That is the point of common knowledge, and it is a partition in the sense of a sector. The common knowledge will aggregate to the single pt, and approximate a binomial because all traders will be decorrelating the common knowledge from their portfolio. In the finite world that is a tendency to a fair coin binomial with a small trade frequency, being the coin toss. A lot of this stuff boils down to adaptive processes that keep multiple binomials balanced. Sharing liquidity is equivalent to sharing coin tosses among your portfolio set.
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