Broken Symmetry

Excellent Sentences from Joff Wild at IAM

However, how do you measure value when IP can be so frustratingly intangible - what price that collaborative relationship with a competitor that a piece of IP may enable, for example? One at least partial solution to this conundrum may be to make royalty rates far more transparent. One suggestion was that all licensing deals agreed in the US should be publicly recorded at the USPTO so that people could see the sums involved. This would have to be compulsory as no-one would do it voluntarily.

From the IAM Blog.

Bleg for Economists: Empirical Tests of the Rational Hypothesis

Folks, aside from the lab experiments (which I know produced mixed results), what empirical evidence do we have of the validity of the rational hypothesis? As best I can tell, the last work done in this regard were the nonparametric tests of WARP by Varian and Bronars in the 1980s.

Those studies, of course, were of aggregates of household consumption over long time periods. Has anybody tested the rational hypothesis against revealed preferences outside a laboratory by tracking individual consumer behavior?

The question comes to this: Is there a data set for a large population that tracks the time-series of acts of consumption for each individual in the population over some period of time?

If the rational hypothesis is applied to predict how individuals will behave, then it should be based on empirical data about individual behavior, should it not? Where is that data?

Twitter Updates

Have now been added to Broken Symmetry on the right. If you're already tweeting, be sure to follow me. I'm riemannzeta. If you tell me you read Broken Symmetry, I'll be more likely to reciprocate.

More Systems Theory from Judge Posner

My remaining proposals are of measures to improve regulatory performance, as distinct from the organization of financial regulation. First, we need a program that will rotate financial regulatory staff among the different financial regulatory agencies, to broaden the perspectives of regulators, reduce the "stovepiping" of information that may relate to a wide range of companies and financial markets, expose regulators to new ideas, reduce turf warfare based on misunderstandings, and make a career in financial regulation more interesting and challenging.

At his Atlantic Correspondents blog. This is a prescription that could be drawn directly from Ciskszentmihalyi's systems theory as applied to cultural economics.

Highlights from the 2009 IP Business Congress

Monday and Tuesday of this week I attended the second annual IP Business Congress, which this year was venued at the Four Seasons Hotel in Chicago. There were almost 400 attendees at the event, which was a good turnout given the economic climate. Attendees represented stakeholders in nearly every part of the IP Market, both primary and secondary. As expected, the panels organized by IAM magazine were excellent and informative, especially the question and answer sessions afterward. This is an event that I expect to put on my calendar annually.

Highlights for me as an attendee to this event included (1) the first panel on Monday on the state of IP rights in China, India, Japan, Europe, and the United States; (2) the panel on patent pools on Monday afternoon; (3) the panel on open innovation on Monday afternoon; and (4) the Gala dinner on Monday night. Tuesday's panels were also excellent, but of less interest to me because of my more direct involvement with many of the issues addressed on Tuesday.

State of IP Rights Internationally

Harvey (expert on China) kicked things off by noting how IP rights had been a strong influence on the development of rule of law more generally in China: IP was the first private property right to be recognized by the Chinese government after the cultural revolution. Harvey also explained that in number of lawsuits, there is more IP litigation in China than in any other nation. The picture he painted was of a thriving IP system in China that was operating decoupled from the rest of the IP world. The coupling of China's IP system into the rest of the world's will produce winners and losers of epic proportion, and now is the time for us to think strategically about how to prepare our clients and customers for this inevitable merge of the Chinese system into the rest of the world.

McGinley (EPO Officer) followed Harvey with sobering statistics on the patent application bubble that is growing inside the US, EPO, and Japanese patent offices: 2 million applications althogether are now pending inside these offices. Given how the rate of examination has not kept up with the rate of growth in filing, McGinley suggested that the system was beginning to resemble a pyramid scheme! This was a brave position for a government official to take, but everybody in the system should appreciate what McGinley is trying to do. Where might we have been had more financial regulatory authorities here in the U.S. pointed out the pyramid-scheme-like growth of the subprime mortgage market? McGinley was short on answers as to how to solve the problem, but he did suggest that Chinese officials were probably at the top in terms of training practices and the reduction of systematic errors in examination. This seemed unsurprising to this listener given the on-the-ground experience of many Chinese with more complex manufacturing workflows!

The presenter from Japan had little of interest to say, and presented some confusing interpretations of statistics on patenting in Japan. For example, he pointed out that the largest number of patents issued in Japan were to computer companies rather than pharma companies. Pharma companies need only one well-drafted and prosecuted patent to protect their products. This is not very surprising, and is true everywhere in the world.

