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view/download model file: uniform et triangulaireVERSIONmai2013.nlogo
A prisoner dilemma game with emotions. The payoff of a player i is given by
Other player
cooperate defect
cooperate (green) G - C -C
player i
defect (red) G - X 0
X is uniform in [0 1]. It is i’s idiosyncratic emotion (shame) when she violates the cooperative norm and faces a cooperator. If X= 0 then we have a prisoner’s dilemma.
to setup
to go
- choose randomly a number of “moving-turtles”:
- the moving-turtles inspect their sample (number of reds and greens in the sample) and decide to cooperate or defect in the next period by choosing a best response to the sample configuration. With a probability “Tremble” the choice is stochastic.
- once the choice is made an updating procedure follows: each moving-turtle update his choice (color may change)
- All turtles update their fitness given the choice of the player (including the passive player who sticked to their last choice in the current period.
- All global variables are updated (%-cooperators, %-defectors, mean-emotion of cooperators and defectors, mean fitness in the population, segregation ) as well as the The state space of population configuration (colors)
- a statistic of unhappy defectors is computed : unhappy defectors are those turtles who would like to cooperate given the proportion of cooperators in the population but who are forced to defect given the chosen environment configuration.
Defining fitness: Fitness of a turtle over one period is the average payoff in the prisoner’s dilemma given the proportion of cooperators (X is excluded from the calculus). Total fitness equals to the sum of the turtle’s fitness over a number of period of length “memory”. Normalized_fitness of a turtle equals to (total_fitness + ( C * memory ) ) / ( memory * (G + C) ).
The rate of cooperation
Segregation emerges almost always with local interaction and small sample size when the bifurcation point is below 50%.
criminality on my web page http://perso.telecom-bretagne.eu/rogerwaldeck/data/applet/criminality/criminality_prog_18.html .
R. Waldeck. Segregated cooperation. in JASSS .
The segregation and interaction procedure has been inspired from Sebastian Grauwin
http://ccl.northwestern.edu/netlogo/models/community/Segreg-vs-coord . All errors my own.
;;; BY ROGER WALDECK 2013 : In this version:
; emotions are represented by ligth or darker cells depending on their intensity
; all individual update their fitness and not only passive ones (cf. Jasss paper);
; fitness is updtated according to actual play
extensions [array]
globals [
Xmax ; max emotion
radius-n ; radius of a neighborhood
%-cooperators ; proportion of green players : scale 100
list-%-cooperation ; list of length "memory " of %-cooperators over the last memory periods
mean-coop ; mean of the above list
sd-coop ; standard deviation of the above list
%-emotion-cooperators ; mean emotion of cooperators scale 100
%-emotion-defectors ;
cooperators ; number of greens = cooperator
defectors ; number of reds
emotions-cooperators ; list of emotions of cooperators
emotions-defectors
mean-emotion ; mean emotion in the population on scale 100
tab ; array by who number of actions (cooperate, defect) of turtles
tab-emotion ; array by who population of emotions of players
population ; number of turtles
G ; payoff from cooperation
tab-fitness ; array by who number of normalized fitness.
mean-fitness-cooperators ; for each period computes the average normalized fitness of cooperative turtles with Normalized_fitness of a turtle is equalt to (total_fitness + ( C * memory ) ) / ( memory * (G + C) )
mean-fitness-defectors ;
mean-fitness
N-size ; the size of the sample chosen by turtles given the move in the period (moving-turtles)
X_c ; threshold level of emotion for a turtle to cooperate ; if emotion of turtle is greater than X_c his best response is to cooperate. If matching was population wide the turtle with emotion > X_c (= C * 100 / %-cooperators) would cooperate.
