From Natural to Artificial Systems

From Natural to ArtificialSystems

Models of Competition andModels of Competition andCooperationCooperation

By Rob Cranston, Walter Proseilo,Chau Trinh & Owen Pang

Table of Contents

q Introductionq Modeling a Society of Mobile

Heterogeneous Individualsq Transmitting Cultureq Deciding Whether to Interactq Choosing How to Behaveq Summary

v An agent is anything thatcan be viewed as perceivingits environment throughsensors and acting upon thatenvironment througheffectors.

(from Intelligent Agents byDr. Jacob)

Introduction

What is an agent?

Introduction (cont.)

Competition – event inwhich persons compete

Cooperation –association of personsfor common benefit

Mathematica

v Powerful Multi-Use Tool.v Thousands of built in

functions.v Easy to use programming

tool.v Used for all simulations in

this presentation.

Mathematica As AProgramming Language

vRule based language – good for simulations

vVery strong pattern matching

vRules for our simulations rely on this. Thepattern matching is used to determine whichrule is carried out on the agent

Mathematica ToolkitSimulating Society

v “Simulating Society” byGaylord & D’Andria

v Simulations involvinggroups of agents

v Builds on others work anduses Mathematica as thetool for the simulations

v All simulations in ourpresentation are from thisbook

Modeling a Society of MobileHeterogeneous Individuals

Overview of the system

vDecentralized

vDiscrete

vDynamic

Modeling a Society of MobileHeterogeneous Individuals

Discrete dynamical system properties

vSpace is represented in 2-D

vEach cell is defined as a state

vThe system evolves over time

vCells updated using rules

Modeling a Society of MobileHeterogeneous Individuals

Simulation

vSquare n x n lattice

vPopulation of density - p

vThe system evolves time steps - t

Modeling a Society of MobileHeterogeneous Individuals

Populating Society

vAn empty site has a value of 0vA site occupied by an individual has a value

which is a list

Note: it is useful to focus on the lattice sites rather than on theindividuals.

Modeling a Society of MobileHeterogeneous Individuals

Executing a Time Step

vTime step is executed in two or moreconsecutive partial-steps

v In each partial-step, a set of rules is applied toeach site in the lattice

Modeling a Society of MobileHeterogeneous Individuals

MovementvOne agent per cell

vNeighborhood

vDirectionvWalk rules for updating

a lattice site have the form: walk[site, N, E, S, W, NE, SE, SW, NW, Nn, Ee, Ss, Ww]

Ww Ee

Nn

Ss

SW

NW NE

W

S

N

E

SE

Modeling a Society of MobileHeterogeneous Individuals

Each lattice occupied by an agent becomes empty unless:

Cell remains occupied by the agent, who chooses arandom direction to face

Scenario #1 Scenario #2

â

â

à ß

Modeling a Society of MobileHeterogeneous Individuals

InteractionvPerson to Person

vPerson to Group

Evolving the SystemvThe system evolves over t time steps, starting

with the initial lattice configuration and society

Modeling a Society of MobileHeterogeneous Individuals

Running the Simulation:

Random Walkers

Step 1 Step 2 Step 3 Step 498 Step 499

Transmitting Culture

What is CulturalTransmission?

Axelrod’s Model ofTransmission of Culture

Transmitting Culture

Axelrod’s ModelvConsists of a Meme

list of Features andTraits

vA = {3, 2, 1, 7, 5}

vN = {4, 8, 1, 2, 5}

A

N

Transmitting Culture

The Systemv A = {3, 2, 1, 7, 5}

v N = {4, 8, 1, 2, 5}

Cultural Exchangev A = {3, x, 1, 7, 5}

v N = {4, 8, 1, 2, 5}

Where x is a randomly chosen integer between 2 and 8.

A

N

Transmitting Culture

Modification to Axelrod’s Modelv Incorporating mobility

v Incorporating bilateralcultural exchange

Other ModelsvSocial Status and

Role ModelsBill Gates

Transmitting Culture

Running the Simulation

Deciding Whether to Interact

To Interact or Not to InteractvGood behavior versus bad behavior

The Prisoner’s Dilemma [Revisited]vPayoffs resulted from interaction

vBenefit if positive payoff

vCost if negative payoff

Deciding Whether to Interact

The SystemvSquare n by n lattice

Populating SocietyvEmpty site has 0vGood & Bad guysvSite occupied by an individual has a list I = {a, b, c, d, e}

I

Deciding Whether to Interact

Executing the Interaction Partial-Step

vMemory Checking

vRefuse or Accept Interaction

vUpdate List

Deciding Whether to InteractRunning the Simulation

Graph of Good Guy vs. Bad Guy

Deciding Whether to InteractPublic Knowledge

Graph of Good Guy vs. Bad Guy

Deciding Whether to InteractPublic Knowledge

Graph of Good Guy vs. Bad Guy

Deciding Whether to InteractSignals

“I suggest youdeactivate youremotion chip fornow.”

Patrick Stewart inStar Trek: FirstContact (1996)

http://www.geocities.com/Area51/Vault/126/

Deciding Whether to InteractUse of Vibes

Graphs of Good Guysand Bad Guys

Deciding Whether to Interact

Study - The UNIX Case:vIntroductionvToo many variations of UNIX

vSetting a Standard

vUNIX International Inc. (UII)

vOpen Software Foundation (OSF)

vTwo types of Companies

Deciding Whether to Interact

Study - The UNIX Case:vUses Landscape Theoryvsize: si

vpropensity: pij

vconfiguration: X

vdistance: dij

vfrustration: Fi(X)

venergy: E(X)

Deciding Whether to Interact

Study - The UNIX Case:vAssumptionsvCooperation

vCompetitionv Additional parameters α and β used to indicate close

rivals

v Nash Equilibrium

Deciding Whether to Interact

Study - The UNIX Case:vResults: Only two configurations that were also Nash

Equilibriums

Alliance 1 Alliance 2Sun DECAT&T HPPrime ApolloIBM Intergraph

SGI

Configuration AAlliance 1 Alliance 2Sun AT&TDEC PrimeHP IBM

ApolloIntergraphSGI

Configuration BSpecialistGeneralist

Choosing How to Behave

IntroductionvBeing good vs. being bad

vAdaptation

vIntrospection

Choosing How to Behave

Choosing One’s Interaction Behavior withAnother Individual

vBased on the Behavioral History of the OtherIndividual

vReciprocity

Choosing How to Behave

Stebbins’ Model

vPollyanna

vSociopath

vNice retaliator

vMean retaliator

Choosing How to Behave

The SystemvSquare n by n lattice

Populating SocietyvEmpty site has 0

vSite occupied by an individual has a list

I = {a, b, c, d, e}

I

Choosing How to Behave

Executing a Time Step

vDeciding

vInteracting

vMoving

Choosing How to BehaveGraph of the Four Behavior Strategies

Choosing How to Behave

Posch’s ModelvIntrospective

model

vSatiation

Graph of Posch’sModel

By Rob Cranston, Walter Proseilo,Chau Trinh & Owen Pang

From Natural to ArtificialSystems

vSummary

vQuestions

vWebnotes:http://www.cpsc.ucalgary.ca/~pango/533/

The End

March 27th Revision 4