Basheer from India gave in many ways the most interesting presentation. His was mostly a diplomatic presentation of facts about the IP market in India, where the political agenda is driven by the success of generic drug manufacturers. As a few BS readers may know, Basheer is also one of the authors of the consistently excellent (but very detailed!) Spicy IP blog. From listening to Basheer, one could piece together a picture of India in a critical state, in which more or less IP protection could result from a sharp push in either direction. Too difficult to call for the time being. On my view, it seems that Indian biotech and pharma researchers have a regulatory arbitrage over their U.S. counterparts, who have many years of redtape to cut through before carrying out even relatively safe clinical trials! Note that beating heart transplants are now being carried out in Indian hospitals. There are many high-risk, high-reward medical treatments now avaiable in India that may never be available in the United States. Another trend to watch carefully.

The first question/comment for this panel was also notable. It came from Sherry Knowles of GSK, who noted that Chinese generic manufacturers were getting drugs to market before US manufacturers by simply scraping clinical data off the clinicaltrials.gov website on which U.S. manufacturers, such as GSK, have to post their data by law! There's one for the USTR to call to Chinese government attention.

Patent Pooling

The Monday afternoon panel on patent pools included Sisvel founder Dini, Hinman from Verizon, and Michel from the FTC. Dini gave a great pitch for hiring independent administrators (such as Sisvel) for allocating profits among patent pool participants, and for getting such admins involved at as early a stage as possible. Michel gave a presentation of the recent history of FTC regulation of patent pools, including a summary of the federal court holdings relating to Rambus's participation in JEDEC. Hinman talked about the perils of patent pool participation, and noted that even opt-out could be anti-competitive. Referring to one patent pool in particular, he pointed out that all but two industry participants had entered. I saw Michel scribbling notes!

The upshot is that if your company is involved with patent pools, you need to hire experienced outside counsel with knowledge at the interface of IP and Antitrust law to help ensure your business strategy reduces the risk of antitrust liability. Your author knows and works with a few such experts, and is happy to make an intro. Note that most corporate lawyers or IP lawyers will not be aware of the perils of competition law because the Bush and Clinton administrations were relatively lax on this front. All indications are that the Obama administration will be more active in enforcing competition law.

Open Innovation

By now the term "open innovation" has become relatively well-known within the business community. Some IP owners may believe that open innovation represents a form of socialism -- an alternative to a system of property rights. Attendance to this panel would have been the antidote to such misunderstandings of this theory. Panelists Weedman from P&G, Simonton from Exelixis, and Bergelt from the Open Innovation Network (and formerly of Paradox) talked about the dynamic growth that the feedback loops established by open innovation networks facilitate for the companies that take open innovation seriously.

Because the theory of open innovation is a paradigm shift from traditional neoclassical economic theories, only a handful of businesses (including P&G and Exelixis) have been fortunate enough to find leaders willing to foster the organizational commitments necessary to make open innovation work. This business model is the future of every large public corporation in the world. Watching these businesses continue to outgrow their competitors, others will eventually follow.

Gala Dinner

One of the best parts of the event was meeting the attendees. Over drinks before the Gala dinner, I had the chance to catch up with Niels Reimers, who later that evening was inducted into the IP Hall of Fame for his path-breaking work in technology transfer. In this rare moment of opportunity, I had the chance to ask Niels about how he worked at Stanford. By Niels's description, he was practicing the same technique followed by the best founders and managers in Silicon Valley both then and now -- "management by walking around." Dave Packard and Bill Hewlett, Bill Perry at ESL, and Nils at Stanford were all doing management by walking around. Niels's personal accounts of his work connecting Stanford music department (!) professor John Chowning with Hamamatsu corporation engineers were a highlight among highlights for this event.

Later, when Niels cited the Teece Model of innovation in his acceptance speech, I nearly fell out of my chair. The same model was cited by FTC Commissioner Tom Rosch in his speech about new theories in competition law on June 1, 2009. Note that Teece was also cited in the explanation of systems theory provided in your author's letter comment to the FTC on the Evolving IP Marketplace.

Final Thoughts

Another highlight made possible by my attendance to the event, but not directly related thereto, was an invitation to a breakfast with Congressman Bill Foster on Tuesday morning. I am already a fan. Foster is an entrepreneur and physicist who decided (after 22 years of building superconducting magnets to detect subatomic particles) to roll up his sleeves and try to help fix government. I'm pretty sure there's nobody else in Congress who would know what the title of this blog refers to. The discussion of the patent system and innovation at this breakfast was the best I've heard ever anywhere, but it also revealed to me the underlying problem facing patent reform: nobody has a complete view of the whole system. Almost everybody (at least) focuses on the broken incentives and procedures facing them in their subsystem, without stepping back to see how all of the subsystems coalesce into an competitive and innovative ecosystem. Nonetheless, the kinds of questions asked and answers given at this breakfast suggest that already the level of discourse has progressed far beyond the pat answers that were served up last year when patent reform was before Congress. There is more widespread awareness at least of how the public has been manipulated to some extent by the more technologically sophisticated and media-connected subset of stakeholders in the system. Perhaps we will have sensible patent reform after all. Here's to that hope.

