A game theory-inspired model shows how the areas around train doors become crowded at rush hour. The model could eventually be used as a tool for designing safer public venues.
When two parties interact, such as countries vying for resources or prize winners deciding how to split their winnings, the situation can be modelled using game theory, which assumes both parties make rational, strategic decisions.
at Northumbria University in Newcastle upon Tyne, UK, and his colleagues used a combination of game theory and the physics of complex systems to work out how crowds might move, based on modelling how an individual reacts to the crowd surrounding them.
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Previous models have applied this physics-inspired game theory to certain aspects of crowds, such as how a crowd member might navigate to an exit. Bonnemain and his team focused instead on modelling the crowd member鈥檚 immediate environment, taking into account the other individuals that were within touching distance.
But the model also assumed that the crowd member would look beyond this local area and adjust their behaviour in response either to potential obstacles or to 鈥渋ntruders鈥� 鈥� people or objects moving through the crowd without deviating from a fixed course.
鈥淎 key aspect of this work is anticipation,鈥� says Bonnemain. 鈥淚t鈥檚 the ability the pedestrian has to understand how the intruder will go through the crowd.鈥�
When Bonnemain and his team ran simulations based on equations they developed, they noticed the virtual members of their crowds behaved in ways that mimicked real-world scenarios, such as the bunching of crowds observed when a large object, like an ambulance, is trying to pass through.
The model also replicated other phenomena. For instance, it reproduced the tendency of the area around train or metro doors to become packed at busy times, with the density of people highest around the doors as they close. The model also showed that some people will wait on the platform by the doors before they close, as the entrance is too packed.
鈥淭o have this kind of outcome, people need to anticipate that it will be more costly for them to rush in than to wait for the next train,鈥� says Bonnemain.
The model is still in development, but Bonnemain says it could eventually have real-world applications. 鈥淢aybe the most obvious [application] here is how you design venues. If the problem is a burning building, then how do we make it so that the maximum number of people can escape,聽 because you know how the flow of pedestrians works so then you know how and where to put your doors so the maximum amount of people can go through.鈥�
, a crowd modelling consultant in Burton, UK, says the model could be a 鈥渦seful and interesting tool鈥� to analyse crowd behaviour in complex spaces, but that as a way to predict real-world scenarios it lacks more complex factors, such as individual behaviours.
鈥淚t takes just one individual behaving slightly erratically in the middle of a crowd to change the crowd behaviour,鈥� says Still.
Bonnemain says that the work is still at an early stage, but that the early qualitative results are promising. 鈥淭he model we propose is very simple, so it can be refined,鈥� says Bonnemain. 鈥淏ut to describe some situations we need anticipation, and this is a way to do it.鈥�
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