Summary 20599 - Simulations and Modeling Notes Pt.2 (DSBA)
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Course
Simulations and Modeling (20599)
Institution
Università Commerciale Luigi Bocconi
These notes cover advanced simulation models with a focus on Agent-based Models (ABM) and Network Science. ABM is covered with details on agents, decision rules, environment and interactions, including Schelling's segregation model and the Axelrod model. In network science, concepts such as central...
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Simulations & Modeling - Part 2
Agent-based models
What are they useful for?
Features of an ABM
Microsimulations vs ABM
Elements of an ABM
Agents
Decision rules
Interacting agents
Environment
Time
Build an ABM
Schelling’s model - Segregation (1971)
One-dimensional model
Two-dimensional model
Axelrod model
Model formulation
Ants model - Alan Kirman
Entomology 101
Experiment
Results
How do state of the system evolve?
Features of the and model
Restaurant example - Becker, 1991
Evolutionary games - Foster and Young, 1990
Technological process - Arthur and David, 1989 and 1985
Traders
Hunter-gatherer model - Migliano et al.
The model
Conclusions
Age-at-marriage model - Todd & Billari 2005
Marriage environment
How to choose
Outcome with LR1
Outcome with LR2
Adding courtship period to the mating process
Little Italy model - Iozzi et al.
The model
Contact matrices
Network science
Undirected graph
Directed graph
Node degrees
Simulations & Modeling - Part 2 1
, Average degree
Degree distribution
Adjacency matrix
Complete graph
Sparseness
Weighted and unweighted network
Bipartite networks
Paths and Distances
Distance in a graph - Shortest path
Network diameter and average distance
Connectedness
Clustering coefficients
Centrality
Betweenness centrality
Degree centrality
Closeness centrality
Random Network model
Number of links in a random network
Degree distribution of a random graph
Scale-free networks
Random Graph
Small World phenomenon
Clustering coefficient in a random network
Are real networks like random graphs?
Watts and Strogatz’s “Small world” model - 1998
Barbasi and Albert model
Spreading Phenomena
SI model: homogeneous mixing
SIS model: common cold
SIR model
Epidemic models: summary
Network epidemics
SI model on a network: Degree Block Approximation
Early time behavior of an epidemic
SIS model on a network: Degree Block Approximation
SIR model on a network: Degree Block Approximation
Network Epidemics: summary
Community Detection
The basic structure of communities
Cliques
Strong community
Weak community
Methods to find communities
Similarity-based
Divisive method - Girvan-Newman algorithm
Agglomerative method - Louvain Algorithm
Other methods
Simulations & Modeling - Part 2 2
, Agent-based models
An ABM is a class of computational models for simulating the actions and interactions of
autonomous agents with a view to assessing their effects on the system as a whole.
What are they useful for?
Simulation of complex systems
Helps to simulate artificial societies
Features of an ABM
1. Precision: theoretical statements have to be written in a precise way, to be implemented
in a program;
2. Mathematical tractability: is less a limit for formalized theoretical constructions;
3. Bottom-up approach: solving the micro/macro link allowing for interactions, using micro-
based theories.
Microsimulations vs ABM
Microsimulation models take the individual In ABMs the focus is on individual agents,
as the unit of analysis and allow researcher their decision processes, their interactions
to differentiate between individual with other agents and the effects of that
characteristics and idiosyncrasies/habits. interactions on the decision processes.
Although most microsimulations models Whereas in microsimulation models
refer to individual decisions, they are not transition rates vary between heterogeneous
very explicit and detailed about the path individuals, in ABMs decision rules can vary
subjects follow to reach a decision. as well.
Individuals who strive for a higher standard
of living may be assumed to make decisions
differently from those fleeing from war or
political persecutions.
Elements of an ABM
Agents
Collection of agents and their states
Autonomous computational individual or object with particular properties and actions.
An agent is a self-contained, modular and uniquely identifiable individual.
Agents have attributes that allow the agents to be distinguished from and recognized by
other agents.
An agent is autonomous and self-directed.
An agent can function independently in its environment and in its interactions with other
agents, at least over a limited range of situations that are of interest in the model.
Simulations & Modeling - Part 2 3
, An agent has behaviors that relate information sensed by the agent to its decisions and
actions.
An agent’s information comes through interactions with other agents and with the
environment.
An agent’s behavior can be specified by anything from simple rules to abstract models,
such as neural networks or generic programs that relate agent inputs to output through
adaptive mechanisms.
An agent has a state that varies over time.
Just a system has a state consisting of the collection of its state variables, an agent also
has a state that represents the essential variables associated with its current situation. An
agent’s state consists of a set or subset of its attributes. The state of an ABM is the
collective states of all the agents along with the state of the environment.
An agent’s behaviors are conditioned on its state.
As such, the richer the set of an agent’s possible states, the richer the set of behaviors that
an agent can have. In an ABM simulation, the state at any time is all the information
needed to move the system from that point forward.
An agent is social and its dynamic interactions with other agents can influence its behavior.
Agents have protocols for interaction with other agents, such as for communication,
movement and contention for space, the capability to respond to the environment, and
others. Agents have the ability to recognize and distinguish the traits of other agents.
An agent may be adaptive, for example, by having rules or more abstract mechanisms that
modify its behaviors. An agent may have the ability to learn and adapt its behaviors based on
its accumulated experiences. Learning requires some form of memory. In addition to
adaptation at the individual level, populations of agents may be adaptive through the process
of selection, as individuals better suited to the environment proportionately increase in
numbers.
An agent may be goal-directed, having goals to achieve (not necessarily objectives to
maximize) with respect to its behaviors. This allows an agent to compare the outcome of its
behaviors relative to its goals and adjust its responses and behaviors in future interactions.
Agents may be heterogeneous. Unlike particle simulation that considers relatively
homogeneous particles, agent simulations often consider the full range of agent diversity
across a population. Agent characteristics and behaviors may vary in their extent and
sophistication, how much information is considered in the agent’s decisions, the agent’s
internal models of the external world, the agent’s view of the possible reactions of other
agents in response to its actions, and the extent of memory of past events the agent retains
and uses in making its decisions. Agents may also be endowed with different amounts of
resources or accumulate different levels of resources as a
result of agent interactions, further differentiating agents
.
Decision rules
Rules governing the interactions of the agents
Simulations & Modeling - Part 2 4
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