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Agent-based ModelingWeb Science (VU) (706.716)
Elisabeth Lex
ISDS, TU Graz
May 28, 2018
Elisabeth Lex (ISDS, TU Graz) Agents May 28, 2018 1 / 41
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Introduction
Repetition
Information Cascades, HerdingModeling with Bayes’ RuleLinear Threshold ModelProbabilistic Models: SIR, SIS
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Introduction
Today
Agent-based Modeling (ABM)What is ABM?Phenomena that can be modeled using ABMExamples
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Introduction
What is Agent-based Modeling (ABM)?
New approach to modeling systems that consist of autonomous,interacting agentsDynamic processes of agent interaction are simulated repeatedly overtimeThus, an ABM is a model in which agents interact repeatedlyIdeas for an example from nature?
Ant colonies: organizes itself to carry out complex tasks of gatheringfood and building a nest while being extremely resilient if colony isdisrupted (“swarm intelligence”)
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Introduction
What is Agent-based Modeling (ABM)?
New approach to modeling systems that consist of autonomous,interacting agentsDynamic processes of agent interaction are simulated repeatedly overtimeThus, an ABM is a model in which agents interact repeatedlyIdeas for an example from nature?Ant colonies: organizes itself to carry out complex tasks of gatheringfood and building a nest while being extremely resilient if colony isdisrupted (“swarm intelligence”)
Elisabeth Lex (ISDS, TU Graz) Agents May 28, 2018 4 / 41
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Introduction
The need for Agent-based ModelingWe live in an increasingly complex world
Our systems are increasingly complex and interdependent: e.gelectrical infrastructures, telecommunication networks, transportationnetworks, social systems, social networksSome systems have always been too complex to model realistically:e.g models for economic marketsNew tools and modeling approaches available that help us analyzecomplex systemsLots of empirical data available and computational powerExample use cases for ABM: modeling agent behaviour in the stockmarket, supply chains, consumer markets, spreading of epidemics,understanding social systems,..All those are Complex Systems: individual behavior and propertiesbetter understood than behavior and properties of whole system
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Agents
Agent-based models
Agents are autonomous and model intelligent behavior with a simpleset of rulesThe agents are situated in space (e.g. a grid or a network)The agents interact with each other locally (i.e., they are social)The agents have only a partial local informationThere are often different types of agents following different set of rulesThe rules may be deterministic or probabilisticThere are often random elements in the world
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Agents
Agents
Agents are self-contained: identifiable, discrete, has set ofcharacteristics / attributes, behaviours and decision-making capabilityAgents can have memory - then, they can learn and adapt theirbehaviour (dynamic agent attribute)Examples for agents: people, groups, organizations, insects, swarms,robots, biological entities,..
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Agents
Agent-based models
Argent-based models are used to simulate actions and interactions ofautonomous agents and to assess their effects on system as a wholeUnderstanding relations between individual decisions and systembehaviorMicromotives vs. Macrobehavior (Schelling’s book)They are always computational, i.e., simulationsThey are intuitive for implementation, experiments, interpretation
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Agents
Advantages of Agent-based models
ABMs are extensibleABM are interpretable: one can use them to transparently planreal-world conceptsHolistic modeling approach: can be used to answer multiple questions(“many question models”)Typically, individual-level behavior better understood than aggregate(population) level. One can start with sth that is better understoodto understand macro behaviorABMs help tackle complexity and well suited to model behavior
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Agents
Tools to build ABM
Agent-based modeling and simulation toolkits: Repast (Java), Swarm(Objective C, Java), NetLogo, StarLogo, MASON, AnyLogixGenerall tools: e.g. MATLAB, spreadsheets, ABM with programminglanguages (Python, Java,...)
