# A Cooperative Species

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globals [ combo replacement_rate ; set at 5% mutation_rate ;; 2% groups ; just a list of numbers from 1 to N_group p_links ;; total possible links given n nodes p_networks ;; total possible networks from n nodes leaders ;; list of "leaders" in round, to serve as anchors for the layout-spring algorithm followers ;; everyone who isn't a leader avwithingroupvar ;; average within group variance betweenvar ;between-group variance variance_ratio ;; Fst = var(pj) / [Avvar(pij) + var(pj)] = population-wide measure of the degree of non-randomness in who interacts with whom; aka *inbreeding coefficient* ;; = differences in the probability of being paired with an altruist conditional on being an altruist, and the probability of being paired with an altruist conditional on ;; being a non-altruist (defector). ;; one expects cooperation to prevail when Fst > c / b. pop_change ;; expected change in fraction of altruists ] breed [cooperators cooperator] breed [defectors defector] undirected-link-breed [wlinks wlink] ;within-group links undirected-link-breed [blinks blink] ;between-group links ;links-own [memories] turtles-own [ earnings ;; accumulated payoffs payoff N_Neighbors mycosts mybenefits t_threshold groupid ;; groups 1 --> N_groups group_coop ;; previous number of contributors/cooperators in the previous round, withint he group; ;;should be the same for turtles of the same group sorted contrite ;; number = 0 originally, if accidentalyl makes a mistake and defects, then set to 2, which means agent will cooperate next 2 rounds automatically. wingroupvar ;; within group variance of altruism p_i ;; probabilistic interaction; likelihood thta other turtles will interact with this turtle.. test ] to setup clear-all reset-ticks set-default-shape turtles "face happy" set groups [] set leaders [] set followers [] let g 1 repeat N_groups [ set groups lput g groups set g g + 1] create-turtles (N_groups * size_n) [ while [any? other turtles-here] [ let empty_patch one-of patches with [any? turtles-here = false] move-to empty_patch ] set sorted false set groupid 0 ] setup-neighbors ask turtles [ let cnt size_n ;; (i.e. n) let t random cnt + 1 ;; i.e. between 0 and n, n = # in group. Interesting to test differences using n and n-1 as ;; used by Bowles and Gintis. When using n, turtles with t = n will only cooperate if everybody cooperated in the previous ;; round, including oneself! A turtle with t = n + 1 is a DEFECTOR, set below. set t_threshold t set contrite 0 set breed cooperators set color yellow set size 1 set group_coop size_n ;; turtles act initially as if everybody in group cooperated last round ] let pop count turtles let num_d (Percent_Defectors / 100) * pop let new_defectors n-of num_d turtles ask new_defectors [set breed defectors set shape "face sad" set size 1.5 set color red set t_threshold size_n + 1 set group_coop size_n] ;if GAME = "Pairwise Prisoners Dilemma Game" [ask turtles [create-links-with other turtles [set hidden? true]]] ;layout end to start if count turtles > 0 [ if GAME = "Public Goods Game" [Public_goods_game] if GAME = "Pairwise Prisoners Dilemma Game" [PD_pairing] if Replicator_Dynamics? = true AND count cooperators > 0 AND count defectors > 0 [replicator_dynamics] if count turtles > 0 [ if reassortment? = true [setup-neighbors] if starvation? = true [dying-turtles] if kill_defectors? = true [kill-d] ask turtles [if contrite? = true[ ; cooperate if defected in error from previous 1-2 rounds if contrite > 0 [set contrite contrite - 1]]] update-plots ;layout tick ] ] end to setup-neighbors if GAME = "Public Goods Game" [assign_groups] if GAME = "Pairwise Prisoners Dilemma Game" [ create-pairs ;layout ] end to create-pairs ask turtles[ if PD_assortment = "Random" [create-pairs-random] if PD_assortment = "Fixed" [create-pairs-fixed]] end to create-pairs-random set n_neighbors other turtles ;; This will end up being proportional to the population distribution end to create-pairs-fixed ifelse [breed] of self = cooperators [ let p Probability_of_Altruist_meeting_Altruist let r random 100 ifelse r < p [set n_neighbors other cooperators][set n_neighbors defectors]] [let p