Social Capital and Social Networks

globals [ capital-list  total-capital weighted-degree-list total-weighted-degree average-weighted-degree
  P1RProR P1RProNR P1RAntiR P1RAntiNR P2RProR P2RProNR P2RAntiR P2RAntiNR Connections Connected-People Dunbar Bond max-connected-capital ]

links-own [ capital happy? link-weighted-degree-list max-weighted-degree ]

turtles-own [ degree weight-list weighted-degree ]

;; %-Reaction-to-Pro-Behaviour is the probability of Player 2 reacting to pro-group action by Player 1, it is a social norm and applies to all people
;; Reaction to Anti-Behaviour decreases the degree to which social capital reduces the level of anti group action, it has the effect of increasing reaction to anti group action

to setup

  ;; set the initial values of every variable

  clear-all ;; clear all old settings

  ask patches [ set pcolor white]  ;; makes the background white

  ;; set up the network

  create-turtles People [ set color black set shape "person"  ] ;; this sets the group size and the people characteristics

  set connected-people ( 2 + ceiling ( ( People - 2 ) * ( Interdependence / 10 ) ) ) ;; sets the number of people with connections based on the level of Atraction

  set connections (  ceiling ( ( connected-people - 1 ) * ( Interdependence / 10 ) ) ) ;; sets the number of Connections for Connected People based on the level of Attraction

  ask n-of connected-people turtles [ create-links-with n-of connections other turtles ] ;; creates the Connections between Connected People and other People

  set max-connected-capital ( count turtles with [ count my-links > 0 ] - 1 ) * 10 ;; sets the maximum group social capital based on the number of connected people rather than
  ;; all the people in the group, some of whom may not be connected

  repeat 30 [ layout-spring turtles links 0.2 18 1 ] ;; spreads out the network to improve presentation

  ;; set the reward table values

  set P1RProR 1 set P1RProNR -2 set P1RAntiR -1 set P1RAntiNR 2 set P2RProR 1 set P2RProNR 2 set P2RAntiR -1 set P2RAntiNR -2

  ;; set the maximum level of bonding capital for a person following Rbin Dunbar's 150 theory

  set Dunbar (ifelse-value
   People < 6 [ People * 10 ]
   People > 5 and People < 16 [ 50 + ( ( People - 5 ) * 6.6 ) ]
   People > 15 and People < 50 [ 116 + ( ( People - 15 ) * 4.4 ) ]
               [ 263 + ( ( People - 50 ) * 2.9 ) ])

  set Bond Interdependence * Dunbar / ( People * 10 )

  ;; set up the social capital measure using link capital

  ask links [ set capital random Bond + 1
    set thickness capital / 40 set color black set shape "capital"]

  ;; sets the initial capital of each link and link characteristics

  set capital-list [ capital ] of links ;; creates a list of all the link capitals

  set total-capital 2 * sum capital-list / count turtles ;; total-capital is the average of the total link capital per person which is the average weighted degree and group social capital

  ;; set up the social capital measure using turtle degree and link weight

  ask turtles [ set degree count my-links set weight-list [ capital ] of my-links

    set weighted-degree sum weight-list

    set size (1 + weighted-degree / ( 2 * count turtles ) ) ] ;; sets the degree and weighted-degree of each turtle

  set weighted-degree-list [ weighted-degree ] of turtles ;; lists the weighted degrees of all the turtles
  set total-weighted-degree sum weighted-degree-list ;; calculates the total weighted degree of all the turtles combined
  set average-weighted-degree total-weighted-degree / count turtles ;; calculates the average weighted degree which is the social capital of the group

  ;; set up the link view of the weighted degree of the people at each end

  ask links [ set link-weighted-degree-list [ weighted-degree ] of [ both-ends ] of self

  set max-weighted-degree max [ link-weighted-degree-list ] of self ]

  reset-ticks
end 

to go

  every 0.05 [

  if count links = 0 [ set average-weighted-degree 0 set total-capital 0 plot total-capital ask turtles [ die ] stop  ] ;; stops the run if social capital is zero

    ask links [ repeat ( capital ) [ decide reset ] ] ;; Player 1 decides whether to act pro-group or anti-group based on probable rewards

