The idea here is to make a base bot currency built around the SP500 index. Call it the SP currency, and it is a bot tree that just subdivides all the SP betters in units of SP currency.
So, any other group of smartcard connected humans form their own currency, but their peak banker bot bets the SP500 currency. So the club of humans have a Club banker bot pricing Club currency to SP currency. The Club banker bot takes bets from club members, but keeps a long input queue, 3 to 4 club bets must pass before a BP bet is placed, upstream. This sets the weighting of the club, its aggregate adaptation energy.
The club members are semi-acquainted humans, say a household consumer groups in a large town. Household shoppers keep club currency and exchange that for SP currencies from the club bot. SP currency is well known, trades to Walmart points always. SmartCard bot, ClubBot, SPBots, Walmart Bots, all connected in the Wythoff game. But, the householder's club prices have all adapted to the household shopping habits. The net result is the the Club currency will optimally subdivide the set of household good purchased fairly among club members. It reprices all the good these household purchase so that goods suppliers almost never arbitrage the club members.
The math here is that the households actually interject their own adaptation energy between the good suppliers and some nearly neutral money. The Club Bot can then to the yield curve twist, Finding the best set of goods that smopopthly makes HouseHold and Base money variance near stable rational fractions. From their it implicitly creates the compact polynomial generator of the house hold probability of purchase distribution. That polynomial os optimally hedged to the base money.
How advanced is this technology?
Years ago I Huffman encoded the SP index and mapped it to Fibonacci polynomial generators. We have the general theory of Banker bot with spreadsheet testing. So, all we need is Smart Accounts, no cards even. That means a website. This is all pretty sound stuff, I know what I am doing here.
Managing Queues.
I think the queue management is equivalent to adapting the pay off ratios on input and output. These ratios are the Shannon quants computed implicitly. So the complete bot is likely doing the square root in input and output. Or just adjust the queue size. But either way, other bots known the payoff, so its all really a matter of where the queues reside, a frame of reference. The square root function makes the bot exchange at twice the rate of the projection, which is a two period projection. So everything is paced by the root, and that is a one period spectrally bound which always trends toward a minimum adjustment variance. The output bet is the cotangent bet, I think. The bot asks, what is this going to cost me. The input bets are tangent, what are they purchasing.
The optimum queueing strategy fo the club banker bot is to set a larger minimum input put queue. Club members canot have more than one bet in the queue. They are buying or selling club currency for SP currency. But they see the liong queue requirement then buy/sell SP currency in larger chunks, or join another club. Eventually the bet size variance and the queue size variance match; that is the club banker bot strategy. Queued bets pay off immediately, so each member of the club will want its personal banker bot to watch the queue, and prep a bet for tomorrows buying spree.
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