A Simulation of Engineering Hybrid Modeling Strategies Applied to World Cup Soccer

 Given the challenges of modeling multi-scale social phenomena, do hybrids hold the key to unlocking social complexity dynamics?   We introduce hybrid system modeling from engineering and applied mathematics, as a means to capture complex dynamics within interacting, multi-scale social systems. Whereby, hybrid modeling is used in industrial processes and automated control systems, this research uses world cup soccer tournament simulations, to demonstrate successful applications. A predator-prey, theoretical approach is applied with world cup soccer players and teams represented as predators, and the soccer ball as prey. Simulations of multiple soccer tournaments of thirty-two teams were conducted with betting, and without betting, as a pseudo-control measure.

The hybrid application employs combinations of logic strategies with agent-based modeling, cellular automaton, and differential equations, which all interact simultaneously, creating the hybrid systems’ dynamics on multiple scales. Each soccer player has distinct agent attributes, such as error rates for goal shots or passes, level of aggressiveness, and self-confidence. These attributes are continuously adapted based on differential equations during each game. This endows the self-organizing, soccer playing agents with evolutionary learning. Adaptation is dependent upon multi-scale interactions from the ball, other players, crowds, and bettors. The connecting parameter between players’ attributes and spectators, is the game atmosphere inside the simulated soccer stadium. The game atmosphere is dependent on perceptions about soccer ball action, players’ adaptations, as well as the spectator reactions. The soccer crowds are a combination of spectators and bettors. They are modeled as recurrent fuzzy-based, cellular automaton in colors, to capture resulting emotional reaction to the ball. The possible emotional states are represented as changing color schemes, dependent upon game action. Emotional states are set on rule-based interconnections. These include the actual state of an agent, its neighbors’ emotional state, and the odds of winning or losing money betting. This leads to a new emotional state . This enables each agent to be in a state , which is somewhere in-between of all defined This approach overcomes the limitations of conventional cellular automaton, staying only in strict defined states. The global betting odds in the soccer tournament are represented by time discrete, differential equations which iterate from one game to the next. As human behavior is non-deterministic, a Gaussian distribution-based random variance of the above defined deterministic behaviors, is enabled. Thus, the overall hybrid model of social phenomena is a complex adaptive system, whereby agents have an opportunity to interact in their respective environments in each iteration.

The results show pre-game betting has significant impact on the outcome of the final tournament game. The usual tournament winner is dominant in defense, and wins by a large margin. The losing team is usually dominant in offense. Divergence of playing styles does not appear to develop in non-betting simulations. Further research focus is needed to support preliminary evidence that betting may contribute to a team’s unique styles of play, and the ultimate creation of vastly superior teams. The hybrid simulation creates an event-driven, bottom-up, CAS, where emergence can be demonstrated in the unique the styles of play that evolve in each game and each tournament. This research demonstrates that hybrid engineering modeling, characterized by discrete and continuous dynamics with interconnected structure for complexity decomposition, can also be incorporated to complex social systems research. Exploring hybrid applications has the potential to improve our understanding and modeling of global social complex adaptive systems.

Liz Johnson, Complex Systems Institute, Charlotte, NC

Klaus Diepold, Technical University of Munich, Munich, Germany &Institute of  Automatic Control, Munich, Germany

James Mathieson, Clemson Engineering Design Applications and Research, Clemson, SC, USA


Diepold thanks the German Research Foundation (DFG) for funding his part of this research as part of the collaborative research project ‘Managing cycles in innovation processes – Integrated development of product service systems based on technical products’ (SFB 768).


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