   ;; and the change in social capital for each pair is based on rewards for both Player 1 and Player 2

  ask one-of turtles with [ degree > 0 ] [ grow ] ;; people decide whether to add or subtract connections to other people based on their level of social capital

  repeat 30 [ layout-spring turtles links 0.2 18 1 ]

  set max-connected-capital ( count turtles with [ degree > 0 ] - 1 ) * 10 ;; sets the maximum capital of the number of connected people rather than
  ;; all the people in the group, some of whom may be disconnected

  ;; set the NEW values of turtle variables and re-calculate group capital based on people attributes

  ask turtles [
    set degree count my-links
    set weight-list [ capital ] of my-links
    set weighted-degree sum weight-list
    set size (1 + weighted-degree / ( 2 * count turtles ) )
  ]
  set weighted-degree-list [ weighted-degree ] of turtles
  set total-weighted-degree sum weighted-degree-list
  set average-weighted-degree total-weighted-degree / count turtles


  ;; set the NEW values of link capital and re-calculate group social capital based on link attributes

  set capital-list [ capital ] of links
  set total-capital 2 * sum capital-list / count turtles

  ;; reset the link view of the weighted degree of the people at each end

  ask links [ set link-weighted-degree-list [ weighted-degree ] of [ both-ends ] of self

  set max-weighted-degree max [ link-weighted-degree-list ] of self ]



  tick ] ;; go again
end 

to decide

  ;; Player 1 decides whether to act pro or anti Player 2

  ;; set the current pro and anti reaction probabilities
  let ProR ( Reaction-to-Pro-Behaviour / 100 )
  let ProNR 1 - ProR
  let AntiR (1 - ( Capital / ( Reaction-to-Anti-Behaviour * 10 ) ) ) ;; increasing Reaction to Anti Behaviour lessens the reduction impact of higher Capital on AntiR
  let AntiNR 1 - AntiR

  ;; calculate the current pro and anti rewards for Player 1
  let P1RPro ProR * P1RProR + ProNR * P1RProNR
  let P1RAnti AntiR * P1RAntiR + AntiNR * P1RAntiNR

  ;; Player 1 decides on pro or anti group action
  ifelse P1RPro >= P1RAnti  [ set happy? true ]  [ set happy? false ] ;; happy attribute equals do pro, not happy equals do anti
end 

to reset

  ;; based on P1 decision, calculate the increase or decrease in capital for Player 1 plus Player 2, the change in individual link capital
  let ProR ( Reaction-to-Pro-Behaviour / 100 )
   ;; let ProNR 1 - ProR only needed if reward table changed
  let AntiR 1 - ( capital / ( Reaction-to-Anti-Behaviour * 10 ) )
   ;; let AntiNR 1 - AntiR only needed if reward table changed

  ifelse happy? = true

  [ if max-weighted-degree < Dunbar [ set capital capital + ( ProR * 0.01 ) ] ] ;; set new capital for pro action if people at each end have not exceeded capacity
  ;; different equation required if reward table revised
  ;; ( ProR * ( P1RProR + P2RProR ) + ProNR * ( P1RProNR + P2RProNR ) )

  [ set capital capital + ( AntiR * -0.01 ) ] ;; set new capital for anti action, different equation required if reward table revised
  ;; ( AntiR * ( P1RAntiR + P2RAntiR ) + AntiNR * ( P1RAntiNR + P2RAntiNR ) )

  ask links [ if capital >= 10 [ set capital 10 ] ] ;; restricts the capital of a link to the maximum possible
  ask links [ set thickness capital / 40  ] ;; sets the size of the link to match new capital
end 

to grow

 ;; people decide whether to create new connections or break old ones based on their personal level of social capital

 ;; individual person decides whether to add a connection

 if ( weighted-degree / degree ) > ( 10 - ( ( Interdependence ) / 1.5 ) ) and weighted-degree < Dunbar [ create-link-with one-of other turtles
    [ set capital random Interdependence + 1 set thickness capital / 40 set color red set shape "capital" ]
    set degree count my-links set size (1 + weighted-degree / ( 2 * count turtles ) ) ]

 ;; individual person decides whether to sever a connection

 if ( weighted-degree / degree ) <  ( ( 10 - Interdependence  ) / 1.5  ) and ( count my-links > 0 )
    [ ask one-of my-links  [ die ]
    set degree count my-links set size (1 + weighted-degree / ( 2 * count turtles ) ) ]
end