bar 1
  foreach strategy-numbers [ n ->
    set-current-plot-pen (word n)
    plotxy ticks bar
    set bar (bar - (item n strategy-frequencies))
  ]
  set-plot-y-range 0 1
end

to update-players-color
  ask players [set color 25 + 40 * strategy]
end

;;;;;;;;;;;;;;;;;;;;;;;
;;; NETWORK METRICS ;;;
;;;;;;;;;;;;;;;;;;;;;;;

to compute-network-metrics
  plot-accessibility
  compute-avg-clustering-coefficient
  compute-size-of-largest-component
end

to plot-accessibility
  let steps link-radius
  if link-radius = "Infinity" [set steps (n-of-players - 1)]
  let n-of-nbrs-of-each-player
    [(count nw:turtles-in-radius steps) - 1] of players

  set max-n-of-nbrs-of-each-player max n-of-nbrs-of-each-player
  set-current-plot "Neighbors within link-radius"
  set-plot-x-range 0 (max-n-of-nbrs-of-each-player + 1)
                     ;; + 1 to make room for the width of the last bar
  histogram n-of-nbrs-of-each-player

  set avg-nbrs-within-radius mean n-of-nbrs-of-each-player
end

to compute-avg-clustering-coefficient
  set avg-clustering-coefficient mean [ nw:clustering-coefficient ] of players
end

to compute-size-of-largest-component
  set size-of-largest-component max map count nw:weak-component-clusters
end

;;;;;;;;;;;;;;
;;; LAYOUT ;;;
;;;;;;;;;;;;;;

;; Procedures taken from Wilensky's (2005a) NetLogo Preferential
;; Attachment model
;; http://ccl.northwestern.edu/netlogo/models/PreferentialAttachment
;; and Wilensky's (2005b) Mouse Drag One Example
;; http://ccl.northwestern.edu/netlogo/models/MouseDragOneExample
to relax-network
  ;; the number 3 here is arbitrary; more repetitions slows down the
  ;; model, but too few gives poor layouts
  repeat 3 [
    ;; the more players we have to fit into
    ;; the same amount of space, the smaller
    ;; the inputs to layout-spring we'll need to use
    let factor sqrt count players
    ;; numbers here are arbitrarily chosen for pleasing appearance
    layout-spring players links
                  (1 / factor) (7 / factor) (3 / factor)
    display  ;; for smooth animation
  ]
  ;; don't bump the edges of the world
  let x-offset max [xcor] of players + min [xcor] of players
  let y-offset max [ycor] of players + min [ycor] of players
  ;; big jumps look funny, so only adjust a little each time
  set x-offset limit-magnitude x-offset 0.1
  set y-offset limit-magnitude y-offset 0.1
  ask players [ setxy (xcor - x-offset / 2) (ycor - y-offset / 2) ]
end

to-report limit-magnitude [number limit]
  if number > limit [ report limit ]
  if number < (- limit) [ report (- limit) ]
  report number
end

to drag-and-drop
  if mouse-down? [
    let candidate min-one-of players
        [distancexy mouse-xcor mouse-ycor]
    if [distancexy mouse-xcor mouse-ycor] of candidate < 1 [
    ;; The WATCH primitive puts a "halo" around the watched turtle.
      watch candidate
      while [mouse-down?] [
        ;; If we don't force the view to update, the user won't
        ;; be able to see the turtle moving around.
        display
        ;; The SUBJECT primitive reports the turtle being watched.
        ask subject [ setxy mouse-xcor mouse-ycor ]
      ]
      ;; Undoes the effects of WATCH.
      reset-perspective
    ]
  ]
end

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; SUPPORTING PROCEDURES ;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

to check-payoffs-are-non-negative
  if min reduce sentence payoff-matrix < 0 [
    user-message (word
      "Since you are using decision-rule =\n"
      "imitative-positive-proportional-m,\n"
      "all elements in the payoff matrix\n"
      payoffs
      "\nshould be non-negative numbers.")
  ]
end

;;;;;;;;;;;;;;;;
;;; Matrices ;;;
;;;;;;;;;;;;;;;;

to-report max-of-matrix [matrix]
  report max reduce sentence matrix
end

to-report min-of-matrix [matrix]
  report min reduce sentence matrix
end
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CHOOSER
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network-model
network-model
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SLIDER
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min-degree
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TEXTBOX
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TEXTBOX
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Neighbors within link-radius
# of reachable neighbors
# of players
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PENS
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avg. clustering coeff.
avg-clustering-coefficient
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MONITOR
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size of largest comp.
size-of-largest-component
17
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MONITOR
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network density
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3
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link-radius
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BUTTON
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NIL
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CHOOSER
26
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decision-rule
decision-rule
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5

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SLIDER
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Circle -16777216 true false 234 174 42
Rectangle -7500403 true true 181 185 214 194
Circle -16777216 true false 144 174 42
Circle -16777216 true false 24 174 42
Circle -7500403 false true 24 174 42
Circle -7500403 false true 144 174 42
Circle -7500403 false true 234 174 42

turtle
true
0
Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210
Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105
Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105
Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87
Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210
Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99

wheel
false
0
Circle -7500403 true true 3 3 294
Circle -16777216 true false 30 30 240
Line -7500403 true 150 285 150 15
Line -7500403 true 15 150 285 150
Circle -7500403 true true 120 120 60
Line -7500403 true 216 40 79 269
Line -7500403 true 40 84 269 221
Line -7500403 true 40 216 269 79
Line -7500403 true 84 40 221 269

wolf
false
0
Polygon -16777216 true false 253 133 245 131 245 133
Polygon -7500403 true true 2 194 13 197 30 191 38 193 38 205 20 226 20 257 27 265 38 266 40 260 31 253 31 230 60 206 68 198 75 209 66 228 65 243 82 261 84 268 100 267 103 261 77 239 79 231 100 207 98 196 119 201 143 202 160 195 166 210 172 213 173 238 167 251 160 248 154 265 169 264 178 247 186 240 198 260 200 271 217 271 219 262 207 258 195 230 192 198 210 184 227 164 242 144 259 145 284 151 277 141 293 140 299 134 297 127 273 119 270 105
Polygon -7500403 true true -1 195 14 180 36 166 40 153 53 140 82 131 134 133 159 126 188 115 227 108 236 102 238 98 268 86 269 92 281 87 269 103 269 113

x
false
0
Polygon -7500403 true true 270 75 225 30 30 225 75 270
Polygon -7500403 true true 30 75 75 30 270 225 225 270
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NetLogo 6.4.0
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default
0.0
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0.0 1 1.0 0.0
0.2 0 0.0 1.0
link direction
true
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Line -7500403 true 150 150 90 180
Line -7500403 true 150 150 210 180
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0
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