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I believe the answer is the latter, but I'm looking for more detail, hence the question.
For low volume stocks and options I have bid lower than the current bid, and while usually my limit order isn't filled, it has been in the past. Is the market itself responsible for this (a retail investor somewhere sees my limit price and decides to jump on it), or is it the market makers, who if they buy, see my limit price as being within some tolerance that they don't publish?
In the absence of liquidity, the market maker sets the price because hardly anyone else is offering to buy or sell the security. If traders put in more competitive bids and offers, the spread narrows.
The rule of law in US financial markets is NBBO (National Best Bid and Offer) so whoever is offering to buy at the highest price or sell at the lowest price determines the NBBO quote. NBBO could be determined by traders, by traders and the market maker, or just by the market maker.
