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A particularly important problem which awaits a full mathematical theory, concerns the dynamical behaviour of complex systems comprising multiple, interacting, heterogeneous components. There are many technological examples of such systems, including the so-called Internet-of-Things featuring collections of heterogeneous, autonomous machines and algorithms. Nature also arguably features examples in living systems, perhaps even the brain itself. The question therefore arises: How can such systems be represented mathematically and what features of their behaviour can be calculated? Here we discuss such a mathematical theory for representing the collective behaviour of a generic multi-agent population. A key feature of this approach is to account for the strong correlations that develop between agents’ actions – and in particular, their strategies.

multi-agent systems, games, correlations.