MIS 585

Special Topics in IMS

Agent-Based Modeling

Bertan Badur

badur@boun.edu.tr

Department of

Management Information Systems

Boğaziçi University

Outline

IntorductionLifeHeroes and CowardsSimple Economy

Introduction

• Intorduction to Agent-Based Modeling

• By U. Wilensky, W. Rand.• IABM-WR • Chapter 2

Introduction

• learn to construct simple ABMs• “toy models” – not mean models of

real phenomena• thought experiments • objects to think with• simple to construct but• exebits interesting, suprising

emergent behavior

Outline

IntorductionLifeHeroes and CowardsSimple Economy

Life

• In 1970 British mathematician John Horton Conway, Conway (1976)

• cellular automata - the “Game of Life”

• Martin Gardner, • Scientific American colomn

The Game

• Played on checkeboard – graph paper

• N x N cells – • can be

– “alive” or “dead”: state of a cell

• surrounded by– eight neighbour cells

• the grid is “wrap around”• clock ticks – generation

Rules of the Game• Each cell checks its own state and

states of its neighbors and • set itself as “alive” or ”dead”

– if the cell has less then 2 alve neighbors – it dies– if it has more then 3 alive neighbors– it also dies– if it has 2 alive neighbors– it remains in its current state– if it has 3 alive neighors – if dead become alive, if alive, stay alive

NetLogo

• NetLogo has three tabs• Interface tab

– black area – “view”– white area – interface

• set user interface elements; buttoms, siliders..

• observe results: output, plots....

• Code tab• Info tab

The view

• composed of grid of cells – patches• how to open

– click settings in toolbar or– on the visw double click and select edit

• Parameters to set– Location of orgin– max-pxcor, max-pycor 25– patch size: 13 to 8– world wraps hirizonallyi vertically, see

IABM-WR pp 55 Box 2.1 Wrapping

NetLogo Code

• modules – procedures• begin with to• end with end• usually• setup

– initializations

• go– processes taking place advences

clock by tick

• procedures – commands• to proc name• commands• end• Create a button executing procedure setup

• Create a button executing procedure go– forever is cheked – forever button

• write setup procedure• code tab

to setup

end

to go

end

Initialization

to setup

;;

]

end

ask primitive asks selected agents to do actions by commands in brackets

set color of all pathces to redset - primitive is assignmentpcolor – variable for patches

Initialization

to setup

;;clear all setings

;; set dead patches to blue

;; 10% of patches are alive

;; initilize clock

end

to setup

clear-all

ask patches

[

set pcolor blue

if random 100 < 10

[ set pcolor green ]

]

reset-ticks

end

Exercise

• What is the difference between asking exactly 10% of the patches being alive– How do you perform this in general

for any number of patches, exactly X% being alive

• the chance of a randomly seleced patch being alive is 10%

Box 2.2: Agent Centeric Thinking

ask patches [

if random 100 < 10

[set pcolor green] ;; end if

] ;; end ask

• orask patches with [random 100 < 10]

[ set pcolor green ]

] ;; end ask

Asking exactly 10% of patchesto setup ask n-of 0.1*(51*51) patches [ set pcolor green ] ] ;; end ask] ;;end setup• or more generallyto setup let number-of-patches count patches ask n-of 0.1*number-of-patches patches [ set pcolor green ] ] ;; end ask] ;;end setup

go Procedureto go ;; each patch counts its alive neighbors

;; number of green neighboring patches

;; patches with 3 green naigbors turn or stay green

;; patches with 0 or 1 green neighbors turn or stay blue

;; patches with 4 or higher neighbors turn to blue

end

go Implementationto go ask patches [ set live-neighbors count neighbors with [pcolor = green]

] ask patches [ if live-neighbors = 3 [set pcolor green]

if live-neighbors = 1 or live-neighbors = 0 [set pcolor blue]

if live-neighbors >= 4 [set pcolor blue]

]

to setup ask n-of 4 patches [ ask n-of 20 patches in-radius 5

[ set pcolor red ] ]end4 patches are randomly selected for each randomly selected pathc for all patches in radius 5 select 20 randomly set their color to red

clear-allto setup clear-all ;abriviares as – ca - ask n-of 4 patches [ ask n-of 20 patches in-radius 5

[ set pcolor red ] ]endclear-all: clear all default values

using parametersglobals [ num-clusters ]to setup clear-all set num-clusters 4 ask n-of num-clusters patches [ ask n-of 20 patches in-radius 5 [ set pcolor red ] ]end

creating 2 hunters - turtles

create-tutrles 2 ;crt 2

[

set sıze 2

set color yellow

]

create 2 turtles crt or create-tutlesbnild-in turtle variablessize and color

variable for patches

patches-own [

live-neighbors

]

live-neighbors

variable

go procedureto go ask turtles [search]end

to search ifelse tıme-sınce-last-found <= 20 [right (random 181) - 90] [right (random 21) - 10] forward 1end

cifelse boolean condition[ block whan true ][ block when false ] right: turn right by angle in degrees

variable for turtlestutrles-own

[

tıme-sınce-last-found

]

tıme-sınce-last-found

variable for all turtlestime passed since last mushroom has

found by the hunter

add to the search procedure

ifelse pcolor = red [ set tıme-sınce-last-found 0 set pcolor yellow ] [ set tıme-sınce-last-found tıme-sınce-

last-found + 1 ]end if found pcolor is red set tıme-sınce-last-found to 0 set pcolor yellowelse increment tıme-sınce-last-found by one

command center

• select turtles• write commands • hatch 1 [right 160]• show count turtles

firther modifications

• adding ticks• add reset-ticks• to the end of setup• add tick to the begining of go• following motion of hunters• add pen-down to the setup

procedute when initilizing turtles

Stable Patterns• 1 – Still Lifes: stable shapes

unless other shapes collide with them– block, the beehive, the loaf,...