Judge Posner on the Systems Theory of the Financial Crisis

Yet even if all firms that create systemic risk decided to shrink, or to reduce their interactions with other financial firms, systemic risk would not be eliminated. For such risk is a property of the financial system rather than of individual firms. That is, systemic risk is correlated risk. If the entire banking industry were heavily invested in home mortgages, and a housing bubble caused a drastic fall in the value of those mortgages, it wouldn't matter if the industry consisted of 10,000 banks of equal (and therefore equally small) size that had no dealings with other financial firms. The whole industry would be brought down.

Read the whole post here.

Feedback Loops in the All-to-All Network in which we live

Story I heard from Congressman Bill Foster this morning: Last fall, when the Stimulus Bill first went to the House for a vote, Congress members on the floor were watching the markets drop in real time on their blackberries. At the same time, traders in the pits on Wall Street were watching Congress voting on the Bill. Pro voters began berating Con voters as they came to the floor to vote. In effect, traders and their thousands of customers, spread all over the world, were doing the same.

Pause and let that sink in. We live in Robert Musil's world now. If we aren't careful, our decisionmaking can become very tightly correlated very fast.

Consider how many steps the framers of the United States Constitution took to avoid their decisionmaking during the Convention -- or the decisionmaking of actors in different branches of government -- from becoming too correlated.

How to Reduce Systemic Risk: Look at the Rates of Growth and Cross-Correlations

The White Paper last week was a disappointment. It was long on generalities and short on specifics of how and why we ended up in this mess. Lots of people are throwing their hands up in the air. A few are saying that the only way to avoid this problem is to go back -- i.e., to keep banks from ever growing so big again. Both of these are counterproductive. We have learned a few things from watching this crisis enfold that may help us avoid similar crises in the future.

One of those lessons is directly relevant to the argument that banks should simply be limited to a particular size. If there is any lesson that we have learned from this crisis, it is that size doesn't matter. Banks big and small all over the world have been brought to their knees by this crisis.

Systemic Risk = Large-Scale Correlations in Risk

What brought the financial industry all over the world to its knees can be attributed to a single mistake in reasoning, which was made by managers at every bank that ended up insolvent. Their mistake was in assuming that their risk of loss would range only within the boundaries set by local and recent events. The Royal Bank of Scotland, Kaupthing Bank in Iceland, Lehman Brothers in the United States, and your local Savings & Loan -- all made the same basic mistake of assuming that even if things got ugly for them, then there would be plenty of other banks around to pick up the slack. So long as I can depend on my counter-parties to behave exactly as we expect by contract, we will survive.

One thing that's worth noting is that this mistake wasn't fatal to the financial industry before the subprime mortgage bubble. The financial industry survived several bubbles before that, including the dot com bubble only ten years before. What changed?

The answer is cross-correlation. Over the past ten years, the financial industry became more interconnected through the financial engineering of derivatives and increased leverage than it has been ever before in history.

When any system becomes cross-linked beyond a certain low threshold, correlations in the dynamics of the system can spread from local to global. And this is exactly what we are living through. Although the system became exponentially more interconnected over the last ten years, the individual decisionmakers within the system (for the most part) kept their horizons relatively local and short-term. Nobody was looking at the large-scale, long-term trends and worrying about how those could ripple out in the event of a single default. Nobody was looking because no such cascade had ever occurred before.

The first role of any systemic risk regulator should thus be to quantify and limit the amount of cross-correlation in risk within the financial industry. We just can't afford to have every financial institution making the same kinds of bets. If a few are taking their cut from poker players, then the others need to take their cut from craps-players or roulette-players.

Regulating at Scale: Measuring Fundamental Limits to Growth

Systemic risk regulators have to be especially careful about the problem of scale. As numerous commentators have pointed out, there were a few people within the SEC that noticed the problems that might be caused by the unregulated sale of over-the-counter derivatives and the explosion in growth of the subprime mortgage market. How is putting a new agency in charge -- even if it has access to more information -- going to avoid such cascades in the future? In general, I don't think that any such agency will be able to prevent such cascades without having unintended negative consequences. And the scope of the authority needed to effect system-wide regulations is worrisome too from the point of view of suceptibility to political influence. A thumb on the scale at that scale is enough to crush entire markets.