unhappy-turtles ; ; given the prevailing % of cooperators, these turtles would like to cooperate given their emotion (emotion > X_c) but are prisonner of to much defection in their sample
%-unhappy-turtles ; % of unhappy-turtles on scale 100
list-unhappy? ; a list of length "memory " of %-unhappy-turtles over the last memory periods
mean-unhappy? ; mean of the above list
sd-unhappy? ; standard deviation of the above list
random-mixed-pairs ; the mean of the mixed pairs under a random configuration with %-cooperators
mixed-pairs ; number of pairs of green-red neighbors (turtles procedure i.e. ask over all turtles)
segregation ; index of segregation
list-segregation ; creates a list of length "memory of segregation
mean-segreg ; mean of the above list
sd-segreg ; standard deviation of the above list
my-seed1
init_coop
expected_equilibrium
equilibrium ; expected equibrium for triangular distribution
stable ; stable expected equibrium for triangular distribution
unstable ; unstable expected equibrium for triangular distribution
]
turtles-own [
emotion ; emotion of one turtle
a ; emotion minus cost of cooperation C
red-nearby-pondere ; total payoff for a red turtle resulting from green and red turtles in the sample of N-size of the turtle. If Neighborhood is on the sample is with neighbors if not the sample is random.
green-nearby-pondere
fitness_list ; list of lenght "memory" of past and current fitness of each turtle
total_fitness ; sum of fitness-list. - C * memory <= Total fitness <= G * memory
normalized_fitness ; normalized_fitness = (total_fitness + ( C * memory ) ) / ( memory * (G + C) ). If C = 1, normalized_fitness= (total_fitness + C* memory) /2C*memory
numberB ; if numberB = 1 the turtle cooperates if numberB = 0 , the turtle defects
fitness ; Fitness for one period is defined by
; if the turtle cooperates the fitness is given by G - C if all other turtles in the sample cooperate and - C if all defects
; if defect the fitness is given by G if all cooperate and 0 if all defect. It is a prisonner dilemma.
;similar-nearby ; how many neighboring patches have a turtle with my color?
other-nearby ; how many turtles of a different color in the sample of the calling turtle
red-nearby ; count of red turtles in the sample
green-nearby ; count of green turtles in the sample
unhappy? ; if = 1 turtle is unhappy and if equal to 0 the turtle is happy
]
;;;;;;;;;;;;;; SETUP PROCEDURE ;;;;;;;;;;;
to setup
;; (for this model to work with NetLogo's new plotting features,
;; __clear-all-and-reset-ticks should be replaced with clear-all at
;; the beginning of your setup procedure and reset-ticks at the end
;; of the procedure.)
__clear-all-and-reset-ticks
ifelse random_seed
[ use-new-seed ]
[ use-seed-from-user ]
set list-segregation []
set list-unhappy? []
set list-%-cooperation []
set G 1
set Xmax 1
set population ((max-pxcor + 1) * (max-pycor + 1))
set-default-shape turtles "circle"
let populationA random population
ask n-of population patches
[sprout 1
[set color green
if (distribution = "triangular") [ set emotion (Xmax * (random-float 1)^ 0.5 ) ]
if (distribution = "uniform") [set emotion random-float Xmax ] ; chooses a value for emotion less than Xmax
set a (emotion - C)
] ] ; turtle specific parameter: a represents emotion - C of a turtle where C represents the cost of cooperation
ask n-of populationA turtles
[ set color red ]
ask turtles [ set fitness_list [] ]
choose-size
setup-array
update-variables
set init_coop %-cooperators
if distribution = "triangular" [compute-stable-and-unstable]
compute-expected-equilibrium
do-plots
end
to choose-size
;set cooperators count (turtles) with [color = green]
; set %-cooperators (Cooperators * 100 / population)
;; choice of sample size
if (chosen-size = "4-cells") [set radius-n 1 set N-size 4 ]
if (chosen-size = "8-cells") [set radius-n 1.5 set N-size 8]
if (chosen-size = "24-cells") [set radius-n 2.9 set N-size 24]
if (chosen-size = "44-cells") [set radius-n 3.9 set N-size 44]
end
to use-seed-from-user
; set my-seed read-from-string user-input "Enter a random seed (an integer):"
; output-print word "User-entered seed: " my-seed ;; print it out
random-seed my-seed ;; use the new seed
end
to use-new-seed
set my-seed1 new-seed ;; generate a new seed
output-print word "Generated seed: " my-seed1 ;; print it out
random-seed my-seed1 ;; use the new seed
end
to setup-array
set tab array:from-list n-values ((max-pxcor + 1) * (max-pycor + 1)) [0] ; turtles list of 1 (cooperator) and 0 (defectors)
set tab-emotion array:from-list n-values ((max-pxcor + 1) * (max-pycor + 1)) [0] ; turtles list of emotions
set tab-fitness array:from-list n-values ((max-pxcor + 1) * (max-pycor + 1)) [0]
ask turtles [
ifelse [color] of self = green [set numberB 1][set numberB 0] ; for counts the number of green B= 1 and number of red B=0
array:set tab who numberB ; the array are ranged according to who numbers and value = numberB for all turtles
array:set tab-emotion who emotion ]; creates the array of turtles emotions ordered by who numbers
end
;;;;; GO PROCEDURE ;;;;;;
to go
if (ticks >= Max-ticks)[stop]
ifelse neighbourhood = "local" ; if booleab true reports a local neighbourhood if not a random one.
