MIS 643 AgentBased Modeling amd Simulation 20172018 Fall

MIS 643 Agent-Based Modeling amd Simulation 2017/2018 Fall Creating Simple Agent-Based Models

Outline Intorduction Life Heroes and Cowards Simple Economy

Introduction • Intorduction to Agent-Based Modeling • by U. Wilensky and W. Rand • 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 Intorduction Life Heroes and Cowards Simple 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 than 2 alive neighbors it dies if it has more than 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

Net. Logo • Net. Logo 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 hirizonally, vertically, see IABM -WR pp 55 Box 2. 1 Wrapping

Net. Logo Code • modules – procedures • begin with to • end with end • usually • setup – initializations • go – processes taking place advences clock by tick

Procedures • procedures – commands • to procedure_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

Procedures (cont. ) to setup end to go end

Initialization to setup ; ; ask patches [ comands ]. . ; ; other commnads end ask primitive asks selected agents to do actions by commands in brackets set color of all pathces to red set - primitive is assignment pcolor – variable for patches

Initialization - algorithm 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 Centreric Thinking • WR-IABM Chapter 2 • Box 2. 2

Asking Patches Probabilistically • each patch performs the tasks in ask with a probability • probability of a patch being green is 0. 1 • in each run different number of patches turn into green

Probability of a Patch being green ask patches [ if random 100 < 10 [set pcolor green] ; ; end if ] ; ; end ask • or ask patches with [random 100 < 10] [ set pcolor green ] ] ; ; end ask

Asking exactly 10% of patches to setup ask n-of 0. 1*(51*51) patches [ set pcolor green ] ] ; ; end ask ] ; ; end setup • or more generally to setup let number-of-patches count patches ask n-of 0. 1*number-of-patches [ set pcolor green ] ] ; ; end ask ] ; ; end setup

go Procedure - algorithm to 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 Implementation to 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 liveneighbors = 0 [set pcolor blue] if live-neighbors >= 4 [set pcolor blue] ]

clear-all to setup clear-all ; abriviares as – ca ask patches [ set pcolor blue if random 100 < 10 [ set pcolor green ] ] end clear-all: clear all default values

variable for patches-own [ live-neighbors ] live-neighbors different variable for each patch initialized to 0

firther modifications • adding ticks • add reset-ticks • to the end of setup • add tick to the begining or as a last statemet of go procedure

to setup clear-all ask patches [ set pcolor blue if random 100 < 10 [ set pcolor green ] ] reset-ticks end

to 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 liveneighbors = 0 [set pcolor blue] if live-neighbors >= 4 [set pcolor blue] ] ; ; end ask tick ] ; ; end go procedure

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 Intorduction Life Heroes and Cowards Simple Economy

Heroes and Cowards • Each member (player) has an enemy and a friend selectd from other people playing the game

Rules of the game • with people each choose a heroe and an enemy • two stages: • first every one act – cowardly – 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 pseudocode to setup ; ; clear all previous settings variables ; ; make patches white ; ; create a set of turtles read 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 ticks end

setup code turtles-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-ticks end

Interface elements • slider: – variable: number – default 68 • Chooser – variable: personalities – choices: “coward”, “heroe”, ”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 one end

to go ask turtles [ if color = blue [actbravely] if color = red [actcowadly] ] tick end

acting submodels to act-bravely ; ; cıbtext turtle ; ; move toward the mid of your friend and your enemy facexy ([xcor] of friend + [xcor] of enemy) / 2 ([ycor] of friend + [ycor] of enemy) / 2 fd 0. 1 end to act-cowadly ; ; cıbtext turtle ; ; 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. 1 end

Random number generation • sequance of random numbers • initial value is taken from the clock of computer • if you want to strart from the same seed random-seed 137 show random 100 • always generate the same sequance of random numbers 79 89 61

Outline Intorduction Life Heroes and Cowards Simple Economy

Simple Economy • Economies – heterogenous actors – buyers and sellers • in 1996, J. Epstein, R. Axtell, • Suger. Scape •

• 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 they have positive wealth ; ; advence clock end to transact ; ; contecst turtle ; ; decrement wealth of current turtle by one ; ; for one of the other turtles, increment its wealth by one end

go and transact to go ask turtles with [wealth > 0] [transact] tick end to transact set wealth - 1 ask one-of other turtles [set wealth + 1] end

Histogram • • Select a plot title: Wealth Distribution min x cor: 1 nax x cor 500 min y cor 1 max y cor 80 pen update command: histogram [wealth] of turtles pen – select bar

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

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

Version 2 setup turtles-own [wealth] to setup ca crt 500 [ set size 2 set shape "circle" set color green set wealth 100 setxy wealth random-ycor ] reset-ticks end

go and transact to go ask turtles with [wealth > 0] [transact] ask turtles [ if wealth <= max-pxcor [set xcor wealth]] tick end to transact set wealth - 1 ask one-of other turtles [set wealth + 1] end