To deal with systemic risk, any actual regulation will have to gloss over many of the fine details of what particular parties and counter-parties are doing. Getting too involved in these details simply invites corruption anyway. To deal with systemic risk, regulators need to change focus from the short-term and local, to the long-term and global.

For example, has anybody in government ever tried to figure out the highest rate of growth that has ever been achieved by a legitimate (i.e., non-fraudulent, sustainable) large corporation? If a company is growing faster than a certain rate then risk is being spread through the system. Such a company is either a Ponzi scheme or a gamble that some market exists that has not been demonstrated to exist.

A perfectly legitimate way for a systemic risk regulator to operate would be to set a threshold internal rate of return on cashflow -- say 30% annualized -- and then to demand that anybody with a higher IRR has to report to the systemic risk regulator on from whom and to whom that cash is flowing. Such a policy would have flagged the problem with subprime mortgages immediately. The size of the subprime mortgage market did not suddenly go from a few hundred million to billions in a year or two. At the very least, the government should have been carefully scrutinizing it after the cashflow increased by that number of orders of magnitude.

The Big Picture: A Network of Cashflows

At the end of the day, an economy is a network of cashflows. What makes our economy unique in the history of the world is its degree of interconnectedness. Those interconnections are both a blessing and a curse. They are a blessing in that they lower the costs of lending so that more and more people can get access to financing. (Think of Kiva, which is part of that interconnectedness.) The curse is that they permit for system-wide fluctuations to develop even from relatively small losses when decisionmaking is too tightly correlated.

Our goal should not be to go back to the smaller, less interconnected world. It should be to forge ahead into a fully networked economy, but with awareness of and capabilities to manage these global and long-term patterns of growth and decay in the network.

We need to think bigger.

The Glassy State of the Financial Services Industry

How might financial regulators have identified a problem with our market? By looking at cross-correlations like this one:

Again, this is from the paper on synchronized clusters reviewed here.

More on the Glassy Economy

I had to revisit the paper by Yik Wen Goo, Tong Wei Lian, Wei Guang Ong, Wen Ting Choi, and Siew-Ann Cheong, which I reviewed earlier here. As explained in the earlier review, these researchers found correlations in public security prices by looking for cross-correlation at successively longer and longer time scales. Lo and hehold, they were able to identify synchronized clusters that way:

We call these small clusters of very strongly correlated stocks financial atoms. The correlation levels within financial atoms rise significantly above the background level c0, because the dynamics of atomic stocks are coherent over time scales much longer than the average trading interval, which plays the role of the ‘nuclear/electronic’ time scale. The existence of such financial atoms is evident from earlier studies [citations omitted], where they are referred to as synchronized clusters. However, the separation of ‘nuclear/electronic’ and atomic time scales was not recognized. The potential of using financial atoms as effective variables to describe real financial markets is also not widely appreciated.

So not only is it possible that the economy is in a glassy state, there is some numerical data demonstrating that it actually is.

Their use of terminology is unfortunate, because it would be better to think of individuals as the "atoms" of an economy on my view. In that case, corporations would be molecules, and what they call "financial atoms" would be analogous to the chains and sheets of molecules described in the post yesterday on an economy made of glass.

Before I saw the White Paper from the Obama administration, I was hoping they had people that were already doing this kind of analysis. I'm no longer so optimistic. Can I ask for help from anybody and everybody who understands this type of analysis in educating the public and government in its implications? We'll all be better off that way in the end.

More Evidence for Synchronized Flow

Ironman provides an excellent review of some posts on Broken Symmetry, and (even better) provides a beautiful review of how the frequency spectrum of price fluctuations alternates between Gaussian and Levy statistics at Political Calculations:

We thought it would be appropriate to close out this post by reviewing the modern era of the stock market (or rather, most of it!) with our charts that identify the periods where Gaussian rules would apply, and the periods where Lévy flights rule. While we consider the modern era of the U.S. stock market to have begun in January 1952, we'll pick up the action in June 1954, extending to when the most recent period of disorder began in January 2008:

The bottom line here is that you can't understand build up a realistic model of an economy starting from the assumption that preferences are time-independent. The better way to start is with the assumption that preferences are oscillatory. I call this "the fundamental hypothesis of periodicity," and it produces the hypothesis of rationality at the limit of ergodicity -- i.e., when preferences behave the same way from one time-window to the next.

Do Email Traffic Statistics Really Cast Doubt on Small World Theory?

