Game Theory v1

turtles-own [
  prob-s1                ;probability of choosing strategy 1
  prob-s2                ;probability of choosing strategy 2
  strategy1?             ;boolean, "true" if strategy 1 is chosen
  utility                ;payoff received at that round
  potential-utility      ;payoff of choosing other strategy in the same round
  partnered?             ;boolean, "true" if turtle is partnered with another turtle
  partner                ;the opposing turtle in a game
  partner-strategy1?     ;boolean, "true" if partner chose strategy 1
  strategy               ;the learning strategy used by each turtle
]

to setup
  clear-all
  crt number-utility-max [
    set strategy "utility-max"
    set label 1                      ;labels used to identify what strategy a turtle is using
  ]
  crt number-seek-fair [
    set strategy "seek-fair"
    set label 2
  ]
  crt number-predictors [
    set strategy "predict"
    set label 3
  ]
  ask turtles [
    set shape "person"
    set size 2                       ;size used to make turtles easier to see
    set color one-of [red blue]      ;determines if turtles are player 1s (blue) or player 2s (red)
    set partnered? false             ;turtles are initially unpaired
    set partner nobody
    prob-initial                     ;sets turtles indifferent to their strategies
    setxy random-xcor random-ycor
  ]
  reset-ticks
end 

;turtle procedure
;sets initial probabilities

to prob-initial
  set prob-s1 0.5
  set prob-s2 0.5
end 

to go
end -round                          ;releases partners to allow them to look for new ones
  ask turtles [
    partner-up                       ;turtles partner-up if they are next to an opposing player
  ]
  let partnered-turtles turtles with [partnered? = true] 
  ask partnered-turtles [play-a-round]
  ask turtles [
    if prob-s1 > 1 [                 ;probabilites can't exceed 1 or go below 0
      set prob-s1 1
      set prob-s2 0
    ]
    if prob-s1 < 0 [
      set prob-s1 0
      set prob-s2 1
    ]
  ]
  tick
end 

;releases partners

to end-round
  let partnered-turtles turtles with [ partnered? = true]
  ask partnered-turtles [
    release-partner
    ]
end 

;partnered-turtle procedure

to release-partner
  set partnered? false
  set partner nobody
  rt 180
end 

;turtle procedure
;opposing turtles pair up if they're spatially located right next to each other

to partner-up
  if (not partnered?) [              
    rt (random-float 90 - random-float 90) fd 1     
    set partner one-of (turtles-at -1 0) with [ (not partnered?) and (color != [color] of myself) ]
    if partner != nobody [              
      set partnered? true
      set heading 270                   
      ask partner [
        set partnered? true
        set partner myself
        set heading 90
      ]
    ]
  ]
end 

;partnered-turtle procedure

to play-a-round
  let partnered-turtles turtles with [partnered? = true]
  pick-a-strategy                                           ;turtles probabilistically make a decision
  set partner-strategy1? [strategy1?] of partner
  ask partnered-turtles with [color = blue] [
    set-utilities
  ]
  ask partnered-turtles with [strategy = "utility-max"] [
    utility-max
  ]
  ask partnered-turtles with [strategy = "seek-fair"] [
    seek-fair
  ]
  ask partnered-turtles with [(color = blue) and (strategy = "predict")] [
    predict-blue
  ]
  ask partnered-turtles with [(color = red) and (strategy = "predict")] [
    predict-red
  ]
end 
   
;partnered-turtle procedure
;turtles probabilistically select a strategy

to pick-a-strategy
  ifelse random-float 1 < prob-s1 [
    set strategy1? true
  ][
  set strategy1? false
  ]
end 

;player1 partnered-turtle procedure
;looks at the strategy choices and assigns the appropriate utility values

to set-utilities
  ifelse strategy1? = true [
    ifelse partner-strategy1? = true [
      set utility p1s1-utility
      set potential-utility p1s2-utility
      ask partner [
        set utility p2s1-utility
        set potential-utility p2s2-utility
      ]
    ][
    set utility p1s1-utility2
    set potential-utility p1s2-utility2
    ask partner [
      set utility p2s2-utility
      set potential-utility p2s1-utility
    ]
    ]
  ][
  ifelse partner-strategy1? = true [
    set utility p1s2-utility
    set potential-utility p1s1-utility
    ask partner [
      set utility p2s1-utility2
      set potential-utility p2s2-utility2
    ]
  ][
  set utility p1s2-utility2
  set potential-utility p1s1-utility2
  ask partner [
    set utility p2s2-utility2
    set potential-utility p2s1-utility2
  ]
  ]
  ]
end 

;partnered-turtle utility maximizer learning procedure
;if a turtle could've done better by choosing the other strategy, given their partner stays the same,
;then they become more likely to choose the other strategy.  If they're happy with their decision,
;they become more likely to make the same decision

to utility-max
  ifelse strategy1? = true [
    if utility < potential-utility [
      set prob-s1 prob-s1 - (.001 * (potential-utility - utility))
      set prob-s2 prob-s2 + (.001 * (potential-utility - utility))   
    ]
  ][
  if utility < potential-utility [
    set prob-s1 prob-s1 + (.001 * (potential-utility - utility))
    set prob-s2 prob-s2 - (.001 * (potential-utility - utility))
  ]
  ]
end 

