Complex systems are abundant: The society, the economy, the financial system, food webs, energy supply systems are just some examples. The recent development of information technology opened unprecedented opportunities in studying them. On the one hand due to making available huge amounts of data, on the other hand by offering computer power for simulating them.
Networks represent the scaffold of complex systems, on which the functioning processes take place. Complex systems are heterogeneous in many ways. Broad distributions characterize the network degrees, the link weights and the properties of the nodes as well as aspects of their temporal behavior. Most analytical approaches like those with “representative agents’ simplify to an unrealistic level this relevant multitude of heterogeneities. Therefore simulation techniques, like heterogeneous multi-agent modeling becomes increasingly important.
Agent based modeling is a flexible framework to simulate the action and interaction of entities of complex systems. The course will give an introduction to this topic by making students acquainted with the most important concepts and tools. A versatile, open access easy-to-use platform will be presented, which enables to construct own models and simulations. Relevant agent based models will be discussed from the field of biology, sociology, economics and finance. Issues include conflicts and consensus in opinion formation, segregation as a result of homophily, origins of cultural diversity and market simulations. Techniques of model calibration and validation will be presented.
|Complex systems. Heterogeneities on all scales. Earlier approaches. Why agent based modeling? Examples of successful agent based modeling.|
|2||NetLogo tutorial I.|
|Introduction to the open access NetLogo platform. Variables, interactions, actions. Visualization. Statistical analysis.|
|3||NetLogo tutorial II.|
|Getting acquainted in and interactive way. Defining the model. Running the program. Input and output. Some examples.|
|4||Examples from biological modeling|
|Ants, flocking, herding, etc. Biological interactions. Predator-prey systems. Colonies of ants. Flocking of birds, fish schools. Motion of humans in panic situation.|
|5||Agent based models in ecology|
|Ecological interactions. Multiple processes at different organizational levels. Network analysis and system models. Linking population and community dynamics. Variability and stochasticity in ecology. Key system components and adaptability.|
|6||Opinion dynamics models.|
|Discrete and continuous opinion variables. Models of political opinion formation (voter model, Sznajd model). Bounded confidence model and formation of parties. The role of mass media. Adaptive networks.|
|7||The Schelling model of segregation and the Axelrod model of cultural diversity|
|Two state variables with attractive interactions: The Ising model and its social interpretation. Mobile agents. If segregation results from minor homophily how comes the diversity of the society? Axelrod’s multidimensional characterization of individuals. The role of the topology, network adaptation and mass media.|
|8||Evolutionary game theoretical models|
|Game theoretical concepts, Nash equilibria. Basic strategic games: Prisoners’ dilemma, Hawk-Dove, Snowdrift, Tragedy of the Commons etc. Failure of the mean field approach. The role of the topology.|
|The El Farol bar problem. Adaptation, learning and the role of memory. Heterogeneity in the strategies. Relevant parameters, regimes of different behavior in the volatility. Relation to finance. Variants of the Minority game.|
|10||Agent based models in Finance|
|Stylized facts in finance. Heterogeneity of investors. The model of Kim and Markowitz. Levy-Levy and Solomon model. The Santa Fe artificial stock market. Noise traders and fundamentalists. Lux-Marchesi model and its simplified versions.|
|11||Calibration and validation of agent based model|
|Calibration and validation procedures of agent-based models. Absence of a unified procedure and approach. Main methodological aspects. Descriptive output validation, matching computationally generated output against actual data. Predictive output validation, matching computationally generated data against yet-to-be-acquired system data.|
N. Gilbert, Agent-Based Models, Sage Publications 2008.
J.H. Miller and S.E. Page, Complex Adaptive Systems: An Introduction to Computational Models of Social Life, Princeton University Press 2007.
C. Castellano, S. Fortunato, and V. Loreto, Statistical physics of social dynamics, Rev.