The answer is no. MIT Technology Review reports on work published by researchers at the Hebrew University in Jerusalem:

Goldenberg and Levy say that while it is just as easy to email somebody who lives on the same street as somebody on other other side of the world, it turns out we have a huge preference for sending messages over shorter distances... Their conclusion is that far from reducing the importance of geographical location, electronic communication appears to have increased it, probably because people swap more messages with those they have personal interaction with. If that's true, why have we gone so wrong in thinking the world is getting smaller? One source of confusion, argue Goldenberg and Levy, is the famous six-degrees-of-separation experiments peformed originally by Stanley Milgram with letters and later by Steve Strogatz and Duncan Watts using email. These seem to indicate that a "small world" effect is at work in social networks.

The major problem with this criticism is that it misunderstands the point of the Milgram and Watts-Strogatz work. Milgram, Watts, and Strogatz had little data on the dynamics of the network. They were studying the network structure. This looks like sensationalism to me.

If you asked any of them whether they would be surprised to hear that the frequency-spectrum of communication is spatially clustered, I'm sure they would say no.

An Economy Made of Glass

Marvel, Strogatz, and Kleinberg describe "jammed states" and note how they bear a distant relation to spin glasses. Although I hadn't thought much about it before, there are some relevant similarities between glasses and the transitional states described in Kuperman and Zanette.

There are a few properties that make glassy solids interestingly different from crystalline solids. These properties develop from the differences in microscopic structure and dynamics between crystals and glasses.

For example, glasses are viscoelastic -- they're a little bit viscous like honey, and a little bit elastic like rubber, but not quite either. Silly putty is a viscoelastic material that many people will recognize. When you hit a viscoelastic material with a hammer, it will shatter like a crystal (albeit not in the same neat pieces that a crystal shatters). But unlike crystal, if you pull at it or apply even strong forces to it at slower frequency, it will stretch.

At the molecular level, that's because of the cross-linking between the chains and sheets of molecules that make up the material. In a perfect crystal, the molecules are perfectly lined up with soldiers marching in formation. In a glass, there are still orderly groups, but they're not all arranged in nice rows and columns. Instead they're cross-linked to other groups, and the cross-links form and break as the groups slide around past each other when low-frequency forces are applied to the glass.

Another interesting property of glasses related to this cross-linking at the molecular level is the time-dependence of glass transitions. Glasses tend to form when liquids are cooled too fast for them to crystallize. If cooling happens slowly enough, then one might imagine that most fluids would crystallize rather than form glasses. One might imagine that, but it does not appear to be so. As some of the papers I've blogged about here suggest, there seem to be glassy states even at very low energies. A vivid name for this effect in condensed matter physics is "frustration."

By analogy, if an economy is modeled as cross-linked clusters of synchronized oscillations, then we might expect to see viscoelasticity and time-dependent transitions in its equilibriums also. Should bubbles and crashes be modeled as viscoelastic creep?

Such an analogy might offer practical value to financial regulators. Generally speaking, the fragility of a glass will depend on the size and shape of the molecular clusters and the number of cross-links among them. The bigger the clusters and the more the cross-links, the more fragile the glass to external shocks. Smaller clusters and fewer cross-links mean less viscosity and elasticity.

It's interesting too to note that there is always some tradeoff between frictional forces caused by internal viscosity and fragility. You can't make a glass less fragile without increasing the cross-links and thereby increasing viscosity. Of course crystals are less fragile to most perturbations than glasses. But if you happen to pick just the right frequency perturbation, then crystals will explode even more spectacularly than glass -- they have no viscosity because they're perfectly rigid until they break.

What kind of economy do we want? A glass like silly putty or a perfect crystal like ice?

The Energy Landscape of Social Balance

From Seth A. Marvel, Steven H. Strogatz, and Jon M. Kleinberg:

Taken together, the above results give us a first look at the energy spectrum of jammed states in completely connected social networks in which opportunities for greater relational consistency and cooperation are the driving forces for change. Since balanced states—the global energy minima—correspond to two mutually antagonistic cliques, they often represent socially undesirable outcomes such as intractable conflict. Viewed in this light, the presence of jammed states at higher energies suggests the possible beginnings of a companion theory of reconciliation and flexibility in the setting of social balance: since these jammed states show less large-scale antagonism, they may provide pathways to steer conflicts into structures where reconciliation can more easily occur.

Available here. For a variety of reasons, I believe these "jammed states" are related to the "twisted states" described in the paper by Kuperman and Zatteo reviewed earlier.

Found via Physics ArXiv blog.

Financing with Future Royalties

Nice summary of the market from The Deal:

The investor's motivation for making a royalty financing investment is the expectation of receiving a private equity level return (e.g., modeled internal rates of return often exceed 20%) in an asset class (directly or indirectly consisting of intellectual property interests in pharma and biotech assets) that is relatively non-correlated with broader market indices. The investor's return expectations are predicated on its assumption of the risks of the sustainability of future cash flows (for royalty interest transactions) and of the commercialization of assets that have not yet generated meaningful cash flows or made substantial commercial penetration (most frequently in synthetic royalty transactions.) The investor's ability to take on these risks intelligently is predicated on the synthesis of highly specialized capabilities in analyzing the commercial and regulatory landscape for the relevant assets, including assessments on the strength of the underlying intellectual property in the relevant markets, the likelihood of competing or cannibalizing products and the likelihood of market acceptance for the underlying products.

