Leadership Emergence in Teams

turtles-own [lead_expect; how fitting the individual appears to be a leader in general or for the specific task (might change with task)
             lead_schem; how much person thinks of themself as leader (partly due to lead_schem)
             fol_schem;  how much person thinks of themself as follower
             public_lead_hist
             private_lead_hist
             pen-color ; color variable: tutles own a color but don't display it;
             leader_duration;
             leader_stability

]


globals [
burn-in
succesfull_interactions
observer_action
]

links-own [LP_1 LP_2]

to setup
  clear-all
  create-turtles number_of_people
  set-default-shape turtles "person"
  layout-circle turtles 14
  set burn-in 0
  set observer_action 0
  set succesfull_interactions 0

  let color-list [45 12 62 67 18 82 90 97 105 114 124 127 138 139 19 29 blue 49 57 44 14 87 133] ; this is the list with 30 possible colors
  ask turtles [
    set lead_expect m - initial_range / 2 + random (initial_range)
    set lead_schem m - initial_range / 2 + random (initial_range)
    set fol_schem m
    set public_lead_hist 0
    set private_lead_hist 0


    ifelse not empty? color-list [
      let ind one-of range length color-list ; randomly chooses an index
      set pen-color item ind color-list ; Have the turtle choose from color-list using that index
      set color-list remove-item ind color-list   ; Remove indexed value from color-list, otherwise colors will repeat!!
    ] [
      set pen-color gray ; Assign gray if all colors used (technically, should not happen, unless number of turtles > 30)
    ]

    set size (lead_expect / (.7 * m))
    set color gray ; if this is commented out then turtles will appear in their assigned color
  ]

  reset-ticks
end 

to go
  dyadic_interaction
  update
  tick
end 

to dyadic_interaction
    ask one-of turtles [
      if print_reasoning = true [print who]

      let target one-of other turtles
      ask target [
            if print_reasoning = true [print who]
      ]

      ;establishing the link
      if not in-link-neighbor? target [ ; creates a link if there was none sofar
         create-link-with target [
            set LP_1 0
            set LP_2 0
         ]
      ]
      let dyad_lead_hist_a 0
      let dyad_lead_hist_b 0
      ifelse who < [who] of target [ ; the link stores succesfull leadership and successfull followership which are now taken out
        set dyad_lead_hist_a [LP_1] of link (who) ([who] of target)
        set dyad_lead_hist_b [LP_2] of link (who) ([who] of target)
      ] [
        set dyad_lead_hist_a [LP_2] of link (who) ([who] of target)
        set dyad_lead_hist_b [LP_1] of link (who) ([who] of target)
      ]

      ;claiming and granting
      let lead_perc_a (2 * rel_col_hist * public_lead_hist) + (2 * (1 - rel_col_hist) * dyad_lead_hist_a) + lead_expect ; what the individual thinks the other think about them
      let lead_perc_b (2 * rel_col_hist * [public_lead_hist] of target) + (2 * (1 - rel_col_hist) * dyad_lead_hist_b) + [lead_expect] of target ; what the individual thinks about the other

      let aclaim is_claiming (lead_schem + private_lead_hist) (fol_schem - private_lead_hist) lead_perc_a
      if print_reasoning = true [print word "A claimed" aclaim]
      let agrant is_granting lead_perc_b (fol_schem - private_lead_hist)

      let bclaim is_claiming ([lead_schem] of target + [private_lead_hist] of target) ([fol_schem] of target - [private_lead_hist] of target) lead_perc_b
      if print_reasoning = true [print word "B claimed" bclaim]
      let bgrant is_granting lead_perc_a ([fol_schem] of target - [private_lead_hist] of target)

      if lss = "hierarchical" [
         if (aclaim = True) [set agrant False]
         if bclaim = True [set bgrant False]
      ]

      if lss = "hierarchical + status comparison" [
         if (aclaim = True) and lead_perc_a > lead_perc_b [set agrant False]
         if bclaim = True and lead_perc_b > lead_perc_a [set bgrant False]
      ]

      if print_reasoning = true [print word "A granted" agrant]
      if print_reasoning = true [print word "B granted" bgrant]

      ;dyadic score changes
      ask link (who) ([who] of target) [
        (ifelse (aclaim = True) and (bgrant = True) [
          ifelse [who] of end2 = [who] of target [ ; a succesfull interaction stabilises their view on themselfes and the other
             set LP_1 LP_1 + .5 - .5 * abs (LP_1 / max_hist)
             ;set LP_2 LP_2 - .5 + .5 * abs (LP_2 / max_hist)
          ] [
             set LP_2 LP_2 + .5 - .5 * abs (LP_2 / max_hist)
             ;set LP_1 LP_1 - .5 + .5 * abs (LP_1 / max_hist)
         ]
          set color green
        ](agrant = True) and (bclaim = True) [
         ifelse [who] of end2 = [who] of target [
          set LP_2 LP_2 + .5 - .5 * abs (LP_2 / max_hist)
          ;set LP_1 LP_1 - .5 + .5 * abs (LP_1 / max_hist)
        ] [
          set LP_1 LP_1 + .5 - .5 * abs (LP_1 / max_hist)
          ;set LP_2 LP_2 - .5 + .5 * abs (LP_2 / max_hist)
        ]
          set color green
         ][
          set color red
         ])
    ]

