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


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


Simulation

vSquare n x n lattice

vPopulation of density - p

vThe system evolves time steps - t


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.


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


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


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


InteractionvPerson to Person

vPerson to Group

Evolving the SystemvThe system evolves over t time steps, starting

with the initial lattice configuration and society


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


Axelrod’s ModelvConsists of a Meme

list of Features andTraits

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

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

A

N


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


Modification to Axelrod’s Modelv Incorporating mobility

v Incorporating bilateralcultural exchange

Other ModelsvSocial Status and

Role ModelsBill Gates


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


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


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 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


Study - The UNIX Case:vIntroductionvToo many variations of UNIX

vSetting a Standard

vUNIX International Inc. (UII)

vOpen Software Foundation (OSF)

vTwo types of Companies


Study - The UNIX Case:vUses Landscape Theoryvsize: si

vpropensity: pij

vconfiguration: X

vdistance: dij

vfrustration: Fi(X)

venergy: E(X)


Study - The UNIX Case:vAssumptionsvCooperation

vCompetitionv Additional parameters α and β used to indicate close

rivals

v Nash Equilibrium


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 One’s Interaction Behavior withAnother Individual

vBased on the Behavioral History of the OtherIndividual

vReciprocity


Stebbins’ Model

vPollyanna

vSociopath

vNice retaliator

vMean retaliator


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


Executing a Time Step

vDeciding

vInteracting

vMoving

Choosing How to BehaveGraph of the Four Behavior Strategies


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

From Natural to Artificial Systems

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