powered by NetLogo

view/download model file: GeneralMixedEvolutionaryModel.nlogo

This is a generic evolutionary game theoretic model, that allows for mixed strategies.

100 turtles are present intially, with initial-S number of them playing the "S" strategy

Payoffs

The game is symmetric and the payoffs are as follows

| Player 2's action

Player 1's |

Action | S T

------------|-----------------

S | a,a b,c

------------|-----------------

T | c,b d,d

------------|-----------------

Turtles move around randomly. If they find a partner close enough, they play a game, executing their strategies, and reap the payoff determined by the above matrix.

After each round, each turtle that had a partner checks to see if it has a high enough score to reproduce. If it reproduces, its score decreases by a fixed amount, which is then transferred to be the score of its offspring. The offspring copy the parents' strategy (the probability of playing "S"), but the mutate the probability a bit to allow the population to find the best mixed strategy. For simplicity, when a new turtle is created, another randomly selected turtle dies.

Buttons:

SETUP: Setup the world to begin playing.

GO: Have the turtles walk around the world and interact.

GO ONCE: Same as GO except the turtles only take one step.

Sliders:

FIXED-PROBABILITY: set every player's probability of playing strategy S to be this value. You have to press the "FIX-PROBS" button for this to take effect

REPRODUCTION-COST: how much it costs a player to reproduce (the offspring will start with a score equal to the REPRODUCTION-COST

NUM-TURTLES: the total number of turtles, which will take effect once you hit "SETUP"

Plots: STRATEGY-COUNT plots the number of turtles playing each strategy over time

Try and see if p = 1/3 is a stable equilibrium for a dove-hawk game.

Test other games: prisoner's dilemma, coordination, presentation/exam.

Copyright 2002 Uri Wilensky. All rights reserved.

Heavily modified by Lada Adamic 2011

Permission to use, modify or redistribute this model is hereby granted, provided that both of the following requirements are followed:

a) this copyright notice is included.

b) this model will not be redistributed for profit without permission from Uri Wilensky. Contact Uri Wilensky for appropriate licenses for redistribution for profit.

This model was created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227.

globals [ ;;number of turtles with each strategy ] turtles-own [ score prob-S strategy partnered? ;;am I partnered? partner ;;WHO of my partner (nobody if not partnered) ] ;;;;;;;;;;;;;;;;;;;;;; ;;;Setup Procedures;;; ;;;;;;;;;;;;;;;;;;;;;; to setup ca make-turtles setup-common-variables end to hawk-dove set a 2 set b 1 set c 3 set d 0 end to virus set a 4 set b 3 set c 8 set d 2 ask turtles [set shape "monster"] end ;;setup the turtles and distribute them randomly to setup-turtles make-turtles ;;create the appropriate number of turtles playing each strategy setup-common-variables ;;sets the variables that all turtles share end ;;create the appropriate number of turtles playing each strategy to make-turtles crt num-turtles end ;;set the variables that all turtles share to setup-common-variables ask turtles [ set score 5 set prob-S random 100 set partnered? false set partner nobody setxy random-xcor random-ycor set color prob-S + 5 ] end to fix-probabilities ask turtles [ set prob-S fixed-probability * 100 set color prob-S + 5 ] end ;;;;;;;;;;;;;;;;;;;;;;;; ;;;Runtime Procedures;;; ;;;;;;;;;;;;;;;;;;;;;;;; to go clear-last-round ask turtles [ ifelse random 100 <= prob-S [ set strategy "S"] [ set strategy "T"] ] ask turtles [ partner-up ] ;;have turtles try to find a partner let partnered-turtles turtles with [ partnered? ] ask partnered-turtles [ play-a-round ] ask partnered-turtles [ reproduce ] do-plotting tick end to reproduce ;; turtle procedure if score > (2 * reproduction-cost) [ set score score - reproduction-cost hatch 1 [ set score reproduction-cost if (random 100 < 50) [mutate] set color prob-S + 5 ] ask one-of turtles [die] ] end to mutate set prob-S prob-S + (random 2) - 0.5 if (prob-S < 0) [set prob-S 0] if (prob-S > 100) [set prob-S 100] end to clear-last-round let partnered-turtles turtles with [ partnered? ] ask partnered-turtles [ release-partners ] end ;;release partner and turn around to leave to release-partners set partnered? false set partner nobody rt 180 ; set label score end ;;have turtles try to find a partner ;;Since other turtles that have already executed partner-up may have ;;caused the turtle executing partner-up to be partnered, ;;a check is needed to make sure the calling turtle isn't partnered. to partner-up ;;turtle procedure if (not partnered?) [ ;;make sure still not partnered rt (random-float 90 - random-float 90) fd 1 ;;move around randomly set partner one-of (turtles-at -1 0) with [ not partnered? ] if partner != nobody [ ;;if successful grabbing a partner, partner up set partnered? true set heading 270 ;;face partner ask partner [ set partnered? true set partner myself set heading 90 ] ] ] end to play-a-round ;;turtle procedure ifelse (strategy = "S") [ set shape "bird side" set size 1 ifelse ([strategy] of partner = "S") [ set score (score + a) ;set label a ] [ set score (score + b) ;set label b ] ] [ set shape "bird" set size 0.9 ifelse ([strategy] of partner = "S") [ set score (score + c) ;set label c ] [ set score (score + d) ;set label d ] ] end ;; returns the total score for a strategy if any turtles exist that are playing it to-report calc-score [strategy-type num-with-strategy] ifelse num-with-strategy > 0 [ report (sum [ score ] of (turtles with [ strategy = strategy-type ])) ] [ report 0 ] end ;;if a strategy has had any interactions, plot the average score per interaction to do-plotting set-current-plot "strategy-count" set-current-plot-pen "S" plot count turtles with [strategy = "S"] set-current-plot-pen "T" plot count turtles with [strategy = "T"] end ; Copyright 2002 Uri Wilensky. All rights reserved. ; The full copyright notice is in the Information tab.