## WHAT IS IT?

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

## HOW IT WORKS

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.

## HOW TO USE IT

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

## THINGS TO TRY

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.

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.

## PROCEDURES

```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
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
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
set prob-S fixed-probability * 100
set color prob-S + 5
]
end

;;;;;;;;;;;;;;;;;;;;;;;;
;;;Runtime Procedures;;;
;;;;;;;;;;;;;;;;;;;;;;;;

to go
clear-last-round
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? ]
play-a-round
]
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
]
]
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? ]
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 partnered? true
set partner myself
]
]
]
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