Sarah Wolf, Stefanie Winkelmann, Thomas Steinke
Gesine Steudle, Steffen Fürst
01.01.2022 – 31.12.2022
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; a promising approach to participatory decision support on societal challenges is the Decision Theatre (DT, ). It combines empirical information, mathematical modelling and simulation, and a stakeholder dialog format supported by interactive visualization. Agent-based models (ABMs) are an appropriate model structure for that.
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. This is where this project is located.
Goal of the Project:
The vision shaping this project is a high-performance software framework for easy development of ABMs for Decision Theatres. This necessitates, first of all, the definition of a mathematical structure that captures the requirements of DT models. As a step towards such a structure and framework, this project shall transfer the architecture of the Mobility Transition Model (MoTMo) – an interdisciplinary, economics-focused, computational ABM – into mathematical form, and based on this, into an efficiently parallelizable implementation.
In view of efficient parallelization, Graph Dynamical Systems (GDS, ) represent a promising approach [3, 4]: agents, groups of agents, and other entities are nodes in the graph, while possible interactions constitute its edges, which also determine the visibility of the state of other nodes when the transition function of a node is invoked. Parallelization can then be tackled via graph partitioning and subgraphs can be computed in parallel requiring transition functions to be referentially transparent. Moreover, in contrast to the object oriented perspective of almost all existing ABM frameworks, GDSs are a natural language for formally specifying ABMs .
Relevant elements for building models of complex adaptive socio-economic systems include:
– A multi-layer representation of society as part of the model’s underlying graph
– Decision making of single agents along the lines of the rational agent in economics , however, with incomplete information and subjective probabilities evolving through learning within an agent network (e.g., Bayesian updating), and under given constraints (the latter may occur at group rather than individual level).
– A utility function that combines several criteria for individual decisions, which agents can weight differently.
– Mechanisms for representing how outcomes of different choices depend on the agents’ local environment.
With these elements, the project shall allow for generalization of ABMs like MoTMo — the design of the resulting software shall encourage users to take a more mathematical perspective on their models and to shift focus from objects to interaction patterns and networks in the modeled systems. For a theory of political and socio-economic transitions, such as in the case of sustainability, choice theories are essential; this project’s work can help explore functional networks of decision making in ABMs like MoTMo.
The project closely relates to the Thematic Einstein Semester “The Mathematics of Complex Social Systems“.
 S. Wolf, S. Fürst, A. Geiges, M. Laublichler, J. Mielke, G. Steudle, K. Winter, and C.C. Jaeger. The Decision Theatre Triangle for societal challenges. Under review, see https://globalclimateforum.org/wp-content/uploads/2021/04/GCFwp2_2021.pdf, 2021.
 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.
 A. Geiges, S. Wolf, G. Steudle, and S. Fürst. Report of framework for prototyping of parallel Agent-Based Modelling Systems, 2018. http://coegss.eu/wp-content/uploads/2018/11/D3.8.pdf.
 D. Kreps. Notes on the Theory of Choice. Westview Press, 1988
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