game theory


Here is an example of a “neural network.” I suspect that there will be many improvements down the line, but certainly the financial markets are trying to move away from historical data with multivariate analysis on regressions, to real time, data adjustment.

Traders in financial markets know when to cut their losses, or to push aggressively for a deal. Now a new Gordon Gekko-like software trader can do the same.

By becoming more or less aggressive as market conditions change, it can be 5% more profitable than existing trading programs.

Trading software is increasingly replacing human traders in markets such as foreign exchange because programs can react to market events faster.

However, they typically react to market conditions at any moment as if they were static, says Krishnen Vytelingum at the University of Southampton, UK.

In reality, markets like the NASDAQ are very dynamic with frequent, sudden changes in prices and trading behaviour. If trading algorithms could recognise the dynamics of the market they could become more profitable, he says.

Vytelingum has developed a new trading program that can adjust how aggressively it trades to match market conditions, together with Southampton colleague Nick Jennings and trading algorithm pioneer Dave Cliff at the University of Bristol, also in the UK.

Tough tradingIf acting aggressively, the agent will sacrifice more to beat a competitor to a deal, just like a human in an online auction. “If you are on eBay and you really want to get something, you would bid higher and higher, rather than passively waiting for a good price,” says Vytelingum.

The new agent responds to market changes in two ways. Firstly, it can change its aggressiveness by monitoring other traders’ behaviour.

If other traders are being aggressive – for example, by attempting to undercut others – it raises its game to trade even more aggressively. If trading is less competitive, the software acts less aggressively and calmly aims for the biggest profits available.

Secondly, the software can also use past market trends to try to forecast future conditions. If a period of volatility seems likely, the software changes its behaviour more frequently, meaning it is more likely to be ready to exploit any sudden switches in conditions.

“The majority of share trading in Europe is now handled by algorithms,” says Richard Balarkas, CEO of Instinet Europe a leading algorithmic trading firm. Trading software that is able to read and respond to market behaviour like a human is very desirable, he says.

Secret strategiesIn fact some firms may already be using software like Vytelingum’s, says Balarkas. “They don’t tell anyone about it, that’s how they make money.”

New strategies cannot be tested properly in a real market because it is impossible to know everyone else’s hand. Simulated markets provide a more comprehensive test, a method Vytelingum used to develop his program.

“We benchmarked it against the best agents,” he says. Not only could it make 5% more profit on average then more conventional agents, but when all traders used the strategy, the whole market was more efficient.

Almost all of the available market profit was obtained. “This means that as a group everyone benefits,” says Vytelingum.

If the software works this well, the researchers should probably keep it to themselves, says Balarkas. “The real acid test here is whether or not the next time Dave Cliff calls me, it is from his 60-foot yacht.”

Journal reference: Artificial Intelligence (DOI: 10.1016j.artint.2008.06.001)

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Graph Theory is the mathematics of networks. The mathematics seeks to describe properties of networks through statistical physics. The goal, would be the ability to forcast collective human behaviour.

The stockmarket, and financial markets are of course one example of a network. Forcasting of collective human behaviour, could in turn be highly profitable.

Here is an example of a professional money management firm. Although they do not describe themselves as such, a Hedge Fund.

They claim “attractive absolute investment returns” which means a positive return whether markets rise or fall, via “quantitative research, rules based investing and discretionary asset allocation”

Would they classify for a mathematical analysis via graph theory? In that Hedge Funds form a network of sorts and use very similar strategies. The quantitative strategy “may” be computer driven [ignoring for the moment human programming] Computers fed the same market data, will depending on their programming spit out similar strategies.

Returning to the programmers. Most [a bit of a generalization] of the quants have a similar educational background, thus would it be fair to assume that the anomalies that they programme their computers to seek, will be similar, or the same?

Rotella Capital Management (“RCM”) is a quantitative research and technology firm focused on generating attractive absolute investment returns in global markets. RCM strategies combine systematic, rules-based investing with discretionary asset allocation and model selection. The firm employs a robust risk management system in order to maximize profit while managing investment risk.

RCM strategies generally exhibit low correlation to traditional and alternative benchmark indexes. Our clients are premier firms within the institutional, fund of funds, banking, and family office sectors.

Network math probably originated with Leonhard Euler who mathematically analysed the bridges in Konigsberg in East Prussia.

Game Theory has been used to help explain the evolution of networks and why they develop the way that they do. Specifically, why networks develop in a manner that at first blush seems counter-intuitive as, it goes against the “individuals” best interest, that is to say, non-rational.

Biologists have noted that cellular metabolism “should evolve to an optimum” however, what was actually found was that the optimum was bounded by the environment, as the cells adapted, they altered the environment, thus altering again their adaptation.

Sounds a little like market prices.

As networks disseminate information, so prices adapt to the new information. The very act of changing prices however creates an adaption to the price itself, separate from the original information, which creates an adaptation and so on.

Game Theory, invented by von Neumann, took a quantum step forward when John Nash calculated his point of equilibrium.

Within the financial markets, quant strategies have been around for quite some time. Many Hedge Funds are very quant, or mathematical model orientated. The prime example constituting Long Term Capital Management, headed by John Merriwether and including Nobel prize winner Merton Scholes and numerous others.

Their mathematical model was based on reversion to the mean, or Gaussian curve, which is in essence the basis of Efficient Market Theory. Of course, the Fund and LTCM were exposed, and destroyed by a Black Swan event, that in terms of Probability Theory, should have had such an tiny probability that it could be ignored.

Value investors also have their own version of the Gaussian curve, with The Central Value Theory, which basically states that the market will fluctuate above and below a central value, and through calculation of said value, securities can be classified as over/under-valued.

Nash’s equilibrium is not based on a number. That is to say, it is not based on any form of value. As an example of an equilibrium calculation, if I took a map of New Zealand, and placed it on my kitchen floor, the point in New Zealand would correspond exactly with a point on the map.

Equlibrium in the stock market would then correspond with the calculation, with an exact point in the market…equlibrium. The calculation you see calculates STRATEGIES, hence it’s use in Game Theory.

At any point in time, all the market participants, utilizing all their individual strategies, will reach a point where the various strategies cancel each other out, and we have a point of equilibrium, while new, or existing strategies are modified, held, etc.

If, through the amendment of said strategies, repositioning, the equilibrium is tipped, we would again experience imbalance, until a new equlibrium was reached.

We see this in the market all the time. CVX is a perfect example.

The trend from lower levels to the higher levels between $103 and $97 represents the imbalance and overweighting of the successful strategy, as the strategy started to fail, so the various strategies came into balance, equilibrium, and we have the range.

Of course, this chart pattern is almost as old as Technical analysis, the breakout pattern, the breakout being higher/lower, and jumping on which ever direction predominates, which creates an overweighting of a particular strategy, and trend movement to the next equilibrium point, which may or may not be signalled by previous chart data.

The Nash calculation, via Game Theory, let’s you calculate the optimum strategy based on probabilities that you should employ.

Strategies. There are many, yet, depending on how you group them, possibly not that many. I’ll be looking at the various strategies and the calculation at some point in the future.