; In NetLogo, a 'breed' is teh equivalent to a class or type of agent. ; In this model, agents are individualstates, each adapting their portfolio of ; military capabilites based on the replicator equation. breed [ states state ] ; Each state possess the attributes below... ; Agent variables are denoted by the prefix "my." so that they are not confused with ; temporary variables used in particualr methods or global variables states-own [ my.id ; an identificaiton number my.rocks ; a percentage of rocks in their miltiary portfolio my.papers ; a percentage of papers in their military portfolio my.scissors ; a percentage of scissors in their military portfolio my.next.rocks ; the percentage of rocks they will have in the next time step my.next.papers ; the percentage of papers they will have in the next time step my.next.scissors ; the percetnage of scissors they will have in then next time step my.color ; the default color of the state assign randomly during setup ] ; Global veriables are denoted by the prefix "g." to avoid confusion with temporary variables or those ; belonging to particular agents globals [ g.total.rocks ; the total rocks in the system g.total.papers ; the total papers in the system g.total.scissors ; the total scissors in the system g.total.capabilities ; the sum of all rocks, papers, and scissors in the system g.percentage.rocks ; the percentage of total capabilities that are rocks g.percentage.papers ; the percentage of total capabilities that are papers g.percentage.scissors ; the percentage of total capabilities that are scissors g.state.id ; a counter for assigning ids to each state agent during setup g.mathematical.percent.rocks ; the percentage of rocks the mathematical model predicts given the initial conditions g.mathematical.percent.papers ; the percentage of papers the mathematical model predicts given the initial conditions g.mathematical.percent.scissors ; the percentage of scissors the mathematical model predicts given the initial conditions g.r.r.payoff ; the payoff for playing rock against rock g.r.p.payoff ; the payoff for playing rock against paper g.r.s.payoff ; the payoff for playing rock against scissors g.p.r.payoff ; the payoff for playing paper against rock g.p.p.payoff ; the payoff for playing paper against paper g.p.s.payoff ; the payoff for playing paper against scissors g.s.r.payoff ; the payoff for playing scissors against rock g.s.p.payoff ; the payoff for playing scissors against paper g.s.s.payoff ; the payoff for playing scissors against scissors g.rock.payoff ; the estimated value of playing the rock strategy given a popultion of opponents g.paper.payoff ; the estimated value of playing the paper strategy given a population of opponents g.scissor.payoff ; the estimated value of playing the scissors strategy given a population of opponents g.initial.fitness ; the initial fitness of a state prior to modification based on it strategy g.average.fitness ; the average fitness of states based on their strategies g.rock.fitness ; the computed fitness of states that play the rock strategy g.paper.fitness ; the computed fitness of states that play the paper strategy g.scissor.fitness ; the computed fitness of states that play the scissors strategy ] ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; ; SETUP ; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; Setup the simulation. This generates a population based on the total number of "patches" in the world, ; assigning each a random portfolio of rocks, papers, and scissors, normalized by percentage (thus always summing to 1.0). ; Each state is given a random color, but can recolored on the landscape based on their particular military capabilities. to setup ca setup.states setup.globals update.plots tick end ; Ask each "patch" to create a state agent on it, and the initialize each newly created state to setup.states set-default-shape states "square" set g.state.id 0 ask patches [ sprout-states 1 [ setup.state ] ] color.update.states end ; For each state being created, assign it an id, a