social_ecomoic_networks_model.nlogo

extensions [ nw ]

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

  ;; create the turtles
  create-turtles number-of-nodes [
    set size 4
    set color red]

  ;; create a star network
  if network = "star" [
    ask one-of turtles [ ask other turtles [create-link-with myself] ]
  ]
  ;; layout the turtles
  layout-circle turtles 40
  ;; update the utilities
  ask turtles [ set label precision calc-utility 3 ]

  reset-ticks
end

to go
  ;; try to create a new link in the community assuring that it is pairwise stable
  make-link
  ;; try to remove one link in the community that is not pairwise stable
  remove-link
  tick
end

;; make a new link between two of the turtles
;; assure that the link is pairwise stable
to make-link
  ;; choose one of the nodes
  let node one-of turtles
  ask  node [
    ;; make a link
    create-link-with one-of other turtles [
      ;; assure it is pairwise stable
      ;; if not remove the link
      if ([calc-utility] of myself < [label] of myself) or
      ([calc-utility] of node < [label] of node)
      [ die ]
      ]
  ]
  ;; update utility of turtles
  ask turtles [set label precision calc-utility 3 ]
end

;; remove a link between two of the turtles
;; assuring that the end result is pairwise stable
to remove-link
  ;; chose one random link
  let l one-of links
  ;; if there is one
  if l != nobody [
    ;; extract end nodes
    let ab sort [both-ends] of l
    ;; remove the link
    ask l [ die ]
    ;; assure the removal is pairwise stable
    ;; if not reconnect end nodes
    if ([calc-utility] of item 0 ab <= [label] of item 0 ab) and
          ([calc-utility] of item 1 ab <= [label] of item 1 ab)
    [ask item 0 ab [create-link-with item 1 ab ]]
    ;; update utility of turtles
    ask turtles [set label precision calc-utility 3 ]
  ]
end


;; calculate the utility according to the connections model

to-report calc-utility
  let ni [ count link-neighbors] of self
  let nj-sum 0
  let nj 0
  ask link-neighbors [
    set nj [ count link-neighbors] of myself
    if (nj != 0 ) [set nj-sum nj-sum + 1 / nj ]
  ]
  let utility 0
  if (nj-sum != 0) [ set utility 1 + (1 + 1 / ni ) * ( nj-sum) ]
  report utility
end
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GRAPHICS-WINDOW
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ticks
60.0

BUTTON
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NIL
setup
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T
OBSERVER
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1

BUTTON
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NIL
go
T
1
T
OBSERVER
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BUTTON
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go-once
go
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T
OBSERVER
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SLIDER
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delta
delta
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HORIZONTAL

SLIDER
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cost
cost
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HORIZONTAL

SLIDER
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110
number-of-nodes
number-of-nodes
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NIL
HORIZONTAL

MONITOR
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105
314
global wellfare
sum [label] of turtles
3
1
11

CHOOSER
88
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188
66
network
network
"empty" "star"
1

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## Answer 1

As we can see from the model, that we are getting a pair-wise stable network with N/2 seperate fully intraconnected pairs, when we run it for even number of nodes.Also this configuration yields the maximum global welfare (equal to number-of-node * 3). 

## Answer 2

Running our model again for even number of nodes, we see that we get N/2 components seperate components, each of size 2 and the next lowest size of component is 0. Therefore, we can verify that 2 > 0 ^ 2 as 2 > 0. Hence the proposition 2, i.e, a pairwise stable network can be partitioned into fully intraconnected components, each of which has a different number of members, can also be verified. 
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NetLogo 6.2.0
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set layout? false
set plot? false
setup repeat 300 [ go ]
repeat 100 [ layout ]
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default
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Line -7500403 true 150 150 210 180
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0
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