This is the three way barter that has stumped the economists. They think it makes a statement about money, it really makes a statement about futures contracts and banking.
If these parties all want to get one service each, from the other, then flip a fair coin. Otherwise let us consider the repeated trials. We introduce the idea that the may all want the same three services. And there is a fair pit boss.
x,y,z means x service y and y services z; two trades. z has excess services received and x has excess services due. All agents want all three services, so z has to service z at the start of the next service round. z services it self, then the fair pit boss selects the agent with the minimal services due to deposits due. The second decision is based on the ratios of service futures take over service futures promised, for the remaining two. The result is the Markov 3-tuple.
In sand box, we can more easily decompose this. Run the automated three S/L automations. Run them super imposed. The pit boss contract remains, but he manages three different pits. This is what the quarks do, I think. The pit boss rotates through the pits selecting two at a time.
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