random strategy, and a random color to setup.state set my.id g.state.id set g.state.id g.state.id + 1 set my.rocks 0 set my.papers 0 set my.scissors 0 set my.next.rocks 0 set my.next.papers 0 set my.next.scissors 0 state.set.random.strategy let _red random 255 let _blue random 255 let _green random 255 let _colors [] set _colors fput _green _colors set _colors fput _blue _colors set _colors fput _red _colors set my.color _colors set color my.color end ; After creating the states, initialize the global, population level variables. ; The mathematical variables will be initialized and used for comparision against the ; actions of the individual agents. to setup.globals update.globals set g.mathematical.percent.rocks g.percentage.rocks set g.mathematical.percent.papers g.percentage.papers set g.mathematical.percent.scissors g.percentage.scissors set g.r.r.payoff 2 set g.r.p.payoff -2 set g.r.s.payoff 2 set g.p.r.payoff 2 set g.p.p.payoff 2 set g.p.s.payoff -2 set g.s.r.payoff -2 set g.s.p.payoff 2 set g.s.s.payoff 2 set g.rock.payoff 0 set g.paper.payoff 0 set g.scissor.payoff 0 set g.initial.fitness 5 set g.average.fitness 0 set g.rock.fitness 0 set g.paper.fitness 0 set g.scissor.fitness 0 update.mathematical.model end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; ; STEP ; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to step update.globals update.mathematical.model states.update.strategies update.plots tick end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; ; GLOBALS ; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; examine the current population and update the global variables used for plotting purposes to update.globals set g.total.rocks sum [my.rocks] of states set g.total.papers sum [my.papers] of states set g.total.scissors sum [my.scissors] of states set g.percentage.rocks g.total.rocks / (g.total.rocks + g.total.papers + g.total.scissors) set g.percentage.papers g.total.papers / (g.total.rocks + g.total.papers + g.total.scissors) set g.percentage.scissors g.total.scissors / (g.total.rocks + g.total.papers + g.total.scissors) set g.total.capabilities g.total.rocks + g.total.papers + g.total.scissors end to update.mathematical.model ; Solve the replicator equation based on the model's initial conditions. The conditions are established initially at setup ; and then propagated each time step. set g.rock.payoff g.mathematical.percent.rocks * g.r.r.payoff + g.mathematical.percent.papers * g.r.p.payoff + g.mathematical.percent.scissors * g.r.s.payoff set g.paper.payoff g.mathematical.percent.rocks * g.p.r.payoff + g.mathematical.percent.papers * g.p.p.payoff + g.mathematical.percent.scissors * g.p.s.payoff set g.scissor.payoff g.mathematical.percent.rocks * g.s.r.payoff + g.mathematical.percent.papers * g.s.p.payoff + g.mathematical.percent.scissors * g.s.s.payoff set g.rock.fitness g.initial.fitness + g.rock.payoff set g.paper.fitness g.initial.fitness + g.paper.payoff set g.scissor.fitness g.initial.fitness + g.scissor.payoff if g.rock.fitness <= 0 or g.paper.fitness <= 0 or g.scissor.fitness <= 0 [ let _fitnesses [] set _fitnesses fput g.scissor.fitness _fitnesses set _fitnesses fput g.paper.fitness _fitnesses set _fitnesses fput g.rock.fitness _fitnesses let _min min _fitnesses set g.initial.fitness ((_min * -1) + 0.1) set g.rock.fitness g.initial.fitness + g.rock.payoff set g.paper.fitness g.initial.fitness + g.paper.payoff set g.scissor.fitness g.initial.fitness + g.scissor.payoff ] set g.average.fitness g.mathematical.percent.rocks * g.rock.fitness + g.mathematical.percent.papers * g.paper.fitness + g.mathematical.percent.scissors * g.scissor.fitness set g.mathematical.percent.rocks g.mathematical.percent.rocks * g.rock.fitness / g.average.fitness set g.mathematical.percent.papers g.mathematical.percent.papers * g.paper.fitness / g.average.fitness set g.mathematical.percent.scissors g.mathematical.percent.scissors * g.scissor.fitness / g.average.fitness end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; ; STATE ; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to