Two-Thirds Guess Game

globals [
  crowd-guess             ;; the current guess of the crowd
  winning-guess           ;; 2/3 of the crowd-guess value
  history                 ;; list of past correct values (2/3 of average guess)
  winning-guess-patch     ;; patch where we show the last winning guess as a label
]

breed [ skilled a-skilled ]
breed [ unskilled an-unskilled ]

skilled-own [
  strategies              ;; list of strategies
  best-strategy           ;; index of the current best strategy
  prediction              ;; current prediction of the winning value
]

unskilled-own [
  prediction              ;; current prediction of the winning value
]

to setup
  clear-all
  set-default-shape turtles "person"


  ;; initialize the previous crowd guesses randomly so the agents have a history
  ;; to work with from the start
  set history n-values (memory-size * 2) [random 100]
  ;; the history is twice the memory, because we need at least a memory worth of history
  ;; for each point in memory to test how well the strategies would have worked

  set crowd-guess first history
  set winning-guess (crowd-guess * 0.67)

  ;; use one of the patch labels to visually indicate the guess

  ask patch (0.75 * max-pxcor) (0.5 * max-pycor) [
    set winning-guess-patch self
    set plabel-color red
  ]

  ;; create the agents and give them random strategies
  ;; these are the only strategies these agents will ever have though they
  ;; can change which of this "bag of strategies" they use every tick
  create-skilled 100 - number-unskilled-players [
    set color white
    move-to-empty-one-of patches
    set strategies n-values number-strategies [random-strategy]
    set best-strategy first strategies
    update-strategies
  ]

  create-unskilled number-unskilled-players [
    set color orange
    move-to-empty-one-of patches
  ]
  ;; start the clock
  reset-ticks
end 

to go
  ;; update the global variables
  ask winning-guess-patch [ set plabel winning-guess ]
  ;; each agent predicts attendance at the bar and decides whether or not to go
  ask turtles [

    if breed = skilled [
    set prediction predict-crowd-guess best-strategy sublist history 0 memory-size
    ]
  ]

  ;; update the guess history
  ;; remove oldest average guess and prepend latest average guess
  set history fput crowd-guess but-last history
  ;; the agents decide what the new best strategy is
  ask turtles  [ update-strategies ]
  ;; display the new crowd-guess and winning-guess
  set crowd-guess abs (mean [prediction] of turtles)
  set winning-guess crowd-guess * 0.67
  ;; advance the clock
  tick
end 

;; determines which strategy would have predicted the best results had it been used this round.
;; the best strategy is the one that has the sum of smallest differences between the
;; current crowd-guess and the predicted crowd-guess for each of the preceding
;; weeks (going back MEMORY-SIZE weeks)
;; this does not change the strategies at all, but it does (potentially) change the one
;; currently being used and updates the performance of all strategies

to update-strategies

  ;; separate skilled from unskilled players
  ifelse breed = skilled [
  ;; initialize best-score to a maximum, which is the lowest possible score
  let best-score memory-size * 100 + 1
  foreach strategies [ ?1 ->
    let score 0
    let week 1
    repeat memory-size [
      set prediction predict-crowd-guess ?1 sublist history week (week + memory-size)
      set prediction prediction * 0.67
      set score score + abs (item (week - 1) history - prediction)
      set week week + 1
    ]
    if (score <= best-score) [
      set best-score score
      set best-strategy ?1
    ]
  ]
 ]
   ;; now do the unskilled prediction
 [

   set prediction (unskilled-minimum + (unskilled-maximum - unskilled-minimum) * random-float 1)

 ]
end 

;; this reports a random strategy. a strategy is just a set of weights from -1.0 to 1.0 which
;; determines how much emphasis is put on each previous time period when making
;; an attendance prediction for the next time period

to-report random-strategy
  report n-values (memory-size + 1) [1.0 - random-float 2.0]
end 

;; This reports an agent's prediction of the current crowd-guess
;; using a particular strategy and portion of the attendance history.
;; More specifically, the strategy is then described by the formula
;; p(t) = x(t - 1) * a(t - 1) + x(t - 2) * a(t -2) +..
;;      ... + x(t - MEMORY-SIZE) * a(t - MEMORY-SIZE) + c * 100,
;; where p(t) is the prediction at time t, x(t) is the crowd-guess at time t,
;; a(t) is the weight for time t, c is a constant, and MEMORY-SIZE is an external parameter.

to-report predict-crowd-guess [strategy subhistory]
  ;; the first element of the strategy is the constant, c, in the prediction formula.
  ;; one can think of it as the the agent's prediction of the crowd-guess
  ;; in the absence of any other data
  ;; then we multiply each week in the history by its respective weight
  report 100 * first strategy + sum (map [ [?1 ?2] -> ?1 * ?2 ] butfirst strategy subhistory)
end 

;; In this model it doesn't really matter exactly which patch
;; a turtle is on.  Nonetheless, to make a nice visualization
;; this procedure is used to ensure that we only have one
;; turtle per patch.

to move-to-empty-one-of [locations]  ;; turtle procedure
  move-to one-of locations
  while [any? other turtles-here] [
    move-to one-of locations
  ]
end 


; Elements of the El Farol model Copyright 2007 Uri Wilensky.
; Remaining elements Copyright 2016 by Curtis Frye
; See Info tab for full copyright and license.