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The dynamics of a complex system cannot in any sense be described by simply aggregating the individual small-scale interactions.

In many cases it can, so this statement as it stands is much too strong. For example, a country's economy is a huge game of mutual cooperation whose dynamics can be perfectly well described by aggregating a huge number of two-person games (or perhaps "two-player" would be better since one player is often an organization, like a company or the government, rather than a single person)--or in some cases perhaps games with larger numbers of players, but still small-scale.

There may be cases where a system's dynamics can't be described this way; can you give a specific example?

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