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> For there to be equilibrium between supply and demand, several conditions must be met: perfect competition; perfect information; no economies of scale; no barriers to entry; no negative externalities; and no cheating.

What do you mean by that? Prices work well to balance supply and demand in all kinds of `imperfect' markets.

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Arrow-Debreu (1954) showed that under conditions of perfect competition, a general equilibrium must exist. But no comparable existence theorem can be found in the various models with imperfect competition. For example, if you remove the condition "no economies of scale," you exclude convex feasible production sets, and you don't get guaranteed existence. Models of imperfect competition need to add other less plausible assumptions to get back existence of equilibrium. (This won't bother Austrian economists or post-Keynesians, because they reject General Equilibrium Theory as misleading and useless anyway. However, these schools of economics don't frame their ideas in mathematics such that it is possible to prove theorems about the existence, uniqueness, and stability of equilibrium.)

Arrow-Debreu nice result gives you sufficient theoretical conditions for a unique (!) equilibrium to exist.

As you say, in practice, our markets are different, and the conditions don't apply fully. But I don't see how that applies here? There might be multiple equilibria, but that doesn't have anything to do with slave labour.

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