It would be interesting to construct an experiment to see what kinds optimal solution a free market can and can't find (though I have no idea how this would be

It would be interesting to construct an experiment to see what kinds optimal solution a free market can and can't find (though I have no idea how this would be done). In search algorithms you have to worry about merely finding a local maxima rather than a global maximum. In algorithms such as simulated annealing you perturb your solution randomly at the outset, trying to "bump" your solution off of one of those local maxima. What if the free market is prone to getting "stuck" in some locally optimal, globally sub-optimal solution? Depending on initial conditions (price, number of firms in the marketplace, demand, etc.) we could end up with great solutions, but in others with terrible results.