Market makers drop the bid/ask by the ex-dividend amount immediately after it is announced, or arbitrageurs short the stock when the ex-dividend amount is announced and then they cover their short once the ‘overvalued’ stock they sold is back at fair value.

In the US, the price adjustment is done by the stock exchange itself; the price on open is adjusted exactly by the dividend amount. It's not some collective emergent behavior of the market. (I don't know what non-US exchanges do.)