Do functional, competitive markets really exist? The true nature of markets doesn't seem to be equilibrium, but brutal swings between various local optima (which generally are pretty mediocre overall).
markets are dynamic, but not so chaotic to swing brutally (among attractors), as you put it. certainly some markets are in that stage now, but certainly not all or even most.
early on, markets tend to grow to an unsustainable number of participants, and then as participants figure out marketing and their own strengths and fits, they start to whittle down. in the best markets (for consumers; but that are also sustainable for providers), you'd have maybe tens of competitors (i.e., not 3 or 300), depending on market characteristics (like being capital-intensive or not, free cash flow restricted or not, etc.).
the problem with our markets is that we've long given up on providing the right amount of regulation to maintain that consumer-optimum, which can be stable in isolation, but for which the highly dynamic politico-social context often destabilizes. so it takes work and vigilence to maintain the optimum, and we don't have that in most (all?) markets.
This, the existence of Nash equilibria is practically guaranteed according to game theory. And of course switching implies frictional costs, activation energy, and so on in addition to the actual change. If we define “functional, competitive markets” to mean no strange equilibriums then they certainly don’t exist on this planet.
Additionally there are a lot of assumptions that go into proving that markets have Nash equilibria, such as convex utility functions, and perfect information, which is often not true in reality.