states.update.strategies states.update.next.strategy states.set.next.strategy end to states.update.next.strategy ask states [ state.update.next.strategy ] end to state.update.next.strategy ; Each state plays the replicator equation based on it's unique view of the popualtion. ; Agents view the population as if they were invading it, thus they do not count their own strategy ; when evaluating the population as a whole. Thus, each sees the population from a different perspective. let _other.rocks sum [my.rocks] of other states let _other.papers sum [my.papers] of other states let _other.scissors sum [my.scissors] of other states let _total.capabilities _other.rocks + _other.papers + _other.scissors let _prob.encounter.rock _other.rocks / _total.capabilities let _prob.encounter.paper _other.papers / _total.capabilities let _prob.encounter.scissors 1.0 - (_prob.encounter.rock + _prob.encounter.paper) let _rock.payoff _prob.encounter.rock * g.r.r.payoff + _prob.encounter.paper * g.r.p.payoff + _prob.encounter.scissors * g.r.s.payoff let _paper.payoff _prob.encounter.rock * g.p.r.payoff + _prob.encounter.paper * g.p.p.payoff + _prob.encounter.scissors * g.p.s.payoff let _scissor.payoff _prob.encounter.rock * g.s.r.payoff + _prob.encounter.paper * g.s.p.payoff + _prob.encounter.scissors * g.s.s.payoff let _initial.fitness g.initial.fitness if _initial.fitness + _rock.payoff + _paper.payoff + _scissor.payoff <= 0 [ set _initial.fitness (_rock.payoff + _paper.payoff + _scissor.payoff - 0.1) * -1 ] let _rock.fitness _initial.fitness + _rock.payoff let _paper.fitness _initial.fitness + _paper.payoff let _scissor.fitness _initial.fitness + _scissor.payoff let _average.fitness _prob.encounter.rock * _rock.fitness + _prob.encounter.paper * _paper.fitness + _prob.encounter.scissors * _scissor.fitness set my.next.rocks my.rocks * _rock.fitness / _average.fitness if my.next.rocks < 0 [ set my.next.rocks 0 ] set my.next.papers my.papers * _paper.fitness / _average.fitness if my.next.papers < 0 [ set my.next.papers 0 ] set my.next.scissors my.scissors * _scissor.fitness / _average.fitness if my.next.scissors < 0 [ set my.next.scissors 0 ] end to states.set.next.strategy ask states [ set my.rocks my.next.rocks set my.papers my.next.papers set my.scissors my.next.scissors ] end to state.set.random.strategy let _rocks random-float 1.0 let _papers random-float 1.0 let _scissors random-float 1.0 let _total _rocks + _papers + _scissors set my.rocks _rocks / _total set my.papers _papers / _total set my.scissors 1.0 - (my.rocks + my.papers) end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; ; PLOTS ; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to update.plots update.strategy.counts.plot update.mathematical.baseline.plot update.differences.plots end to update.strategy.counts.plot set-current-plot "strategy percentages" set-current-plot-pen "Rocks" plot g.percentage.rocks set-current-plot-pen "Papers" plot g.percentage.papers set-current-plot-pen "Scissors" plot g.percentage.scissors end to update.mathematical.baseline.plot set-current-plot "mathematical baseline" set-current-plot-pen "Rocks" plot g.mathematical.percent.rocks set-current-plot-pen "Papers" plot g.mathematical.percent.papers set-current-plot-pen "Scissors" plot g.mathematical.percent.scissors end to update.differences.plots set-current-plot "Rocks Difference" set-current-plot-pen "Agent" plot g.percentage.rocks set-current-plot-pen "Mathematical" plot g.mathematical.percent.rocks set-current-plot "Papers Difference" set-current-plot-pen "Agent" plot g.percentage.papers set-current-plot-pen "Mathematical" plot g.mathematical.percent.papers set-current-plot "Scissors Difference" set-current-plot-pen "Agent" plot g.percentage.scissors set-current-plot-pen "Mathematical" plot g.mathematical.percent.scissors end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; ;; COLORING PATCHES ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; requires chooser with the following ; "default" ; "rock scale" ; "paper scale" ; "scissor