New territory for game theory...

This new paper in PLoS looks fascinating. I haven't had time yet to study it in detail, but it appears to make an important demonstration of how, when thinking about human behavior in strategic games, fixed point or mixed strategy Nash equilibria can be far too restrictive and misleading, ruling out much more complex dynamics, which in reality can occur even for rational people playing simple games: 

Abstract

Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated. However, economists have argued that iterated reasoning–what you think I think you think–will suppress complex dynamics by stabilizing or accelerating convergence to Nash equilibrium. We report stable and efficient periodic behavior in human groups playing the Mod Game, a multi-player game similar to Rock-Paper-Scissors. The game rewards subjects for thinking exactly one step ahead of others in their group. Groups that play this game exhibit cycles that are inconsistent with any fixed-point solution concept. These cycles are driven by a “hopping” behavior that is consistent with other accounts of iterated reasoning: agents are constrained to about two steps of iterated reasoning and learn an additional one-half step with each session. If higher-order reasoning can be complicit in complex emergent dynamics, then cyclic and chaotic patterns may be endogenous features of real-world social and economic systems.

...and from the conclusions, ...

Cycles in the belief space of learning agents have been predicted for many years, particularly in games with intransitive dominance relations, like Matching Pennies and Rock-Paper-Scissors, but experimentalists have only recently started looking to these dynamics for experimental predictions. This work should function to caution experimentalists of the dangers of treating dynamics as ephemeral deviations from a static solution concept. Periodic behavior in the Mod Game, which is stable and efficient, challenges the preconception that coordination mechanisms must converge on equilibria or other fixed-point solution concepts to be promising for social applications. This behavior also reveals that iterated reasoning and stable high-dimensional dynamics can coexist, challenging recent models whose implementation of sophisticated reasoning implies convergence to a fixed point [13]. Applied to real complex social systems, this work gives credence to recent predictions of chaos in financial market game dynamics [8]. Applied to game learning, our support for cyclic regimes vindicates the general presence of complex attractors, and should help motivate their adoption into the game theorist’s canon of solution concepts

Megabanks: too complex to manage

Having come across Chris Arnade, I'm currently reading everything I can find by him. On this blog I've touched on the matter of financial complexity many times, but mostly in the context of the network of linked institutions. I've never considered the possibility that the biggest financial institutions are themselves now too complex to be managed in any effective way. In this great article at Scientific American, Arnade (who has 20 years experience working in Wall St.) makes a convincing case that the largest banks are now invested in so many diverse products of such immense complexity that they cannot possibly manage their risks:

This is far more common on Wall Street than most realize. Just last year JP Morgan revealed a $6 billion loss from a convoluted investment in credit derivatives. The post mortem revealed that few, including the actual trader, understood the assets or the trade. It was even found that an error in a spreadsheet was partly responsible.

Since the peso crisis, banks have become massive, bloated with new complex financial products unleashed by deregulation. The assets at US commercial banks have increased five times to $13 trillion, with the bulk clustered at a few major institutions. JP Morgan, the largest, has $2.5 trillion in assets.

Much has been written about banks being “too big to fail.” The equally important question is are they “too big to succeed?” Can anyone honestly risk manage $2 trillion in complex investments?

To answer that question it’s helpful to remember how banks traditionally make money: They take deposits from the public, which they lend out longer term to companies and individuals, capturing the spread between the two.

Managing this type of bank is straightforward and can be done on spreadsheets. The assets are assigned a possible loss, with the total kept well beneath the capital of the bank. This form of banking dominated for most of the last century, until the recent move towards deregulation.

Regulations of banks have ebbed and flowed over the years, played out as a fight between the banks’ desire to buy a larger array of assets and the government’s desire to ensure banks’ solvency.

Starting in the early 1980s the banks started to win these battles resulting in an explosion of financial products. It also resulted in mergers. My old firm, Salomon Brothers, was bought by Smith Barney, which was bought by Citibank.

Now banks no longer just borrow to lend to small businesses and home owners, they borrow to trade credit swaps with other banks and hedge funds, to buy real estate in Argentina, super senior synthetic CDOs, mezzanine tranches of bonds backed by the revenues of pop singers, and yes, investments in Mexico pesos. Everything and anything you can imagine.

Managing these banks is no longer simple. Most assets now owned have risks that can no longer be defined by one or two simple numbers. They often require whole spreadsheets. Mathematically they are vectors or matrices rather than scalars.

Before the advent of these financial products, the banks’ profits were proportional to the total size of their assets. The business model scaled up linearly. There were even cost savings associated with a larger business.

This is no longer true. The challenge of risk managing these new assets has broken that old model.

Not only are the assets themselves far harder to understand, but the interplay between the different assets creates another layer of complexity.