• 2 – Oscillators: repeat over time• 3 – Spaceships: move across the

life world • Unstable Patterns: • guns: a pattern with a main part

that repeats like an oscillator and periodically emits spaceships

• In 1983, Stephan Wolfram – physisist and mathematical software entrepreneur

• One dimensional CA with only one neighbor in each side

• classified all possible rules into four behavioral regions– homogenous, periodic, chatoic and

complex• Complexity in nature – due to CA

like simple mechanisms

Outline

IntorductionLifeHeroes and CowardsSimple Economy

Heroes and Cowards

Rules of the game• with people each choose a heroe and an

enemy• two stages:• first every one act – coward

– move be sure that your friend is always between you and your enemy

– hiding from your enemy behind your friend cowardly

• second – behave like a heroe– move between your friend and enemy– protecting your friend from your enemy –

herotic manner

setup pseudocodeto setup ;; clear all previous settings variables ;; make patches white ;; create a set of turtles reand tne number froma slider ;; set x y corrdinates randomly ;; set colors to blue for cowards and red for heroes ;; if mixed is choosen determine crowads and heroes

randomly while settng their colors ;; set one other turtle as their friends and oneother

turtle as their enemies ;; reset ticksend

setup codeturtles-own [friend enemy]

to setup ca ask patches [set pcolor white] crt number [ setxy random-xcor random-ycor if personalities = "cowardly" [set color red] if personalities = “breverly" [set color blue] if personalities = "mixed" [set color one-of [blue red]] set friend one-of other turtles set enemy one-of other turtles ] reset-ticksend

Interface elements

• slider:– variable: number– default 68

• Chooser– variable: personalities– choices: “”” “cowardly”, “brawe”,

”mixed”

• Settings– wrap off

go pseudocode

go at each tick if the agent is heroe act brawely –

in a herotic manner if the agent is cowars act cowardly advance clock by oneend

to go

ask turtles [

if color = blue [act-bravely]

if color = red [act-cowadly]

]

tick

end

acting submodelsto act-bravely;; move toward the mod of your friend and your

enemy facexy ([xcor] of friend + [xcor] of enemy) / 2 ([ycor] of friend + [ycor] of

enemy) / 2 fd 0.1end

to act-cowadly;; set your friend between you and your enemy facexy [xcor] of friend + ([xcor] of friend -

[xcor] of enemy) / 2 [ycor] of friend + ([ycor] of friend -

[ycor] of enemy) / 2 fd 0.1end

Random number generation• sequance of random numbers• initial value is taken from the clock of

computer • if you want to strart from the same

seedrandom-seed 137

show random 100

show random 100

show random 100• always generate the same sequance of

random numbers 79 89 61

Outline

IntorductionLifeHeroes and CowardsSimple Economy

Simple Economy

• Economies – heterogenous actors – buyers and sellers

• in 1996, J. Epstein, R. Axtell, • SugerScape•

• Fixed number of people: 500• each starting out with inital amount of

money: 100• At each tick,• each person gives one of her 1 dollar‘s

to any other person at random• What will happen to the distribution of

money?• constraint – total amount of money fixed

– no one can have negative money– if income is zore, connot give any away

• is there a limiting distribution of money?

• Intiution:– flat –

• initially every body has the saime money• randomly seleced one to give

– normal -

Version 1

to setup

;; clear everything

;; create 500 turtles with an initial wealth of 100 each

;; reset tick

end

setup

turtles-own [wealth]

to setup

ca

crt 500 [

set wealth 100

]

reset-ticks

end

Version 1 to go ;;ask turles to transact if thye have positive or wealth

;; advence clock end

to transact ;; contect turtle ;; decrement wealth of current turtle by one

;; for one of the other turtles, increment its wealth by one

end

go and transactto go ask turtles with [wealth > 0] [transact]

tickend

to transact set wealth wealth - 1 ask one-of other turtles [set wealth wealth + 1]

end

Exercises

• can you move the wealth chacking condition to transact?

• can you use with instead of if?

Monitoring by histogram• Adjust settings world size

– orgine: left button– max-xcor 500– max-ycor 80– patch size 1– no wraping in both dimensions

• Interface – plot– max-x:500, max-y:40– histrogram [wealth] of turtles– pen mode: bar– Color green

Using view with an histogram

• For turtles:– size:2 – color: green– shape: “circle”

• x coordinate of view – wealth• y coordinate of view – randomly

assigned kind of bar of a histogram• During iterations set x coordinate

to wealth if wealth is less then 500

Version 2 setupturtles-own [wealth]

to setup ca crt 500 [ set size 2 set shape "circle" set color green set wealth 100 setxy wealth random-ycor ] reset-ticksend

go and transactto go ask turtles with [wealth > 0] [transact]

ask turtles [ if wealth <= max-pxcor [set xcor wealth]]

tickend

to transact set wealth wealth - 1 ask one-of other turtles [set wealth wealth + 1]

end