scale" ; "rock scale normalized" ; "paper scale normalized" ; "scissor scale normalized" ; "majority" ; to color.update.states if color.map = "default" [ ask states [ set color my.color let _color color ] ] if color.map = "rock scale" [ ask states [ set color scale-color red my.rocks 0 1.0 let _color color ] ] if color.map = "paper scale" [ ask states [ set color scale-color green my.papers 0 1.0 let _color color ] ] if color.map = "scissor scale" [ ask states [ set color scale-color blue my.scissors 0 1.0 let _color color ] ] if color.map = "rock scale normalized" [ ask states [ set color scale-color red my.rocks 0 max [my.rocks] of states let _color color ] ] if color.map = "paper scale normalized" [ ask states [ set color scale-color green my.papers 0 max [my.papers] of states let _color color ] ] if color.map = "scissor scale normalized" [ ask states [ set color scale-color blue my.scissors 0 max [my.scissors] of states let _color color ] ] if color.map = "majority" [ ask states [ if my.rocks > my.papers and my.rocks > my.scissors [ set color red ] if my.papers > my.rocks and my.papers > my.scissors [ set color green ] if my.scissors > my.papers and my.scissors > my.rocks [ set color blue ] ] ] end @#$#@#$#@ GRAPHICS-WINDOW 445 10 878 464 -1 -1 14.1 1 10 1 1 1 0 1 1 1 0 29 0 29 1 1 1 ticks BUTTON 12 12 75 45 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 87 12 150 45 step step NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 161 12 224 45 go step T 1 T OBSERVER NIL NIL NIL NIL PLOT 3 472 444 668 strategy percentages NIL NIL 0.0 10.0 0.0 1.0 true true PENS "Rocks" 1.0 0 -2674135 true "Papers" 1.0 0 -10899396 true "Scissors" 1.0 0 -13345367 true PLOT 3 670 446 845 mathematical baseline NIL NIL 0.0 10.0 0.0 1.0 true true PENS "Rocks" 1.0 0 -2674135 true "Papers" 1.0 0 -10899396 true "Scissors" 1.0 0 -13345367 true CHOOSER 258 11 437 56 color.map color.map "default" "rock scale" "paper scale" "scissor scale" "rock scale normalized" "paper scale normalized" "scissor scale normalized" "majority" 7 BUTTON 258 61 437 94 update map colors color.update.states NIL 1 T OBSERVER NIL NIL NIL NIL TEXTBOX 258 105 436 371 When color.map has selected anything but \"default\":\n\nred means \"Rocks\"\ngreen means \"Papers\"\nBlue means \"Scissors\"\n\nThe intensity of the color may be displayed based on the 0 - 100% scale, or normalized, with the state with the maximum percentage with a given strategy the brightest, and black meaning 0%.\n\nIf \"majority\" is selected, then the color denotes the strategy with the highest percetage in the portfolio. 11 0.0 1 PLOT 447 473 884 593 rocks difference NIL NIL 0.0 10.0 0.0 1.0 true true PENS "Agent" 1.0 0 -2674135 true "Mathematical" 1.0 0 -7500403 true PLOT 448 599 884 719 papers difference NIL NIL 0.0 10.0 0.0 1.0 true true PENS "Agent" 1.0 0 -10899396 true "Mathematical" 1.0 0 -7500403 true PLOT 449 724 886 844 scissors difference NIL NIL 0.0 10.0 0.0 1.0 true true PENS "Agent" 1.0 0 -13345367 true "Mathematical" 1.0 0 -7500403 true @#$#@#$#@ WHAT IS IT? ----------- This is a very simple implementation of the Rock Paper Scissors (RPS) and the Replicator Equation as a mathematical and agent-based model, where the agents are referred to as "states" as future developments will regard their portfolio of Rocks, Papers, and Scissors as military capabilities. HOW IT WORKS ------------ Simply press "Setup" and "Go" to run the model. Payoffs of different interactions, e.g. rock plays paper, can be set under the setup.globals procedure on the "Procedures". In this case, populations of agents are generated at random, with the number of agents being equivalent to the number of patches. Each agent implements the replicator equation is its adaptive strategy, where it adjusts its portfolio of rocks, papers, and scissors to its observation of the population. CREDITS AND REFERENCES ---------------------- Aaron Frank www.aaronbfrank.com contact@aaronbfrank.com @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 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