In addition, markets are prone to feedback loops. A bank owning enough of an asset can itself change the nature of the asset. JP Morgan’s $6 billion loss was partly due to this effect. Once they had began to dismantle the trade the markets moved against them. Put another way, other traders knew JP Morgan were in pain and proceeded to ‘shove it in their faces’.

Bureaucracy creates another layer, as does the much faster pace of trading brought about by computer programs. Many risk managers will privately tell you that knowing what they own is as much a problem as knowing the risk of what is owned.

Put mathematically, the complexity now grows non-linearly. This means, as banks get larger, the ability to risk-manage the assets grows much smaller and more uncertain, ultimately endangering the viability of the business.

The intellectual equivalent of crack cocaine

That's what the British historian Geoffrey Elton once called Post-Modernist Philosophy, i.e. that branch of modern philosophy/literary criticism typically characterized by a, shall we say, less than wholehearted commitment to clarity and simplicity of expression. The genre is represented in the libraries by reams of apparently meaningless prose, the authors of which claim to get at truths that would otherwise be out of reach of ordinary language. Here's a nice example, the product of the subtle mind of one Felix Guattari:

“We can clearly see that there is no bi-univocal correspondence between linear signifying links or archi-writing, depending on  the author, and this multireferential, multi-dimensional machinic catalysis. The symmetry of scale, the transversality, the pathic non-discursive character of their expansion: all these dimensions remove us from the logic of the excluded middle and reinforce us in our dismissal of the ontological binarism we criticised previously.”

I'm with Elton. This writer, it seems to me, is up to no good, trying to pull the wool over the reader's eyes, using confusion as a weapon to persuade the reader of his superior insight. You read it, you don't quite get it (or even come close to getting it), and it is then tempting to conclude that whatever he is saying, as it is beyond your vision, must be exceptionally deep or subtle or complex, too much for you to grasp.

You need some self confidence to come instead to the other logically possible conclusion -- that the text is actually purposeful nonsense, all glitter and no content, an affront against the normal, productive use of language for communication, "crack cocaine" as the writer gets the high that comes from appearing deep and earning accolades without putting in the hard work to actually write something that is insightful.

Having said that, let me also say that I am not in any way an expert in postmodernist philosophy and there may be more to the thinking of some of its representatives than this Guattari quote would suggest.

In any event, I think there's something deeply similar here to John Kay's point in this essay about Warren Buffet. As he notes, Buffet has been spectacularly successful and hence the subject of vast media attention, yet, paradoxically, he doesn't seem to have inspired an army of investors who copy his strategy:

... the most remarkable thing about Mr Buffett’s achievement is not that no one has rivalled his record. It is that almost no one has seriously tried to emulate his investment style. The herd instinct is powerful, even dominant, among asset managers. But the herd is not to be found at Mr Buffett’s annual jamborees in Omaha: that occasion is attended only by happy shareholders and admiring journalists.

Buffet's strategy, as Kay describes, is a decidedly old-fashioned one based on close examination of the fundamentals of the companies in which he invests:

If he is a genius, it is the genius of simplicity. No special or original insight is needed to reach his appreciation of the nature of business success. Nor is it difficult to recognise that companies such as American Express, Coca-Cola, IBM, Wells Fargo, and most recently Heinz – Berkshire’s largest holdings – meet his criteria. ... Which leads back to the question of why Berkshire has so few imitators. After all, another crucial insight of business economics is that profitable strategies that can be replicated are imitated until returns from them are driven down to normal levels. Why do the majority of investment managers hold many more stocks, roll them over far more often, engage in far more complex transactions – and derive less consistent and profitable results?

The explanation, Kay suggests, is that Buffet's strategy also demands an awful lot of hard work and it's easier for many investment experts to follow the rather different strategy of Felix Guattari, not actually working to achieve superior insight, but working to make it seem as if they do, mostly by obscuring their actual strategies in a bewildering cloud of complexity. Sometimes, as in the case of Bernie Madoff, the obscuring complexity can even take the very simple form of essentially no information whatsoever. People who are willing to believe need very little help:

... the deeper issue is that complexity is intrinsic to the product many money managers sell. How can you justify high fees except by reference to frequent activity, unique insights and arcana? But Mr Buffett understands the limitations of his knowledge. That appreciation distinguishes people who are very clever from those who only think they are.

One final comment. I think finance is rife with this kind of psychological problem. But I do not at all believe that science is somehow immune from these effects. I've encountered plenty of works in physics and applied mathematics that couch their results in beautiful mathematics, demonstrate formidable skill in building a framework of theory, and yet seem utterly useless in actually solving or giving insight into any real problem. Science also has a weak spot for style over content.