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