    ; private and public score changes
    if (aclaim = True) and (bgrant = True) [
      set private_lead_hist private_lead_hist + .5 - .5 * abs(private_lead_hist / max_hist)
      set public_lead_hist public_lead_hist + .5 - .5 * abs(public_lead_hist / max_hist)
      ask target [
        set private_lead_hist private_lead_hist - .5 + .5 * abs(private_lead_hist / max_hist)
        set public_lead_hist public_lead_hist - .5 + .5 * abs(public_lead_hist / max_hist)
      ]
      set succesfull_interactions succesfull_interactions + 1
    ]
    if (bclaim = True) and (agrant = True) [
      set private_lead_hist private_lead_hist - .5 + .5 * abs(private_lead_hist / max_hist)
      set public_lead_hist public_lead_hist - .5 + .5 * abs (public_lead_hist / max_hist)
      ask target [
        set private_lead_hist private_lead_hist + .5 - .5 * abs(private_lead_hist / max_hist)
        set public_lead_hist public_lead_hist + .5 - .5 * abs (public_lead_hist / max_hist)
      set succesfull_interactions succesfull_interactions + 1
      ]
    ]
    if (aclaim = False) and (bgrant = False) [
      set private_lead_hist private_lead_hist - .25 + .25 * abs(private_lead_hist / max_hist)
      ;set public_lead_hist public_lead_hist - .25 + .25 * abs (public_lead_hist / max_hist)
    ]
    if (bclaim = False) and (agrant = False) [ask target [
      set private_lead_hist private_lead_hist - .25 + .25 * abs(private_lead_hist / max_hist)
      ;set public_lead_hist public_lead_hist - .25 + .25 * abs (public_lead_hist / max_hist)
    ]]
    ]
end 

to update
  let n 1
  foreach sort-on [(-(lead_expect + public_lead_hist))] turtles [
    the-turtle ->
    ask the-turtle[
      set label n
      set n n + 1
    ]
  ]
  ask turtles [
    ifelse label = 1 and burn-in > 0 [set shape "person business"] [set shape "person"]

   set public_lead_hist (1 - hist_decay) * public_lead_hist
   set private_lead_hist (1 - hist_decay) * private_lead_hist
   set size 1 + (lead_expect + public_lead_hist) / (m + max_hist)
  ]
  ask links [
    set thickness (abs LP_1) / (1.0 * max_hist)
    set LP_1 (1 - hist_decay) * LP_1
    set LP_2 (1 - hist_decay) * LP_2
  ]
  if burn-in > 0 [
      ask max-n-of 1 turtles [(lead_expect + public_lead_hist)] [
      set leader_duration leader_duration + 1
      set leader_stability leader_duration / (ticks - burn-in)
      ; percent
      ;
    ]
  ]
  if burn-in = 0 and (max [public_lead_hist] of turtles > .50 * max_hist) [
    set burn-in ticks
  ]
 set observer_action observer_action - .5
end 

to-report is_claiming [li fi lp]
  let alpha (li + lp) * .05
  let beta (fi) * .1
  let prob_claim random-beta alpha beta
  if print_reasoning = true [print word "Probability of claiming " prob_claim]
  report random-float 1 > (1 - prob_claim)
end 

to-report is_granting [lp_other fi]
  let alpha 0.05 * lp_other
  let beta  0.1 * (2 * m - fi)
  let prob_grant random-beta alpha beta
  if print_reasoning = true [print word "Probability of granting " prob_grant]
  report random-float 1 > (1 - prob_grant)
end 

to scandal
  let leader-turtle max-one-of turtles [((lead_expect + public_lead_hist) / m)]
  ask links with [end1 = leader-turtle or end2 = leader-turtle] [
    die
  ]
    ask max-n-of 1 turtles [((lead_expect + public_lead_hist) / m)]  [ ; right now targets the "leader" based on size; can change to leader_schem
    set public_lead_hist 0 - max_hist
  ]
  set observer_action 1
end 

to kill
 ask max-n-of 1 turtles [((lead_expect + public_lead_hist) / m)]  [
   die
  ]
  set observer_action 1
end 

to task-change
  ask turtles [
    let change random (m / 4) - m / 8
    print(change)
    set lead_expect lead_expect + change
    set lead_schem lead_schem + change
  ]
  set observer_action 1
end 

to-report random-beta [ #alpha #beta ]
  if #alpha <= 0 [set #alpha 0.1]
  if #beta <= 0 [set #beta 0.1]
  let XX random-gamma #alpha 1
  let YY random-gamma #beta 1
  report XX / (XX + YY + .0001)
end