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Agents
Selected models1 Life2 Schelling Model3 Viruses on networks4 Ising model5 Forest fire
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Life
Life (1/3)
Developed by mathematician John ConwayBased on cellular automata (CA): 2-dimensional grid partitioned intocellsEach cell assumes one of a finite nr of states at any point in time -On or OffValue of each cell is determined by set of rules, based on cell’sprevious state and value of its immediate 8 neighboursEach cell updated at each time step according to the rules
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Life
Life (2/3)
Life has 3 rules that determine next state of each cell:Rule 1: The cell will be On in the next generation if exactly three ofits eight neighboring cells are currently On.Rule 2: The cell will retain its current state if exactly two of itsneighbors are On.Rule 3: The cell will be Off otherwise.
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Life
Life (3/3)
Life as ABM:Each cell is an agentStates of cell (On and Off) are the possible states of an agentCell update rules represent an agent’s behaviourThe states of all the agents taken together at a specific time in thesimulation is the state of the model (system)Grid is the environment of Life - minimal function as reference pointto determine agent’s neighborhood
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Life
Example of Life
(a) Initial stage (b) After 40 times
Figure: Life simulation: (a) initial random layout of cells in the On state, (b) afterall cells updated 40 times
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Life
Observations from Life Model
Rules are simple and use only local information as each cell’s state isbased on its current state and the state of its immediate neighborsResulting patterns of Life depend on initial conditions - eachsimulation gives different patterns of On and Off cellsPatterns can emerge in systems that are completely described bysimple, deterministic rules based on only local informationBased on simple rules of behavior and nature of agent interactions,systems can show collective intelligence, even without existence of acentral authority
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Life
Netlogo Example of the Life Model
http://ccl.northwestern.edu/netlogo/Go to File/Model Library/Computer Science/Cellular Automata/Life
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The Schelling Model
The Schelling Model
A small preference for a specific kind of neighbors lead to totalsegregationShows how global patterns (spatial segregation) can arise from localpreferences (homophily)A simple robust mechanism leads to segregationSegregation achieved even if no one explicitly aims for it
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The Schelling Model
How does the Schelling Model work? (1/2)
Assume a population of individuals (aka agents) of type 𝑋 or 𝑂Types represent immutable characteristics (e.g., age)Two populations are initially placed into random locations of aneighborhood gridAfter placing all agents, each cell is either occupied by an agent oremptyThe neighbor relationships among the cells can be represented verysimply as a graph: cells are the nodes, edges are inserted between twocells that are neighbors on the grid
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The Schelling Model
How does the Schelling Model work? (2/2)
Now, determine if each agent is satisfied with its current locationAgent is satisfied if is surrounded by at least 𝑡 of its own type ofneighboring agentsThreshold 𝑡 applies to all agents in the model (in reality everyonemight have a different threshold they are satisfied with)The higher 𝑡, the higher the likelihood that agents will not besatisfied with their current locationExample:
For example, if 𝑡 = 3, agent 𝑋 is satisfied if at least 3 of its neighborsare also 𝑋If fewer than 3 are X, then the agent is not satisfied, and it will want tochange its location in the gridAny algorithm can be used to choose new location (e.g., randomselection, nearest available location, 1 row at a time)
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The Schelling Model
Example
(a) Initial stage (b) After one round
Figure: Left image: all dissatisfied agents have an asterisk next to them. Rightimage: shows new configuration after all dissatisfied agents have been moved tounoccupied cells (1 row at a time) where they are satisfied. May cause otheragents to become unsatisfied, then new round of movement begins
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The Schelling Model
Netlogo Example of the Schelling Model
http://ccl.northwestern.edu/netlogo/Go to File/Model Library/Social Science/Segregation
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The Schelling Model
Observations from Schelling’s Model
Spatial segregation takes place even though no individual agentactively seeks itSegregation doesn’t happen due to built-in model agents that arewilling to be in the minorityIdeally, all agents are carefully arranged in an integrated patternHowever, from random start hard for agents to find such integratedpatternsAt more general level, Schelling model is an example of how fixedcharacteristics (e.g., ethnicity) can become highly correlated withmutable characteristicsE.g. decision where to live, which over time conforms to similarities inagents immutable types, producing segregation
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Virus on a Network
Rep: How does the epidemics work?
