Who decides stock prices?

Who sets the value? Because 'supply and demand' isn't a conscious entity that can make decisions or manually adjust the listed price of something.

Imagine you're in a market buying and selling coins. A person approaches you and asks for the prices at which you would buy and sell coins. You respond, "I would buy at $9 and sell at $10." The person thanks you and moves on to ask others the same question. After some time, they discover that the lowest price they can buy at is $9.50, and the highest price they can sell at is $9.45. These are the prices at which they actually end up buying and selling. In the past, this was done manually, with people talking on the phone and shouting in trading pits. Today, however, electronic systems aggregate all the prices in real-time.