Fundamentally, why does a the share price change?

It is obvious that an increase in demand for a share increases it's price provided the number of shares remains constant. However what I am actually asking is why the share prices actually change (i.e the market prices). Is it driven by people who sell there shares for a minimum price that they enter manually? More my fascination with this is when most people use online trading platforms where you can simply press buy and sell and it will automatically find the best price, surely the price of a stock is determined by the average current price people are selling there shares for, at a price they enter manually.

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Supply = Volume of Shares on Offer

Demand = Volume of Shares being Bid on

Price = Average Price where Supply crosses Demand

If supply > demand and price of S/D crosses are significantly lower than current price, price falls

If demand > supply and price of S/D crosses are significantly higher than current price, price rises

How much the price moves depends on how much volume is being traded that day. More liquid stocks = higher volumes = more price movement, less liquid stocks = lower volumes = less price movement. Caveat being that even if prices move less (lower volumes) in illiquid stocks they can move extremely (higher volatility) widely if someone comes in with size.

Participants can range from AM houses entering in / exiting / resizing a stock, HFs going long / short / covering a short / starting an activist campaign, market makers providing liquidity, insiders liquidating some of their holdings, underwriters unwinding their exposures, derivatives writers delivering on their obligations, corporates buying back stock, retail scalpers coming in / out, retail whales loading up on stock / exiting / shorting etc. All of this happens concurrently and will be reflected in volumes, ownership tables, S /D differentials etc.

Was obsessed with finance, now do product in tech
 

This. So many people yell "Why is XYZ stock going up?? The fundamentals aren't changing!!!" Well, it's really only because of the demand > supply. "Fundamental valuation" is only a model that helps us understand supply and demand, it by no means determines it. 

"Markets can stay irrational longer than you can stay solvent."
 

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