The models originally come from biologyHow viruses and diseases spread in social networksWe have different types of nodesInfected (I): people who got the virusSusceptible (S): people who do not have virus but can check itRecovered (R): people who had the virus but got recovered and cannot catch it again (in some models people can become immune)Various model: SI, SIR, SIS, SIRS
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Virus on a Network
Netlogo Example of the Epidemics
http://ccl.northwestern.edu/netlogo/Go to File/Model Library/Networks/Virus on a Network
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Virus on a Network
Questions
What happens in SI model after long time?
Everyone is infectedWhich model do we have if we set gain-resistance-chance to 0?SISWhen we will have an outbreak in SIS?E.g. if recovery chance is low and transmission rate is high
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Virus on a Network
Questions
What happens in SI model after long time?Everyone is infectedWhich model do we have if we set gain-resistance-chance to 0?
SISWhen we will have an outbreak in SIS?E.g. if recovery chance is low and transmission rate is high
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Virus on a Network
Questions
What happens in SI model after long time?Everyone is infectedWhich model do we have if we set gain-resistance-chance to 0?SISWhen we will have an outbreak in SIS?
E.g. if recovery chance is low and transmission rate is high
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Virus on a Network
Questions
What happens in SI model after long time?Everyone is infectedWhich model do we have if we set gain-resistance-chance to 0?SISWhen we will have an outbreak in SIS?E.g. if recovery chance is low and transmission rate is high
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Virus on a Network
Phase transition
Outbreak depends on the relation between dynamical parameters andthe network structureWith fixed dynamical parameters in what kind of the network anoutbreak is more likely?With higher or lower average degree?
Higher degreeOften there is a very small margin for parameters and the networkstructure where the system goes quickly from one state into anotherPhase transition
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Virus on a Network
Phase transition
Outbreak depends on the relation between dynamical parameters andthe network structureWith fixed dynamical parameters in what kind of the network anoutbreak is more likely?With higher or lower average degree?Higher degree
Often there is a very small margin for parameters and the networkstructure where the system goes quickly from one state into anotherPhase transition
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Virus on a Network
Phase transition
Outbreak depends on the relation between dynamical parameters andthe network structureWith fixed dynamical parameters in what kind of the network anoutbreak is more likely?With higher or lower average degree?Higher degreeOften there is a very small margin for parameters and the networkstructure where the system goes quickly from one state into anotherPhase transition
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Forest Fire
How does the Forest Fire work?
The forest is a grid of cellsA cell is either occupied by a tree or emptyThe fire starts on the left edge of the forestIt spreads to the neighboring trees in all four directionsNorth, south, east, westFire can not skip an empty cellThere is no wind
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Forest Fire
Netlogo Example of the Forest Fire model
http://ccl.northwestern.edu/netlogo/Go to File/Model Library/Earth Science/Fire
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Forest Fire
Questions
With density around 50% how much of the forest burnsWith different initial settings do the same tree burn?Each point that represents a tree burning is born and then diesIt never moves whatsoeverThe fire is made of burning trees that do not moveBut the fire itself moves!Local vs. global levelEmergence of properties at a global level that do not exist on thelocal level
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Forest Fire
Questions
Again phase transition around 59%Reaching the other edge of the gridFor which scenarios could we apply the forest fire on the Web?
Viral marketing
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Forest Fire
Questions
Again phase transition around 59%Reaching the other edge of the gridFor which scenarios could we apply the forest fire on the Web?Viral marketing
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Ising
How does the Ising model work?
The model originally comes from physicsIt models the magnetization of a materialThe cells are organized in a gridEach cell has a spin 𝑠𝑖: it is represented by +1 or -1The cells can flip their spinThe energy of a cell is calculated from its four neighbors (north,south, east, west) as 𝐸𝑖 = ∑𝑗 𝑠𝑖𝑠𝑗The total energy is 𝐸 = ∑𝑖 𝐸𝑖The system always tries to reach the state of the minimal energy withsome randomness, which increases with temperature
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Ising
Netlogo Example of the Ising model
http://ccl.northwestern.edu/netlogo/Go to File/Model Library/Chemistry & Physics/Ising
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Ising
Questions
What happens when the temperature is low?
