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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.

- Each player has a cost of cooperating C and a random emotion between 0 and 1.
- Each player may have two actions “cooperate” (color green) and defect (color red);
- At each period of time a number of moving turtles are chosen. They draws a sample of k other players (depending on the slider “chosen size”) and on the type of neighborhood (local or random). They choose a best response to the current proportion of cooperators in their current sample. However with a probability “tremble” the strategy chosen is randomly. A local neighborhood with chosen size = 4 corresponds to a Von Neumann neighborhood and when chosen size = 8 to a Moore neighborhood. The interaction structure is chosen at the setup and remains the same during the run.
- We use two different concepts for payoffs : fitness corresponds to what is effectively earned by turtles in the game that is to the payoffs corresponding to a prisoner’s dilemma. Best responses are computed with the use of payoffs given by the above table i.e. including emotions X.

to setup

- At initialisation a population of cooperators (green ) and defectors (red ) is created. Each agent get a random X from a uniform distribution.
- Choose the environment: random or local and size of the interaction sample (4 , 8 24 , 44).

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) ).

- your seed: random or chosen by you.
- Interaction structure: choose the neighbourhood type local or random and choose the sample size with the “chosen-size” = 4 or 8 or 24 or 44.
- Choose the trembles in your best response ( slider “tremble”)
- choose the type of distribution of emotions (triangular or uniform) and the cost of cooperation C.

The rate of cooperation

Segregation emerges almost always with local interaction and small sample size when the bifurcation point is below 50%.

- Vary the cost of cooperation and compare expected predicted equilibrium under different local interaction structures.
- Change the number of moving turtles.

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