In an offline (consumer) market the situation is usually that a retailer does not get offers that differ from the price. He lowers it if noone is buying.
That's completely wrong regarding markets.
When folks ask about stock markets I always suggest, simply think of a street with houses for sale.
{You may be thinking of literally "retail", like a candy shop selling candy bars - that's irrelevant, forget it. That's not a "market".}
So, in all events simply think of a street with houses for sale.
I know that a stock price (like any price on a free market) is determined by supply and demand
The price of a stock is nothing more than: the most recent price one was sold at.
That's all it is.
Your sentence:
I know that a stock price (like any price on a free market) is determined by supply and demand
... is about "philosophy". So, we could say something like "the price of Utilities tends to be stable" or "tech stocks really go upwards in summer" or "if there are a huge number of buyers the price tends to go up".
The price of a stock is nothing more than: the most recent price one was sold at.
If there is more demand than supply for a certain stock its price will raise and vice versa.
That's not "fundamentally" true at all...
The price of a stock is nothing more than: the most recent price one was sold at.
If you trade thin markets, it's completely possible that the price just doesn't change for long periods of time. There can be a zillion bids and/or offers, but (obviously) the price only changes when a sale happens.
Recall that The price of a stock is nothing more than: the most recent price one was sold at.
However, my question is who really moves the price?
The price of a stock is nothing more than: the most recent price one was sold at.
I don't know what the phrase "moves the price" means.
Possible confusion about retail shop analogies?
Could you be thinking about literally "retail", like a candy shop selling candy bars. So, someone puts a "price sticker" on a candy bar. That's irrelevant, forget it. That's not a "market".
Is there some mechanism that lowers price if there is no buy order in a certain amount of time?
The price of a stock is nothing more than: the most recent price one was sold at.
There's no "mechanism" to "change" the price.
I guess, God could go back in time and change the deal between the two people who made the most recent sale!
Or in the Star Trek universe where they have time travel you could "change" the price, again by going back in time and altering reality so that the most recent sale was at a different price.
Putting aside time travel examples, the phrase "change the price" is utterly meaningless.
My understanding is that the order book is a list of prices someone would accept to buy/sell for.
That's completely correct.
(Although it's a strange way to say it. You normally simply say:
The order book is a list of offers to buy and offers to sell.
(Or you might just say "the order book is a list of bids and asks".)
But doesn't this only happen if someone really fills an order at a lower/higher price (a limit order?).
That sentence makes no sense. The situation is:
The price of a stock is nothing more than: the most recent price one was sold at.
The order book is a list of offers to buy and offers to sell.
That's all there is to it.
If I go to a broker's website, check the price and think a certain stock is too expensive and I will not buy, does this move prices at all
Are you asking is there a mechanism where people simply checking the most recent sale price (ie, "using a web site") affects the market in some way ... no.
In an offline (consumer) market the situation is usually that a retailer does not get offers that differ from the price. He lowers it if noone is buying.
You appear to be thinking of a RETAIL analogy.
That has utterly no connection in any way, whatsoever, at all, to a market. That analogy is completely, totally wrong and just has nothing to do with trading / stock markets.
Possible confusion about retail shop analogies?
Retail analogy: candy shop, grocery shop.
Markets: houses on a street being bought and sold; Tsukiji fish market; a stock market.
There is absolutely no connection, at all, whatsoever, in any way between the two. This could be a basic confusion here?