[update-tab1]
[update-tab2]
update-variables
tick
do-plots
end
to update-tab1
ask-concurrent n-of moving-turtles turtles [
set red-nearby (count other turtles in-radius radius-n with [numberB = 0] )
set green-nearby (count other turtles in-radius radius-n with [numberB = 1] )
set red-nearby-pondere ( red-nearby * C ) ; payoff from defecting from a best reponse equivalent game
set green-nearby-pondere (green-nearby * a ) ; payoff from cooperating from a best reponse equivalent game
let incert random 100
ifelse incert < tremble
[ let alea2 random 2
ifelse alea2 = 0 [set numberB 1] [set numberB 0] ]
[ let alea random 2 ; if not tremble then chose strategy optimally
if red-nearby-pondere = green-nearby-pondere
[ifelse alea = 0 [set numberB 1] [set numberB 0]] ; if payoff are equal then choose randomly
if red-nearby-pondere > green-nearby-pondere [set numberB 0] ; if payoff fom greens < payoffs from reds then choose 0 defect
if red-nearby-pondere < green-nearby-pondere [set numberB 1] ; ; if payoff fom green > payoofs from red then choose 1 cooperate
array:set tab who numberB ; updtate the strategy of the randomly chosen by turtle1
] ]
ask turtles [
set red-nearby (count other turtles in-radius radius-n with [numberB = 0] )
set green-nearby (count other turtles in-radius radius-n with [numberB = 1] )
ifelse numberB = 1
[set fitness (green-nearby / N-size ) * G - C ]
[set fitness (green-nearby / N-size ) * G ]
ifelse ( length fitness_list < memory)
[set fitness_list lput fitness fitness_list ]
[ set fitness_list but-first fitness_list set fitness_list lput fitness fitness_list]
set total_fitness sum fitness_list ; computes the total fitness earned by a turtle over a number of period of length memory
set normalized_fitness (total_fitness + ( C * memory ) ) / ( memory * (G + C) ) ; computes the normalized fitness earned by a turtle over a number of period of length memory
; [set normalized_fitness (total_fitness + memory ) / ( memory * 2 ) ]
array:set tab-fitness who normalized_fitness
]
end
; the next is the procedure with a random sample of size N-size
to update-tab2
ask-concurrent n-of moving-turtles turtles [
let sample n-of N-size other turtles ; with [who != self] OK
set red-nearby count sample with [numberB = 0] ;OK
set green-nearby count sample with [numberB = 1]
set red-nearby-pondere red-nearby * C
set green-nearby-pondere green-nearby * a
let incert random 100
ifelse incert < tremble
[let alea2 random 2
ifelse alea2 = 0 [set numberB 1] [set numberB 0] ]
[ let alea random 2
if red-nearby-pondere = green-nearby-pondere
[ifelse alea = 0 [set numberB 1] [set numberB 0] ]
if red-nearby-pondere > green-nearby-pondere [set numberB 0] ; the turtle defect
if red-nearby-pondere < green-nearby-pondere [set numberB 1]] ; cooperate
array:set tab who numberB
]
ask turtles [
set red-nearby (count other turtles in-radius radius-n with [numberB = 0] )
set green-nearby (count other turtles in-radius radius-n with [numberB = 1] )
ifelse numberB = 1
[set fitness (green-nearby / N-size ) * G - C ]
[set fitness (green-nearby / N-size ) * G ]
ifelse (length fitness_list < memory)
[set fitness_list lput fitness fitness_list ]
