Who decides the stock price?

The analogy is slightly off.

Instead, imagine a different kind of store:

The store is empty. There are shelves, they’re empty too.

In come “sellers” with a bunch of goods. Let’s say there’s only one item for sale: canned tuna.

Different sellers come in and offer cans of tuna for sale. They write the price they’re willing to accept (sell the tuna for) on a piece of paper and place it on a board that’s hanging on a wall in the middle of the store.

From another door in come buyers. They write a price they’re willing to pay for a can of tuna and also place it on the board, in a different section.

Then, a clerk comes in and matches buyers and sellers, if there are matches to be made. A match can be made when there’s a “buy” note with a price equal to or greater than some “sell” note.

You may say this clerk “sets” the price, but that’s not really true. The price essentially sets… itself since the logic for matching is very simple and automatic (there are lots of nuances in real life, but that’s the high level idea).

In the actual stock markets, those “clerks” used to be brokers (the folks you see on the floor of the NYSE on TV) but nowadays they’re largely replaced by computer software that does the “matching”.

The “price” you see on a finance website is just the most recently “matched” price. Nobody really “set” it and it’s really just a snapshot of a point in time.