Probability_of_Defector_meeting_Altruist let r random 100 ifelse r < p [set n_neighbors cooperators] [set n_neighbors other defectors]] end to-report find-partner let partner one-of N_Neighbors if partner = nobody [set partner one-of turtles] report partner end to assign_groups ask turtles [setxy random-pxcor random-pycor while [any? other turtles-here] [ let empty_patch one-of patches with [any? turtles-here = false] move-to empty_patch ] set groupid 0 ] let unassigned turtles ;; start with group 1 and loop to build each group let current 1 while [any? unassigned] [ ;; place a randomly chosen set of group-size turtles into the current ;; group. or, if there are less than group-size turtles left, place the ;; rest of the turtles in the current group. ask n-of (min (list size_n (count unassigned))) unassigned [ set groupid current set n_neighbors other turtles with [groupid = current] ] ;; consider the next group. set current current + 1 ;; remove grouped turtles from the pool of turtles to assign set unassigned unassigned with [groupid = 0] ] ask turtles [ ;; if i'm in a group, move towards "home" for my group if groupid != 0 [ face get-home let p [neighbors] of get-home let area (patch-set get-home p) let my_patch one-of area move-to my_patch ] ;; wiggle a little and always move forward, to make sure turtles don't all ;; pile up lt random 5 rt random 5 fd 1 ] end ;; Courtesy of Uri Wilensky: ;; figures out the home patch for a group. this looks complicated, but the ;; idea is simple. we just want to lay the groups out in a regular grid, ;; evenly spaced throughout the world. we want the grid to be square, so in ;; some cases not all the positions are filled. to-report get-home ;; turtle procedure ;; calculate the minimum length of each side of our grid let side ceiling (sqrt (max [groupid] of turtles + 1)) report patch ;; compute the x coordinate (round ((world-width / side) * (groupid mod side) + min-pxcor + int (world-width / (side * 2)))) ;; compute the y coordinate (round ((world-height / side) * int (groupid / side) + min-pycor + int (world-height / (side * 2)))) end to PD_pairing ;; Pairwise Prisoner's Dilemma Game ask turtles [ let partner find-partner ;if partner = nobody [die] ;; dies if isolated! let utility 0 let total_cost 0 let total_benefit 0 let personal_cost 0 ifelse member? self cooperators [set personal_cost cost] [set personal_cost 0] set total_cost total_cost + personal_cost ifelse member? partner cooperators [set total_benefit total_benefit + benefit ;; if partner is a cooperator, add benefit to 'totalbenefit' recorder. set utility utility + Benefit - personal_cost] ;; if neighbor is a cooperator, then add benefit... [set utility utility - personal_cost] ;;if neighbor is a defector, then no benefit and subtract personal cost, if any... set payoff utility set earnings earnings + payoff set mycosts total_cost set mybenefits total_benefit ] end To Public_goods_game foreach groups [ ?1 -> let group_share 0 let thisgroup turtles with [groupid = ?1] ask thisgroup [ set mycosts 0 let t group_coop let r random-float 1 ;; ERROR ifelse contrite > 0 [ ;; if contrite > 0, then cooperate, unconditionally, otherwise... set breed cooperators set shape "face happy" set size 1 set color yellow ;; then cooperate set group_share group_share + Benefit set mycosts cost] ;;ERROR IS BOTH ERROR TOWARD COOPERATING AND ERROR TOWARD DEFECTING. [ifelse t >= t_threshold ;;if enough other group members contributed last round then COOPERATE. [ifelse r <= error_rate[ ;; HERE, ERROR MEANS DEFECTING INSTEAD OF COOPERATING set breed defectors set shape "face sad" set size 1.5 set color red if contrite? = true [if r <= error_rate AND t >= t_threshold [set contrite 2 ]] ] [set breed cooperators set shape "face happy" set size 1 set color yellow ;; then cooperate set group_share group_share + Benefit set mycosts cost]] [ifelse r <= error_rate[ ;; HERE, ERROR MEANS COOPERATING INSTEAD OF DEFECTING set breed cooperators set shape "face happy" set size 1 set color yellow set group_share group_share + Benefit set mycosts cost] [set breed defectors set shape "face sad" set size 1.5 set color red]]] ] ask thisgroup [ set payoff (group_share / (size_n - 1)) - mycosts ;; payoff is b/n or