[set fitness_list but-first fitness_list set fitness_list lput fitness fitness_list]
set total_fitness sum fitness_list
; ifelse C != 1
set normalized_fitness (total_fitness + ( C * memory ) ) / ( memory * (G + C) )
; [set normalized_fitness (total_fitness + memory ) / ( memory * 2 ) ]
array:set tab-fitness who normalized_fitness
]
end
to update-variables
update-colors
update-globals
update-unhappy
report-segreg
end
to
update-colors ; set the color of the turtle according to its decision in the current period
ask turtles [
ifelse (array:item tab who) = 1 [set color scale-color 65 (emotion ) 1.8 0][set color scale-color 15 (emotion ) 2 0 ] ;[set color green][set color red]
]
end
to update-globals
set Cooperators count (turtles) with [numberB = 1]
set Defectors count (turtles) with [numberB = 0]
set %-cooperators (Cooperators * 100 / population)
ifelse (ticks < memory)
[set list-%-cooperation fput %-cooperators list-%-cooperation
set mean-coop mean list-%-cooperation ] ;manque sd dev
[set list-%-cooperation fput %-cooperators list-%-cooperation
set list-%-cooperation but-last list-%-cooperation
set mean-coop mean list-%-cooperation
set sd-coop standard-deviation list-%-cooperation ]
ifelse Cooperators != 0
[ set X_c ( C * 100 / %-cooperators) ]
[ set X_c (Xmax + 1) ] ; fix a number bigger than X max
if count (turtles) with [numberB = 1] != 0 [ set emotions-cooperators [emotion] of turtles with [numberB = 1] ] ; creates a list of emotion for green turtles
if count (turtles) with [numberB = 0] != 0 [ set emotions-defectors [emotion] of turtles with [numberB = 0] ]
ifelse Cooperators != 0
[ set %-emotion-cooperators ( sum emotions-cooperators * 100 ) / (Cooperators ) ] ; l'�motion moyenne par cooperateur A VOIR SI IFELSE PERTNENT
[ set %-emotion-cooperators "na" ]
ifelse count (turtles) with [numberB = 0] != 0
[set %-emotion-defectors ( sum emotions-defectors * 100 ) / (Defectors )]
[set %-emotion-defectors "na" ]
ifelse count (turtles) with [numberB = 1] != 0
[ ifelse count (turtles) with [numberB = 0] != 0
[set mean-emotion ( ( %-cooperators * %-emotion-cooperators + (100 - %-cooperators ) * %-emotion-defectors ) / 100 )]
[set mean-emotion %-emotion-cooperators] ][set mean-emotion %-emotion-defectors]
if Cooperators != 0
[ set mean-fitness-cooperators (100 * sum [normalized_fitness] of turtles with [numberB = 1] / cooperators ) ]
if count (turtles) with [numberB = 0] != 0
[ set mean-fitness-defectors (100 * sum [normalized_fitness] of turtles with [numberB = 0] / defectors )]
set mean-fitness (100 * sum [normalized_fitness] of turtles / population )
end
to update-unhappy
ask turtles
[ ifelse ( [emotion] of self ) > X_c and ([numberB ] of self = 0 )
[ set unhappy? 1 ]
[ set unhappy? 0 ]
]
set unhappy-turtles count turtles with [unhappy? = 1 ]
ifelse defectors != 0 [ set %-unhappy-turtles (unhappy-turtles * 100 / Defectors )]
[set %-unhappy-turtles 0 ]
ifelse (ticks < memory)
[ set list-unhappy? fput %-unhappy-turtles list-unhappy?
set mean-unhappy? mean list-unhappy? ]
[ set list-unhappy? fput %-unhappy-turtles list-unhappy? set list-unhappy? but-last list-unhappy?
set mean-unhappy? mean list-unhappy?
