Commitment and Repeated Play
Everything so far has assumed a single simultaneous move. Two changes to that assumption alter the answers completely: acting first in a way that cannot be undone, and playing the same opponents tomorrow.
Commitment is worth paying for
Ordinarily, having more options is better. In a game it can be strictly worse, because your options are visible to the other side and shape what they do.
A firm that can quietly withdraw from a market whenever conditions turn is more flexible than one that has committed to quote continuously. It also gets less flow, because the counterparties who choose where to route know the quote may not be there when they need it. The flexible firm's own optionality is what costs it the business.
A posted quote is the everyday example. It is a binding offer: anyone may trade against it at that price, immediately, without asking. That constraint is not a regulatory inconvenience, it is the entire product. A price you would honour only if you still felt like it is worth nothing to the person who needs to trade now, which is why immediacy is the thing a market maker actually sells.
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