Market is internally consistent

MSFT pays $6B for AQNT, which had a market cap of about $3B. The result? MSFT's market cap is down by about $3B.

The market is consistent - although it may or may not turn out to be right.

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Not necessarily. a)

Not necessarily.
a) Microsoft was interested in AQNT, this itself is information that should affect the share value of AQNT
b) AQNT once being bought by Microsoft benefits from Microsoft's capital investments, technologies, know-how etc, this should also affect its future income.

There is also a more deeper problem which is that "market cap" is an ill defined concept. Market cap is an aggregate of different holder estimates which depend on their individual time preference, risk aversion etc.

The concept of market price makes sense for something approaching commodity, it makes sense for a single share, for a troy ounce of gold, but the market capitalization is not a market price or a market value.