;partnered-turtle competitive learning procedure
;If a turtle loses to their opponent, then they become less likely to make the same decision.  They're 
;indifferent to ties though

to seek-fair
  ifelse strategy1? = true [
    if utility < [utility] of partner [
      set prob-s1 prob-s1 - (.001 * (([utility] of partner) - utility))
      set prob-s2 prob-s2 + (.001 * (([utility] of partner) - utility))     
    ]
  ][
  if utility < [utility] of partner [
    set prob-s1 prob-s1 + (.001 * (([utility] of partner) - utility))
    set prob-s2 prob-s2 - (.001 * (([utility] of partner) - utility))
  ]
  ]
end 

;player1 partnered-turtle predictor learning procedure
;They look at whether or not their partner made their best decision.  The turtles assume that their partner will tend 
;towards making the best decision.  They then respond with their best decision.    

to predict-blue
  ifelse partner-strategy1? = true [
    ifelse [potential-utility] of partner > [utility] of partner [
      ifelse p1s1-utility2 > p1s2-utility2 [
        set prob-s1 prob-s1 + .001 * ([potential-utility] of partner - [utility] of partner)
        set prob-s2 prob-s2 - .001 * ([potential-utility] of partner - [utility] of partner)
      ][
      set prob-s1 prob-s1 - .001 * ([potential-utility] of partner - [utility] of partner)
      set prob-s2 prob-s2 + .001 * ([potential-utility] of partner - [utility] of partner)      
      ]
    ][
    ifelse p1s1-utility > p1s2-utility [
      set prob-s1 prob-s1 + .001 * ([utility] of partner - [potential-utility] of partner)
      set prob-s2 prob-s2 - .001 * ([utility] of partner - [potential-utility] of partner)
    ][
    set prob-s1 prob-s1 - .001 * ([utility] of partner - [potential-utility] of partner)
    set prob-s2 prob-s2 + .001 * ([utility] of partner - [potential-utility] of partner)
    ]
    ]
  ][
  ifelse [potential-utility] of partner > [utility] of partner [
    ifelse p1s1-utility > p1s2-utility [
      set prob-s1 prob-s1 + .001 * ([potential-utility] of partner - [utility] of partner)
      set prob-s2 prob-s2 - .001 * ([potential-utility] of partner - [utility] of partner)     
    ][
    set prob-s1 prob-s1 - .001 * ([potential-utility] of partner - [utility] of partner)
    set prob-s2 prob-s2 + .001 * ([potential-utility] of partner - [utility] of partner)
    ]
  ][
  ifelse p1s1-utility2 > p1s2-utility2 [
    set prob-s1 prob-s1 + .001 * ([utility] of partner - [potential-utility] of partner)
    set prob-s2 prob-s2 - .001 * ([utility] of partner - [potential-utility] of partner)
  ][
  set prob-s1 prob-s1 - .001 * ([utility] of partner - [potential-utility] of partner)
  set prob-s2 prob-s2 + .001 * ([utility] of partner - [potential-utility] of partner)
  ]
  ]
  ]
end 

;player2 partnered-turtle predictor learning procedure

to predict-red
  ifelse partner-strategy1? = true [
    ifelse [potential-utility] of partner > [utility] of partner [
      ifelse p2s1-utility2 > p2s2-utility2 [
          set prob-s1 prob-s1 + .001 * ([potential-utility] of partner - [utility] of partner)
          set prob-s2 prob-s2 - .001 * ([potential-utility] of partner - [utility] of partner)
      ][
        set prob-s1 prob-s1 - .001 * ([potential-utility] of partner - [utility] of partner)
        set prob-s2 prob-s2 + .001 * ([potential-utility] of partner - [utility] of partner)
      ]
    ][
    ifelse p2s1-utility > p2s2-utility [
        set prob-s1 prob-s1 + .001 * ([utility] of partner - [potential-utility] of partner)
        set prob-s2 prob-s2 - .001 * ([utility] of partner - [potential-utility] of partner)
    ][
      set prob-s1 prob-s1 - .001 * ([utility] of partner - [potential-utility] of partner)
      set prob-s2 prob-s2 + .001 * ([utility] of partner - [potential-utility] of partner)
    ]
    ]
  ][
  ifelse [potential-utility] of partner > [utility] of partner [
    ifelse p2s1-utility > p2s2-utility [
        set prob-s1 prob-s1 + .001 * ([potential-utility] of partner - [utility] of partner)
        set prob-s2 prob-s2 - .001 * ([potential-utility] of partner - [utility] of partner)
    ][
      set prob-s1 prob-s1 - .001 * ([potential-utility] of partner - [utility] of partner)
      set prob-s2 prob-s2 + .001 * ([potential-utility] of partner - [utility] of partner)
    ]
  ][
  ifelse p2s1-utility2 > p2s2-utility2 [
      set prob-s1 prob-s1 + .001 * ([utility] of partner - [potential-utility] of partner)
      set prob-s2 prob-s2 - .001 * ([utility] of partner - [potential-utility] of partner)
  ][
    set prob-s1 prob-s1 - .001 * ([utility] of partner - [potential-utility] of partner)
    set prob-s2 prob-s2 + .001 * ([utility] of partner - [potential-utility] of partner)
  ]
  ]
  ]
end