[sam h]

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What are some of the assumptions that a solid free market economy relies upon? What, if anything, should be done if those assumptions turn out to be false?

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There are multitudes, since the "free market" is really just a fictional model rather than an empirical entity.

The biggest assumption, or perhaps fallacy, is that anything resembling a "free market" has ever existed. In fact, the term is self-contradictory - markets are constructed upon rules and human institutions, ones that require government for enforcement. They therefore cannot be "free."

The second biggest assumption is that the role of the state
in the economy should be minimized as much as possible since intervention is equated with "rent seeking" and inefficiencies. Curiously enough, the historical fact is that the vast majority of examples of great economic growth in individual nations have been induced by states that were fairly interventionist.

The third biggest assumption is that individuals are rational actors with transitive preferences. Obviously, this is untrue. But for the purpose of modeling economic phenomena it is often the case that the models are still powerful even under violation of this assumption.