More Organic Economics

From Neurophilosophy:

Neuroimaging has revealed that remembering and simulating the future are now known to depend on common neural substrates; the core network activated in both cases includes the hippocampus, poserior cingulate gyrus, inferior parietal lobule, and medial frontal and lateral temporal cortices. Interestingly, activity in this network is greater during simulation of future events than during remembering. This may reflect processes that do not occur during remembering, such as the recombination of memory fragments or, if imagining the future involves merely recasting the past, the addition of a new "timestamp" to the memory of a past experience.

See earlier post on Organic Economics here.

2009 IP Business Congress and some Shameless Self-Promotion

Broken Symmetry readers may or may not realize that your author's day job involves patent procurement and enforcement. Your author was recently honored to have been named one of the World's Leading IP Strategists by Intellectual Asset Management magazine -- a peer nominated process mediated by IAM.

From June 21 through 23, I will be in Chicago for the 2009 IP Business Congress. IAM sets a standard of excellence for the industry, and this event promises to be no exception, with a list of industry luminaries speaking. If you've got the time, it'll be worth dropping in.

And if you are planning on attending, are a reader of Broken Symmetry, and are interested in meeting up, just click on the link on the left and email me. I always enjoy meeting readers.

A Systems Theory of Financial Regulation

From Geithner and Summers:

First, existing regulation focuses on the safety and soundness of individual institutions but not the stability of the system as a whole. As a result, institutions were not required to maintain sufficient capital or liquidity to keep them safe in times of system-wide stress. In a world in which the troubles of a few large firms can put the entire system at risk, that approach is insufficient.

Perfectly consistent with Summers's column on "Regulatory Systems Design" almost a year ago today.

For a systems theory of patent law, see Question 9 here.

More on Group Selection Theory

From the Independent:

In his study, published in the journal Science, Dr Bowles takes on the proponents of the selfish-gene theory of human evolution by suggesting that natural selection worked on groups of people co-operating together, rather than just individuals.

See also earlier posts from Broken Symmetry relating group selection theory to Tribal Leadership and Executive Compensation.

Entropy in Highly Correlated Systems: Market Equilibrium as Stable Synchronized Flow

The review article linked to the post on Tsallis entropy provides an excellent introduction to this generalization of Boltzmann-Gibb (BG) statistics. In particular, section 2.2 explains how BG statistics obtain at certain limits of the generalized q-statistics (a/k/a Tsallis entropy). What are these limits?

First, BG statistics apply at the limit of independence. So, for example, in a series of N binary events, Tsallis entropy is approximately 2^[N(1-q)]-1/(1-q), and if the events are independent, q = 1 and this reduces to the BG entropy 2^N. This limit is not all that surprising.

Second, BG statistics also apply at the limit of perfect correlation. So, for example, if events are correlated at all scales in accordance with some power law N^r, then the Tsallis entropy is approximately N^[r(1-q)]-1/(1-q). If and when q takes on the value q* = 1 - 1/r, then again BG statistics obtain, albeit to a different set (of rescaled) microscopic variables.

That is really surprising. What that means is that we might see normal (i.e., gaussian statistics) apply even to highly correlated "equilibrium" states. One can't help wondering whether, in fact, that is exactly what we are calling a market equilibrium.

Statistics are all well and good, but what is going on at the micro level to produce these statistics? Tsallis talks in very general terms about "multi-fractal" states. What's that mean? Sounds cool at least, doesn't it?

The paper from Zanette and Kuperman I posted on Friday provides some interesting clues about how microscopic dynamics go from uncorrelated to correlated through a phase transition. The figure posted shows how the number of clusters with different phase characteristics is maximized during phase transitions, and that the process of going from uncorrelated to correlated states involves "cross sync" of spatially dispersed clusters during the phase transition.

Read in conjunction with the papers on Tsallis entropy, I think a picture of how the micro dynamics change with the macro statistics starts to emerge. In particular, we should see Levy statistics during phase transitions, and Gaussian statistics in periods of relatively good syncrhonization/high correlation.

It's a new way to model markets, but the math is all there, folks. Look at the statistics for price shifts within a window to see if they're gaussian or levy distributed. If gaussian, then buyers and sellers are either acting completely independently of one-another (possible, but unlikely) or counterparties are acting synchronously in accordance with share perfectly antisymmetric expectations of future value/revenue (more likely). If levy, then the perfectly antisymmetric synchronized flow among buyers and sellers has broken out into multiple cross-synced clusters.

