Tuesday, April 21, 2009

The Tractability of Market Equilibria

In the last few years there has been a growing number of papers in Game Theory, such as this one, that belie what I believe is a widespread and tacit assumption that markets can and will find a predictable long-term equilibrium if left to their own devices.

To quote Kamal Jain: "If your laptop can't find it, neither can the market."

The provable lack of tractable computability for a rapidly increasing number of simple, game-theoretic equilibrium problems carries with it the implication that most real markets are inherently unstable for all practical purposes. Furthermore, it suggests that the use of regulation to placate risk aversion will almost certainly have adverse, unintended consequences that limit the credibility of any claims of improved stability. It also provides yet another reason why so many hedge funds and self-styled quants fail at the game of attempting to apply predictive analytics to real markets.

Markets are essential tools for price discovery when optimizing resource allocation, but in some cases this does not imply that the market will have a stable equilibrium. Unfortunately for those averse to risk, and risk does carry a real cost in the markets, regulation generally has a limited ability to guarantee stability while imposing detrimental costs with respect to efficient and accurate price discovery.

Psychologically and sociologically we have a pervasive preference for stability, and it therefore is something of an inconvenient truth that not only are most things in life not stable but they cannot be made stable, even when discussing many human socioeconomic interactions.  As with many things, it will be easier to convince ourselves that we can control complex economic systems than to accept the fact that we probably cannot.

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