I've done more thinking on the upcoming CASTrader dark markets, as well as partial diversity. I came up with a simple formula to measure the diversity of the CASTrader dark market as it relates to CASTrader's design: something I'll call the Diversity Ratio. The Diversity Ratio is defined as:
Diversity Ratio = (Dollar Volume on the dark market) / (Dollar Volume arbitraged between the dark market and the real market)
If this ratio is greater than one, it means different strategies within CASTrader are trading with each other and creating partial diversity by offsetting each other. The arbitrageurs are effectively consolidating these trades into one "net trade" that gets transmitted to the real markets via the arbitrageurs. This is the learning phase of CASTrader. Ideally, when CAStrader first starts trading the real market, the Diversity Ratio will be very high, while CASTrader sorts out what strategies work in the real world as opposed to the world of backtesting. Hopefully, the good strategies will cannibalize the capital of the strategies that don't work.
If the ratio approaches one (by definition it can't go below one), then the system is approaching zero diversity. Hopefully whatever net trading strategy has emerged at this point is a good one, because all others are essentially worse. This is basically what happened at the end of the simulation of CASTrader I. It's pretty much inevitable that the diversity ratio will tend towards one, due to the power law distribution of wealth.