The next step in Channel theory is mutual entropy, or how does on sector know it is safe to expand distribution. Looking back at the post on contraction, what we want is knowledge of the conditions that let all the various sectors move from the contracted yield curve to the expanded yield curve. We will find simplification in the problem because we know we have a constant value of signal to noise ratio at equilibrium.
It seems the mathematicians are hard at work on the problem. And it has become a big issue in Internet searching, how does one search trust the links established by previous searches, and how fast to a set of search links converge. In economics, it has to do with finding an agreement between the arrival of wages and the arrival of goods. When should a producer change delivery quants in order to short the queue waiting to buy goods. If he changes to much, then wages go down to far. it is not just price discovery, but quant discovery also. This is what distinguishes channel theory from the Keyesian and monetarists.
Example: When does a collection of taders at the corner become a market? When the mean their distribution over the variance reaches a sufficient value, we will create a matching function, in our heads, and forever quantize that place as the market.
Looking at Mutual Entropy definiton we need to estimat the mutual probability of arrivals in the first equation. If the merchant cannot get that right, then he invests a lot and gets no customers.
The mathematicians read my blog, they will help us out.
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