globals [ changed? ;; track for any changes made steps ;; number of changes in choice made score-per-round ;; total score of all agents in one round cooscore ;; toal score of all cooperators in one round comscore ;; total score of all competitors in one round coocount ;; number of agents employing cooperate strategy comcount ;; number of agents employing compete strategy unfcount ;; number of agents employing unforgiving strategy tftcount ] ;; number of agents employing tit-for-tat strategy patches-own [ cooperate? ;; cooperate or compete score ;; individual score obtained by agent strategy ] ;; choose from one of 4 strategies based on score obtained in one round ;; strategies include cooperate, compete, unforgiving, and tit-for-tat to setup clear-all ;; clear everything ask patches [ ifelse random 100 < initial-cooperation ;; sets up appropriate number of cooperators and competitors based on user input [ set cooperate? true ] [ set cooperate? false ] recolor-patch ] set steps 0 ;; reset steps to 0 reset-ticks ;; reset ticks to 0 end to go set changed? false ;; default variable to false set score-per-round 0 ;; reset total score to 0 before each round set cooscore 0 ;; reset total cooperate score to 0 before each round set comscore 0 ;; reset total compete score to 0 before each round set coocount 0 ;; reset cooperate strategy count to 0 before each round set comcount 0 ;; reset compete strategy count to 0 before each round set unfcount 0 ;; reset unforgiving strategy count to 0 before each round set tftcount 0 ;; reset tit-for-tat strategy count to 0 before each round ask patches [ compute-score ] ;; patches will compute and store their respective scores ask patches [ select-strategy ] ;; patches will choose and carry out their respective strategies if (not changed?) [ stop ] ;; if not changes were made, stop sequence tick end to compute-score let total-cooperaters count neighbors with [ cooperate? ] ;; count total number of neighbors who are cooperating set score 0 ;; reset individual score to 0 ifelse cooperate? [ set score ( total-cooperaters + 1 ) * 0.8 ;; cooperators get score of # of neighbors who cooperated multiplied by 0.8 set score-per-round ( score-per-round + score ) ;; adds up the total score set cooscore (cooscore + score ) ] ;; adds up the total cooperate score [ set score ( total-cooperaters * 0.8 ) + ( count neighbors / 2 ) ;; competitors get score of neigbors who cooperated additional 4 points set score-per-round ( score-per-round + score ) set comscore ( comscore + score ) ] ;; adds up the total compete score end to select-strategy ifelse pcolor = blue ;; assigns a specific strategy to each agent based on their first cooperate or compete choice and score obtained. [ if score > 5 ;; cooperators who obtained a high score will keep cooperating [ cooperate-strategy set coocount ( coocount + 1 ) ] ;; adds up the total number of agents who always cooperate if score < 3 ;; cooperators who obtained a low score will employ an unforgiving strategy [ unforgiving-strategy set unfcount ( unfcount + 1 ) ] ;; adds up the total number of agents who are unforgiving if score < 3 and score > 5 ;; cooperators who obtained an average score will employ a tit-for-tat strategy [ tit-for-tat-strategy set tftcount ( tftcount + 1 ) ] ] ;; adds up the total number of agents who use the tit-for-tat strategy [ if score < 6 ;; competitors who obtained a low score will change to a cooperative strategy [ cooperate-strategy set coocount ( coocount + 1 ) ] ;; adds up the total number of agents who always cooperate if score > 8 ;; competitors who obtained a high score will keep competiting [ defect-strategy set comcount ( comcount + 1 ) ] ;; adds up the total number of agents who always compete if score <= 8 and score > 6 ;; competitors who obtained an average score will employ a tit-for-tat strategy [ tit-for-tat-strategy set tftcount ( tftcount + 1 ) ] ] ;; adds up the total number of agents who use the tit-for-tat strategy end to cooperate-strategy ;; agents will always cooperate if pcolor = red [ set cooperate? true set changed? true set steps ( steps + 1 ) ] recolor-patch end to defect-strategy ;; agents will always compete if pcolor = blue [ set changed? true set cooperate? false set steps ( steps + 1 ) ] recolor-patch end to tit-for-tat-strategy ;; agents will choose to cooperate or compete based on its neighbors ifelse cooperate? [ if count neighbors with [pcolor = red] > count neighbors with [pcolor = blue] ;; agents who cooperate and has more neighbors competing than cooperating will compete [ set cooperate? false set changed? true set steps ( steps + 1 ) ] ] [ if count neighbors with [pcolor = blue] > count neighbors with [pcolor = red] ;; agents who compete and has more neighbors cooperating than competing will cooperate [ set changed? true set steps ( steps + 1 ) set cooperate? true ] ] recolor-patch end to unforgiving-strategy ;; agents will cooperate until only 2 or less of its neighbors are competing, where they will compete as well if count neighbors with [pcolor = red] <= 7 [ set changed? true set steps ( steps + 1 ) set cooperate? false ] recolor-patch end to recolor-patch ifelse cooperate? [ set pcolor blue ] [ set pcolor red ] end @#$#@#$#@ GRAPHICS-WINDOW 258 30 672 465 50 50 4.0 1 10 1 1 1 0 1 1 1 -50 50 -50 50 0 0 1 ticks 30.0 BUTTON 10 30 73 63 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 76 30 139 63 NIL go T 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 10 68 182 101 initial-cooperation initial-cooperation 0 100 50 1 1 % HORIZONTAL PLOT 10 204 239 354 No. of Agents ticks # 0.0 0.0 0.0 0.0 true true "" "" PENS "Comp." 1.0 0 -2674135 true "" "plot count patches with [pcolor = red]" "Coop." 1.0 0 -13345367 true "" "plot count patches with [pcolor = blue]" MONITOR 85 155 155 200 compete count patches with [pcolor = red] 17 1 11 MONITOR 10 155 80 200 cooperate count patches with [pcolor = blue] 17 1 11 MONITOR 10 357 80 402 NIL steps 17 1 11 MONITOR 692 217 796 262 avg score score-per-round / count patches 4 1 11 PLOT 693 313 919 463 Average Score per round ticks Score 0.0 0.0 0.0 0.0 true true "" "" PENS "Total" 1.0 0 -16777216 true "" "plot score-per-round / count patches" "Coop." 1.0 0 -13345367 true "" "plot cooscore / count patches with [pcolor = blue]" "Comp." 1.0 0 -2674135 true "" "plot comscore / count patches with [pcolor = red]" MONITOR 693 265 796 310 avg coo score cooscore / count patches with [pcolor = blue] 4 1 11 MONITOR 800 265 903 310 avg com score comscore / count patches with [pcolor = red] 4 1 11 MONITOR 10 105 80 150 total count patches 17 1 11 MONITOR 684 28 761 73 Cooperate coocount 4 1 11 MONITOR 763 28 840 73 Compete comcount 4 1 11 MONITOR 763 75 840 120 Tit-for-Tat tftcount 4 1 11 MONITOR 684 75 761 120 Unforgiving unfcount 4 1 11 PLOT 843 28 1129 178 Strategies Employed per round ticks # 0.0 0.0 0.0 0.0 true true "" "" PENS "Cooperate" 1.0 0 -13345367 true "" "plot coocount" "Compete" 1.0 0 -2674135 true "" "plot comcount" "Tit-for-Tat" 1.0 0 -1184463 true "" "plot tftcount" "Unforgiving" 1.0 0 -5825686 true "" "plot unfcount" @#$#@#$#@ ## WHAT IS IT? This model aims to study the effects of cooperating and competing within a society - Competitors gain more individually - Cooperators help the society to gain more collectively Based on the Prisoner’s Dilemma or Game Theory, the Prisoner's Dilemma is usually defined between two players and within Game theory which assumes that players act rationally. Realistic investigations of collective behaviour, however, require a multi-person model of the game that serves as a mathematical formulation of what is going on within a human society. Various aspects of multi-person Prisoner's Dilemma have been investigated, but till today there is still no consensus about its real meaning. The multi-person Prisoner's Dilemma considers a situation when each of N participants has a choice between two actions: cooperating with each other for the "common good" or defecting (following their selfish short-term interests). As a result of their choice, each participant receives a reward or punishment (payoff) that is dependent on its choice as well as everybody else's. ## HOW IT WORKS Each patch will either cooperate (blue) or compete (red) at the start of the model Each patch will receive a score based on its own choice and the choice its immediate (8) neighbours have chosen In the next round, each patch will be assigned a strategy and behave accordingly based on the previous round Payoff - Cooperators get 1 point for every agent who chooses to cooperate within its surrounding multiplied by a factor of 0.8 - Competitors get the score of cooperators plus an additional 4 points. Strategies - Always Cooperate - Always Compete - Tit-for-Tat - Unforgiving Strategies are assigned to each agent based on their choice of action and the respective score it received from it. Agents who do well while cooperating will continue to cooperate, while agents who do poorly while cooperating will change their strategy, and agents who do fairly average while cooperating will employ a tit-for-tat strategy. Similarly, agents who do well while competing will continue to compete, while agents who do poorly while competing will change their strategy, and agents who do fairly average will employ the tit-for-tat strategy. ## HOW TO USE IT Buttons - Setup: setup the world to begin the simulation - Go: have the patches select a strategy and act accordingly Slider - Initial Cooperation: determine the initial percentage of cooperators in the world Plots - Number of Agents: indicates the number of agents who cooperated or competed throughout the simulation - Average Score per round: indicates the average score an agent would get from either cooperating or competing in a round - Strategies Employed per round: indicates the number of agents using each strategy ## THINGS TO NOTICE Notice the strategies used during the simulation and compare it to the end result. How has the use of each strategy changed over time. Are the payoff curves the same for all agents? How do they differ? How is the total payoff to all agents related to the number of cooperators? Notice when do agents who compete score highest and when do they score similar to those who cooperate. ## THINGS TO TRY Try sliding the initial-cooperation slider to configure the starting number of cooperators. How does it affect the score of the agents. How does it affect the strategies employed by agents? ## EXTENDING THE MODEL Derive and use a proper formula instead of using logic to assign strategies to the agents. Incorporate space into the model and allow patches to move about and interact with different patches. This allows patches to form coalitions and also the ability to choose to participate in a round of interaction or not. Doing so enables the user to increase the number of strategies available to choose from as well. Extend the model so that each agent interacts with everyone else instead of simply interacting with its immediate neighbours. As the sample increases, how does this affect the result? ## RELATED MODELS PD N-Person Iterated PD Basic Evolutionary ## CREDITS AND REFERENCES ccl.northwestern.edu psychology.ucdavis.edu http://www-cs-faculty.stanford.edu/~eroberts/courses/soco/projects/1998-99/game-theory/npd.html Miklos N. Szilagyi. An Investigation of N-person Prisoners' Dilemmas. 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