set sd-unhappy? standard-deviation list-unhappy? ]
end
to report-segreg
ifelse (cooperators != 0) and (defectors != 0)
[ set random-mixed-pairs ( N-size * (%-cooperators / 100) * (1 - (%-cooperators / 100)) * population ) ; scale 0 to 100
ask turtles
[ set other-nearby (count other turtles in-radius radius-n with [numberB != [numberB] of myself]) ]
set mixed-pairs (sum [other-nearby] of turtles) / 2
set segregation 100 * (1 - (mixed-pairs / random-mixed-pairs)) ]
[set segregation 0 ]
ifelse (ticks < memory)
[set list-segregation fput segregation list-segregation
set mean-segreg mean list-segregation ]
[set list-segregation fput segregation list-segregation set list-segregation but-last list-segregation
set mean-segreg mean list-segregation
set sd-segreg standard-deviation list-segregation ]
end
to do-plots
set-current-plot "Emotions"
; set-current-plot-pen "%-cooperators"
; plot %-cooperators
set-current-plot-pen "emotion of cooperators/cooperator"
if %-emotion-cooperators != "na" [ plot %-emotion-cooperators]
set-current-plot-pen "emotion of defectors/defector"
if %-emotion-defectors != "na" [plot %-emotion-defectors]
set-current-plot-pen "mean-emotion"
plot mean-emotion
set-current-plot "Average Fitness over memory periods"
; set-current-plot-pen "%-cooperators"
; plot %-cooperators
set-current-plot-pen "mean-fitness-cooperators"
plot mean-fitness-cooperators
set-current-plot-pen "mean-fitness-defectors"
plot mean-fitness-defectors
set-current-plot-pen "mean-fitness"
plot mean-fitness
set-current-plot "unhappy-turtles"
;set-plot-x-range 0 number-ticks
set-current-plot-pen "%-unhappy-turtles"
plot %-unhappy-turtles
; set-current-plot-pen "unhappy-turtles"
; plot unhappy-turtles
set-current-plot "Segregation"
;set-plot-x-range 0 number-ticks
set-current-plot-pen "segregation"
plot segregation
set-current-plot-pen "mean-segreg"
; plot mean-segreg
set-current-plot "cooperation"
set-current-plot-pen " %-cooperators"
plot %-cooperators
set-current-plot-pen "expected_equilibrium"
plot expected_equilibrium
set-current-plot "Average Cooperation over memory periods"
auto-plot-on
if (ticks >= 100) [set-plot-x-range (ticks - 100) ticks]
set-current-plot-pen "mean-coop"
plot mean-coop
set-current-plot-pen "mean-coop + 2 sd-coop"
plot (mean-coop + 2 * sd-coop)
set-current-plot-pen "mean-coop - 2 sd-coop"
plot (mean-coop - 2 * sd-coop)
; set-current-plot "histogram emotions"
; set-histogram-num-bars 10
; histogram [emotion] of turtles
; set-current-plot "cooperators emotions"
; set-histogram-num-bars 20
; histogram emotions-cooperators
; set-current-plot "defectors emotions"
; set-histogram-num-bars 20
; histogram emotions-defectors
end
to compute-expected-equilibrium
if (distribution = "uniform")
[ let delta (1 - 4 * C)
ifelse delta > 0 [ set unstable 100 * (0.5 - sqrt(delta) / 2 )
ifelse init_coop <= unstable
[set expected_equilibrium 0]
[set expected_equilibrium 100 * (0.5 + sqrt(delta) / 2) ]]
[ set unstable 0 set expected_equilibrium 0 ]]
if (distribution = "triangular")
[ifelse equilibrium != []
[ifelse init_coop <= unstable
[set expected_equilibrium 0]
[set expected_equilibrium stable]]
[set unstable 0 set expected_equilibrium 0 ]
]
end
;this procedure produce the list of stable and unstable equilibria from the triangular (excluding full defection )
to-report solve [eta ]
let x1 1
set eta []
while [x1 >= 0.00001]
[ let x (1 - (C / x1 ) ^ 2)
if abs (x - x1) <= 0.001
[
let s 0
if eta != [] [
set s item 0 eta ]
if abs (s - x) > 0.01
[ set eta fput x eta ]]
set x1 x1 - 0.00001
]
report eta
end
to compute-stable-and-unstable
set stable []
set unstable []
set equilibrium solve equilibrium
if equilibrium != []
[
foreach equilibrium [
ifelse abs ( (2 * C ^ 2 ) / ( ? ) ^ 3 ) < 1
[set stable fput ? stable ]
[set unstable fput ? unstable]]
set stable 100 * (item 0 stable) print stable
set unstable 100 * (item 0 unstable) print unstable
]
end