Throwing Coins - Inequality and Tax

; Throwing Coins - Inequality and Tax.nlogo; Rupert Nagler Jan 2020

globals [
  gini-index-reserve ; actual Gini %
  lorenz-points ; list of Lorenz points
  coins ; number of thrown coins
  tails ; number of tails - results
]

turtles-own [
  wealth ; actual wealth of turtle
  tax ; actual amount of wealth tax turtle has payed
]

to setup
  clear-all
  ask patches [set pcolor 104]
  setup-turtles
  set coins 0
  set tails 0
  update-lorenz-and-gini
  reset-ticks
end 

to setup-turtles
  create-turtles num-turtles [
    set heading 0
    set color yellow
    set shape "circle"
    ifelse random-init-wealth? [; random distributuion
      set wealth random-float init-wealth
    ][; equal distribution
      set wealth init-wealth
    ]
    set tax 0
    ; place turtle on plain according id(own) on x-axsis and wealth on y-axsis
    setxy (who / num-turtles * 100) wealth
  ]
end 

to go
  playing
  taxing
  move-turtles
  if not any? turtles [stop]
  update-lorenz-and-gini
  tick
end 

to playing ; each turtle throws coin
  ask turtles [ ; leverage is the fraction of wealth to bet
    set wealth win (wealth * leverage) + wealth * (1 - leverage); compute new wealth on thrown coin
  ]
end 

to-report win [stake] ; function to compute new wealth according to coin throw with multiplicative and additive win
  let m mult-heads ; initialise with win factors
  let a add-heads
  set coins coins + 1
  if one-of list false true [ ; throw coin, in case loose change to loose factors
    set m mult-tails
    set a add-tails
    set tails tails + 1
  ]
  report (stake * m) + a
end 

to taxing
  if tax-factor > 0 [ ; do we have to compute taxes?
    let notax-turtles [self] of no-turtles ; empty unsorted list of turtles
    let sumtax 0
    ask turtles [ ; pay wealth tax
      ifelse wealth > tax-limit [ ; is there a tax to pay?
          set tax wealth * tax-factor
          set wealth wealth - tax ; turtle pays tax
          set sumtax sumtax + tax ; add to total tax collected
        ] [
          set tax 0
          set notax-turtles lput self notax-turtles ; add to list of notax-turtles
        ]
    ]
    let count-notax-turtles length notax-turtles ; number of notax-turtles
    ifelse redist-all? or (count-notax-turtles <= 0) [ ; do we have to redistribute to all turtles?
      let mtax (sumtax / count turtles) ; divide total tax between all turtles
      ask turtles [ ; redistribute tax to all turtles
        set wealth wealth + mtax ; redistribute
      ]
    ] [; divide total tax between all no-tax-turtles
      let mtax (sumtax / count-notax-turtles)
      ask turtle-set notax-turtles [ ; changes list into agentset
        set wealth wealth + mtax ; redistribute
      ]
    ]
  ]
end 

to move-turtles ; according to new wealth
  ask turtles [
    if turtles-die? [ ; should bancrupt turtles die?
      if wealth < 1.0E-10 [die]
    ]
    set ycor (wealth + min [wealth] of turtles) / max [wealth] of turtles * 100
  ]
end 

to update-lorenz-and-gini
  ; recompute value of gini-index-reserve and the points in lorenz-points for the Lorenz and Gini-Index plots
  let sorted-wealths sort [wealth] of turtles
  let total-wealth sum sorted-wealths
  let wealth-sum-so-far 0
  let index 0
  let c-turtles count turtles
  set gini-index-reserve 0
  set lorenz-points []
  ; now actually plot the Lorenz curve -- along the way, we also calculate the Gini index
  repeat c-turtles [
    set wealth-sum-so-far (wealth-sum-so-far + item index sorted-wealths)
    set lorenz-points lput ((wealth-sum-so-far / total-wealth) * 100) lorenz-points
    set index (index + 1)
    set gini-index-reserve gini-index-reserve + (index / c-turtles) - (wealth-sum-so-far / total-wealth)
  ]
end