Incubator Projects



Towards a Framework for Decision Theatre Models


Project Heads

Sarah Wolf, Stefanie Winkelmann, Thomas Steinke

Project Members

Gesine Steudle, Ste ffen Fürst

Project Duration

01.01.2022 – 31.12.2022

Located at



Complex social processes are at the heart of many areas in which (political) decisions are highly necessary, e.g. climate protection, spread of epidemics, urban development, social inequality. Mathematical modeling of the underlying systems can support decision making; in particular, agent-based models (ABM), that represent a system on the level of its interacting elements, are helpful tools [1]. However, there is a research gap between complex, empirically grounded ABMs from many disciplines, that are hard to grasp mathematically, and rather recent work in mathematics that considers much simpler ABMs.


To address this gap, the project developed and investigated a basic mathematical structure for ABM of socio-technical systems. This includes agents and their interactions, a social structure (network), a common environment (local and global fields) and feedbacks between all these elements [2,3]. Based on this structure, the project further provided a framework for large-scale agent-based models [4,5]. The project closely relates to the Thematic Einstein Semester “The Mathematics of Complex Social Systems“.


The structure for ABM of socio-technical systems transferred the architecture of the Mobility Transition Model (MoTMo)[6] – an interdisciplinary, economics-focused, computational ABM – into mathematical form. This showed how typical memory mechanisms in a co-evolutionary process between (mobility) decisions and adaptive developments of the social structure and technical (infra)structure can be captured via a state space extension to formulate a reduced computational ABM as a Markov process, in particular, an iterated random function [7]. Thus the ground for mathematical analysis of complex socio-technical systems was laid.


The high performance computing open source framework, Vahana.jl [4,5], uses the structure of synchronous graph dynamical systems [8] to allow for efficient parallelization of ABM with a focus on (social) networks. The framework seamlessly supports distribution across multiple compute nodes, enabling simulations that would otherwise be infeasible on a single machine. At the same time, implemented in Julia, Vahana.jl promotes rapid model development and experimentation by utilizing Julia’s interactive Read-Eval-Print Loop (REPL) environment.

Selected Publications

[1] Wolf, S., Fürst, S., Geiges, A., Laubichler, M., Mielke, J., Steudle, G., Winter, K. and Jaeger, C., 2023. The Decision Theatre Triangle for societal challenges—An example case and research needs. Journal of Cleaner Production, 394, p.136299.

[2] Steudle, G., Winkelmann, S., Fürst, S. and Wolf, S., 2024. Understanding Memory Mechanisms in Socio-Technical Systems: The Case of an Agent-Based Mobility Model. Advances in Complex Systems. DOI

[3] Steudle, G., Fürst, S., Wolf, S., 2022. Reduced Mobility Transition Model (R-MoTMo), Version 1.0.0. CoMSES Computational Model Library. DOI

[4] Fürst, S., Conrad, T., Jaeger, C., Wolf, S., 2024. Vahana.jl – A framework (not only) for large-scale agent-based models. Submitted.

[5] Code:; Documentation:; Presentation at juliacon 2023:


[6] Global Climate Forum, 2022. The Mobility Transition Model (MoTMo),

[7] Diaconis, P. and Freedman, D., 1999. Iterated random functions. SIAM review 41(1), pp. 45-76.

[8] A. Adiga, C.J. Kuhlman, M.V. Marathe, H.S. Mortveit, S.S. Ravi, and A. Vullikanti. Graphical dynamical systems and their applications to bio-social systems. International Journal of Advances in Engineering Sciences and Applied Mathematics, 11(2):153–171, Dec 2018.

Related Pictures

Typical simulation outputs from R-MoTMo

Agents coordinate on using cars (left) or using public transport (right). Memory mechanisms in complex socio-technical systems can lead to path-dependencies in parts of the system while a state space extension that captures social and technical structures allows to study the system as a Markov process.

Structure of Vahana

The framework extends synchronous graph dynamical systems to enable different types of nodes (agents) and edges, a spatial and global layers (environment).

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