Is there a way to prevent the market from crashing precipitously at unpredictable intervals? I don't know, but I would think that keeping the market constantly in a phase transition would be a more stable mode of operation -- less susceptible to systemic failures -- than a mode of perfectly correlated expectations.

Cross Synchronized Clusters in an Axelrod-inspired Model

From M. N. Kuperman and D.H. Zanette:

[T]he segregation of oscillators into clusters is not necessarily associated with the synchronization of all the individual phases. In particular, two oscillators may belong to the same synchronized cluster with respect to some of their phases -- which, in the asymptotic state, adopt identical values -- but to different clusters with respect to the other phases. This phenomenon, which we have called cross synchronization, discloses a highly complex form of collective organization, consisting of coherent clusters mixed with respect to the internal variables which specify the individual states. It is interesting to note that Axelrod's model does not exhibit a regime corresponding to cross synchronization. This kind of regime would however make sense as a possible distribution of cultural divrsity over a real population, in the form of partially overlapping cultural domains.

Available here.

What the picture shows is that during phase transitions, spatially local regions within a network may be described by dynamics that share similiarities with multiple spatially far regions elsewhere in the network. By analogy to Axelrod's model, cultural diversity is maximized during phase transitions through a mechanism whereby most local cultures share some but not all traits with many other spatially distant local clusters.

The model has direct implications for those with a normative goal of increasing diversity within a population.

The Structured Rule of Reason Approach to Antitrust Regulation

From a speech given by Commissioner Rosch on June 1, 2009:

In sum, while I do not believe that antitrust law has yet to settle on the right economic theory (or group of theories as the case may be) to accurately account for the complexities of rational and irrational seller and buyer conduct, I think in the last few years, developments in economic thinking have brought us much closer to that objective. And just as in the 1960s, quantum physics was reborn stronger than ever, I am hopeful that as these ideas are incorporated into the mainstream thinking among members of the judiciary and the antitrust bar, we will soon see new life breathed into the antitrust laws through a doctrinal framework that can best identify and prevent anticompetitive conduct.

Commissioner Rosch falls squarely within the American tradition of pragmatism, which takes an opportunistic rather than a loyal attitude toward methodological commitment.

A careful reading of this speech suggests that industry incumbents may need to be more careful in their pre- and post-acquisition strategy. Separately, I am happy to report that patent law and policy fits very well within the framework of experimentation theory as articulated by Farrell and Teece. See an earlier post on this topic here.

Problems with Models of Intertemporal Choice

From The New Palgrave Dictionary of Economics:

For the exponential discount function, the discount rate is independent of the horizon, τ. Specifically, the discount rate is –ln(δ) and the discount factor is δ... The exponential discount function also has the property of dynamic consistency: preferences held at one point in time do not change with the passage of time (unless new information arrives).

...but new information arrives all the time Does it make sense for us to continue to base economics on an assumption that new information arrives only rarely?

Happy Flu

Internet does not exist per se, it is merely the volatile aggregate of information, flowing around. For the past few years - following the emergence of the so-called Web 2.0 - information diffusion has been more and more orchestrated by bloggers instead of mainstream media. This paradigm shift has given us the opportunity to understand how word of mouth works by providing an actual framework in which a resource could be observed while spreading.

That's from happy flu. Be sure to check out the video.

Via the Complexity and Social Networks blog.

The Problem with the Principle of Revealed Preferences and a Suggested Solution

In Chapter 5 of the Foundations of Economic Analysis, Paul Samuelson sets forth what he calls "The Pure Theory of Consumer's Behavior," which he identifies with the analysis of utility. According to Samuelson, many economists "separate economics from sociology upon the basis of rational or irrational behavior, where these terms are defined in the penumbra of utility theory. It would seem extremely important, therefore, to know clearly what is contained in the conventional utility analysis, if only to understand the consequences of denying its validity." (at 90)

What is utility? It is not happiness in Bentham's sense, or welfare in some general sense. Nor is it a physiological or psychological. "Originally great importance was attached to the ability of goods to fill basic biological needs," writes Samuleson, "but in almost every case this view has undergone extreme modification."

Why? Because of "the recognition that a cardinal measure of utility is in any case unnecessary; that only an ordinal preference, involving 'more' or 'less' but not 'how much,' is required for the analysis of consumer's behavior."

This is a weak explanation for why consumer behavior should be considered independent of psychology or biology. Why would biology or psychology demand that preferences be cardinal rather than ordinal when a measure of consumer behavior does not? Samuelson does not say. This makes the fact that evolutionary biology, social psychology, and sociology have made a come back recently less surprising, does it not?