b/(n-1) ?? set earnings earnings + payoff set group_coop count cooperators with [groupid = ?1] ] ] end to replicator_dynamics if Replicator_options = "Relative Payoff" [Relative_Payoff] if Replicator_options = "Variance Ratio" [Variance_Replicator] if Replicator_options = "Replicator Equation" [Replicator_equation] if Replicator_options = "Imitation" [Imitate] end ;; probability of changing to another strategy is proportional to the difference between the *mean* payoffs for defectors and cooperators. ;; turtle only can switch if the payoffs are larger for the other strategy. to Relative_payoff ifelse mean [payoff] of cooperators > mean [payoff] of defectors [ ;; if cooperators making more payoff, then select the defectors to change ask defectors [let pr random-float 1 if pr <= RD1 [delete_defectors]]] [ ;; if defectors making more, then ask cooperators to change ask cooperators [let pr random-float 1 if pr <= RD1 [delete_cooperators]]] end to dying-turtles ;; turtles die if their earnings (or possibly their payoffs) get below zero. let consuming ((benefit - cost) / size_n) / 2 ask turtles [ set earnings earnings - consuming if earnings < 0 [die]] ;ask turtles [setup-neighbors] ;; must reset potential partners to avoid calling on dead turtles! end to kill-d ;;RULE This just means that half the cost is deducted from earnings each round a turtle has no cooperators to cooperate with let consuming ((benefit - cost) / size_n) / 2 ask turtles [ let g 0 ask N_neighbors [if member? self cooperators [set g g + 1]] if g = 0 [set earnings earnings - consuming] ] end to Variance_replicator ;; based on variable 'popchange' ;; According to Bowles and Gintis, the ratio of between-group variation (of altruists) to the total variation (which is the weighted-average within-group variation + the between- ;; group variation) must be greater than the ratio c/b for evolution to favor altruism. ;; This ratio is also the probability of being paired with an altruist minus the probability of being paired with an altruist conditional on being an altruist or non-altruist, ;; respectively, or P(A|A) - P(A|N). This seems more of a predictive tool than an algorithm to change the population. variances let c count turtles let new_agents pop_change * c ;; let c_r round new_agents ifelse c_r > 0 [;; add more cooperators, kill defectors let c_d count defectors let c_min min (list c_r c_d) let deleted_defectors min-n-of c_min defectors [payoff] ask deleted_defectors [delete_defectors]] ;;add more defectors, kill cooperators [let p_cr c_r * -1 ;; convert to a positive number let c_c count cooperators let c_min min (list p_cr c_c) let deleted_cooperators min-n-of c_min cooperators [payoff] ask deleted_cooperators [delete_cooperators] ] end to Replicator_equation ;; let Pr(i) = the proportion of strategy i ;; let $i = the payoff of strategy i, since I can't write the pi symbol here. ;; the new proportion of strategy i in the population at time t+1 is given by: ;; Pr(i)t+1 = Pr(i)$(i) / Sum of Weights ;; the weight for each strategy is given by the numerator let expected_coop_change coop_pay - (count cooperators / count turtles) let expected_defect_change coop_def - (count defectors / count turtles) let c expected_coop_change * count turtles ;; gives the number of turtles that will be changed let c_r round c ;rounded ifelse c_r > 0 [ ;; add more cooperators, kill defectors let c_d count defectors let c_min min (list c_r c_d) let deleted_defectors min-n-of c_min defectors [payoff] ask deleted_defectors [delete_defectors]] ;;add more defectors, kill cooperators [let p_cr c_r * -1 ;; convert to a positive number let c_c count cooperators let c_min min (list p_cr c_c) let deleted_cooperators min-n-of c_min cooperators [payoff] ask deleted_cooperators [delete_cooperators] ] end to imitate ;; this probably won't work, because its not clear how turtles will decide to imitate.. ;; if all agents imitate most successful agent in their group, then it creates immediate within-group homogeneity ;setting it initially to 4 closest agents, von Neuman, or Moore neighborhood, can't remember which. ask turtles [ let other_a min-n-of 4 other turtles [distance self] let max_a max-one-of other_a [payoff] if [payoff] of max_a > [payoff] of self [ ifelse [breed] of max_a = cooperators [delete_defectors] [delete_cooperators] set t_threshold [t_threshold] of max_a ;; copying the threshold (for public goods games), not just the strategy! set group_coop t_threshold ] ] end to delete_defectors ;; hatch and die let i [groupid] of self hatch-cooperators 1 [ set groupid i let mygroup other turtles with [groupid = i] ;create-wlinks-with mygroup let cnt size_n ;; (i.e. n) let t random cnt ;; t will be automatically between 0 and n and therefore not a defector set t_threshold t set color yellow set size .5 set group_coop t_threshold ;; will initially act as if just enough turtles have cooperated in previous round ] die end to delete_cooperators let i [groupid] of self hatch-defectors 1 [ set groupid i let mygroup other turtles with [groupid = i] ;create-wlinks-with mygroup set t_threshold size_n + 1 ;; requires more turtles to cooperate than actually exist, therefore a defector set shape "face sad" set size 1 set color red set group_coop 0 ;; will initially act as if just enough turtles have cooperated in previous round ] die end to variances let jmin min [groupid] of turtles let jmax max [groupid] of turtles let j jmin let avgrouplist [] let bgrouplist [] repeat jmax [ let grouplist [] ask turtles with [groupid = j] [ ifelse [breed] of self = cooperators [set grouplist fput 1 grouplist] [set grouplist fput 0 grouplist] ;; set 1 if altruist, 0 otherwise ] ask turtles with [groupid = j] [ set wingroupvar variance grouplist ] set j j + 1 ] let j2 min [groupid] of turtles repeat jmax [ let num count turtles with [groupid = j2] let numi count turtles with [groupid = j2 AND breed = cooperators] ;; counts number of cooperators let pj numi / num ;; frequency of altruists in the group let f num / count turtles let gvar mean [wingroupvar] of turtles with [groupid = j2] ;; every turtle in the group should have the same within group variance, but just in case, i take the average here. set avgrouplist fput (f * gvar) avgrouplist set bgrouplist fput pj bgrouplist set j2 j2 + 1 ] set avwithingroupvar variance avgrouplist ;; reports the weighted-average within-group variance of altruists set betweenvar variance bgrouplist set variance_ratio betweenvar / (avwithingroupvar + betweenvar) p_change end to p_change ;; change in the fraction of altruists population in total population let b Benefit let c Cost let var_pj betweenvar let var_pij avwithingroupvar let p ((b - c) * var_pj) - (c * var_pij) set pop_change p end to-report coop_pay;; proportion of cooperators*payoff of cooperators divided by sum of weighted payoffs let expected_coop (count cooperators / count turtles) * mean [payoff] of cooperators let expected_def (count defectors / count turtles) * mean [payoff] of defectors let total_payoff_c expected_coop / (expected_def + expected_coop) report total_payoff_c end to-report coop_def let expected_coop (count cooperators / count turtles) * mean [payoff] of cooperators let expected_def (count defectors / count turtles) * mean [payoff] of defectors let total_payoff_d expected_def / (expected_def + expected_coop) report total_payoff_d end to-report RD1 ;; veresion 3. Qij = B($j - $i) ;; probability that agent will switch from less profitable strategy to more profitable strategy ;; B has to be sufficiently small so that Qij is always <= 1 ! let B .1 ;; just trying random numbers let payoff_c mean [payoff] of cooperators let payoff_d mean [payoff] of defectors ifelse payoff_c > payoff_d [ ;; probability that defectors will switch to cooperation... let Qij B * (payoff_c - payoff_d) report Qij] [ ;; probability that cooperators will switch to defection... let Qij B * (payoff_d - payoff_c) report Qij] end to-report RD2 ;; Replicator Dynamics Version #2 for Cooperators ;; Pr(i)t+1 = Pr(i) - a * Pr(i)(1-P)B($j - $i) let B .1 ;; randomly assigned let p_c (count cooperators / count turtles) ;; proportion of turtles that are cooperators let p_d (count defectors / count turtles) ;; proportion defectors let payoff_c mean [payoff] of cooperators let payoff_d mean [payoff] of defectors let expected_p p_c - ( p_c * (1 - p_d) * B * (payoff_d - payoff_c)) report expected_p end

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