The cells will align their spinsWhat happens when the temperature is high?The alignment is not likely anymoreThere is a specific temperature, which separates those two modes:
2𝑙𝑛(1+
√2) on an infinite grid
Phase transitionFor what phenomenon ca we use Ising model on the Web?Opinion dynamics, consensus reaching, etc.
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Ising
Questions
What happens when the temperature is low?The cells will align their spinsWhat happens when the temperature is high?
The alignment is not likely anymoreThere is a specific temperature, which separates those two modes:
2𝑙𝑛(1+
√2) on an infinite grid
Phase transitionFor what phenomenon ca we use Ising model on the Web?Opinion dynamics, consensus reaching, etc.
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Ising
Questions
What happens when the temperature is low?The cells will align their spinsWhat happens when the temperature is high?The alignment is not likely anymoreThere is a specific temperature, which separates those two modes:
2𝑙𝑛(1+
√2) on an infinite grid
Phase transitionFor what phenomenon ca we use Ising model on the Web?
Opinion dynamics, consensus reaching, etc.
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Ising
Questions
What happens when the temperature is low?The cells will align their spinsWhat happens when the temperature is high?The alignment is not likely anymoreThere is a specific temperature, which separates those two modes:
2𝑙𝑛(1+
√2) on an infinite grid
Phase transitionFor what phenomenon ca we use Ising model on the Web?Opinion dynamics, consensus reaching, etc.
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Wealth Distribution
How does the wealth distribution work?
We have population living on a grid of cellsEach cell has an amount of grain and an grain capacityPeople collect grain from the cells and eat (some of) the grain tosurviveHow much grain each person accumulates is her wealthInitially, a roughly equal distributionEach person attempts to move to a cell with more grain (if free)People have a life expectancy and can die and can also die if theyhave no grainIf a person dies an offspring is born with a random amount of grain(no inheritance)
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Wealth Distribution
Netlogo Example of the Wealth Distribution model
http://ccl.northwestern.edu/netlogo/Go to File/Model Library/Social Science/Wealth Distribution
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Wealth Distribution
Questions
What kind of wealth distribution do we expect to see?
A power-law distribution! Why?Because agents are heterogeneousThey have different visions, metabolism, life expectancy, and so onThose agents who gain an initial advantage will keep that advantagePreferential attachment
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Wealth Distribution
Questions
What kind of wealth distribution do we expect to see?A power-law distribution! Why?
Because agents are heterogeneousThey have different visions, metabolism, life expectancy, and so onThose agents who gain an initial advantage will keep that advantagePreferential attachment
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Wealth Distribution
Questions
What kind of wealth distribution do we expect to see?A power-law distribution! Why?Because agents are heterogeneousThey have different visions, metabolism, life expectancy, and so onThose agents who gain an initial advantage will keep that advantagePreferential attachment
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Wealth Distribution
Summary
Agent-based modelingWhy? To model complex systems and to study emergent phenomena,e.g. from animal behavior, social sciences, ecology, ...Complex system: individual behavior and properties better understoodthan behavior and properties of whole systemExamples for ABM: Life, Schelling, Epidemics, Ising, Forest Fire,Wealth distribution
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Wealth Distribution
Take away
We can model and understand real-world phenomena by constructingmodels that exhibit complex emergent behavior resulting from local,simplified agent interaction.
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Wealth Distribution
How would you build an ABM?
Pro tip: Take an established model and see whether you can buildupon itRequires model literacy!
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Wealth Distribution
How would you build an ABM?
Pro tip: Take an established model and see whether you can buildupon itRequires model literacy!
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Wealth Distribution
Thanks for your attention - Questions?
Elisabeth Lex (ISDS, TU Graz) Agents May 28, 2018 41 / 41