But how does this utility analysis of consumer behavior work then? Starting from the assumption of ordinal preferences, Samuelson postulates the existence of a utility function. To help the reader in visualizing his argument, assume for now that there are only two types of goods or activities, A and B, that a consumer can choose. If we assign the quantity of good or activity A to the x-axis and the quantity of good or activity B to the y-axis, then the utility function would be a set of lines in the x-y plane. None of these lines cross; each represents a set of x,y pairs (or bundles of A and B) which produce the same amount of utility for the consumer. The lines are called "indifference curves."

How does this get us to a theory of consumer behavior? We get there with just two additional assumptions:

The utility analysis rests on the fundamental assumption that the individual confronted with given prices and confined to a given total expenditure selects that combination of goods which is highest on his preference scale.

(at 97) In other words, given a budget, a consumer behaves so as to maximize her utility by selecting the bundle of goods that includes as many of the goods that she ranks highly as possible.

There are two assumptions here. First, that the consumer maximizes utility. Second, that the particular bundle of goods selected reveals that the consumer prefers that bundle over any other.

As one might guess from the title of this post, I see problems with one of these assumptions, and it is not the assumption of maximization. As Richard Feynman has noted, for example, the behavior of many systems (human and non-human) can be described as a constrained extremization. It would be more surprising to find out that consumer behavior does not maximize or minimize some quantity.

The problem is with the principle of revealed preference. What the principle suggests is that the preferences (and hence utility) of a consumer can be measured indirectly (i.e., revealed) by observing what bundle of goods is preferred. The problem is that, by construction, a preference is revealed only when a transaction occurs. Although everybody has experienced an increase and decrease in preferences for particular goods over time (such as hunger and thirst), the principle of revealed preferences gives us no way to measure how preferences evolve in time between transactions. Relatedly and in addition, to make a complete "measurement" of consumer preferences for an entire set of goods, one must assume that the ranking of preferences does not change over time (or at least that it changes in deterministic ways). Otherwise there is no logically coherent way to rank the entire set of preferences.

Why do economists make these assumptions? They assume revealed preferences because there are few obvious alternative methods for measuring preferences. They assume time-independence of preferences because there is no other way to measure the entire preference function. Ultimately, they make both of these assumptions because with them, one can make reasonable forward-looking forecasts about how an economy will change as a result of shifts in supply or demand for a particular good. Reasonable, but not perfect!

There are alternatives for measuring preferences. On this blog a year ago I started writing about one. Consider as an alternative to the ordinal ranking of preferences a cardinal measurement of preferences. The preferences of a consumer for a particular good could be measured by counting how often the consumer consumed the particular good within a specific window of time. This measurement of consumer preference would take units of frequency. So if a consumer ate 5 apples in a day, we would say that the consumer had preference 5 apples per day. If the consumer ate only 1 orange per week, then we would say that the consumer had preference 1/7 oranges per day.

Notice how this alternative method of measuring preferences is consistent with the principle of revealed preferences in the sense that within a particular window of time we can rank preferences for each consumer. Within the window of the one week observed, the consumer preferred apples to oranges. If the preferences of this particular consumer are stable over many weeks, then the preference function observed through revealed preferences will be either almost or exactly the same as the preference function measured directly through frequency of consumption and then ranked. This condition of stability is called "ergodicity" by physicists.

But notice also how this method of measuring preferences provides additional flexibility. In particular, the model permits for us to treat preferences as varying with the time-scale of observation. Over the course of a month, consumers might not have much interest in oranges. But over the course of a year, there may be a more substantial preference for oranges.

In addition, the alternative method of measuring preferences permits us to get more information out of the fact of exchange. Whereas before an exchange was our only source of information about the preferences of the parties to the exchange, now with our independent measurement of preferences we can use the fact of exchange as an additional source of information.

Let's say Charlie sells A to Warren for B. If we know that Charlie uses an A / week and B / day, then we can infer that Charlie probably has either some inventory of B or expects to get access to more B within the next day. The fact of exchange tells us about the model that Charlie and Warren have in mind in forecasting their future needs based on their memory of the history of their preferences. In other words, the fact of exchange in view of measured frequencies of preferences still tells us something about their subjective valuation, but it tells us something more subtle than that Charlie prefers B to A and Warren vice-versa. It tells us how often Charlie and Warren expect to use A and B given their current inventory and history of consumption.

For earlier Broken Symmetry posts on related topics see here and here.

In a nutshell, my suggestion is to replace the principle of revealed preferences with a hypothesis of periodicity. The principle of revealed preferences would still obtain in the limit of ergodicity.