Let's say company FOO is trying to increase their $20 stock price.
They agree to sell a share for $100. Of course, nobody buys.
Now their buddy buys the share for $100. And maybe sells it back for the same price.
Suddenly the stock price, which is defined to be the last price seen, has increased 5x.
What prevents this from happening?
In a more liquid stock, like say Apple or Google, this is pretty difficult to achieve. That is because there are so many more actors trading the stock than simply Manipulator A and B. Naturally, more transactions and volume leads to a more transparent "equilibrium" price.
The scenario you posited is very possible in less liquid stocks. Manipulators have done exactly what you are asking. Mainly the reason people don't do this is because it's illegal. It is both stock manipulation and fraud, which are felonies.
One distinction worth pointing out though is the difference between deliberate manipulation and simply irrational investing. If actors A and B genuinely believe this stock is undervalued and that the $100 per share valuation is justified, then transacting above market price is not illegal. It is when actors A and B willingly manipulate the price of the security based on nothing other than financial gain that this becomes illegal.
Edit: Tangentially related, but a lot of traders just went to prison for a similar thing called "spoofing". Basically the traders would enter Buy orders way above market price like you are suggesting, which would trigger other algorithms (the legal ones) to transact at a price above current market value, bumping up the share price. The original algo would immediately cancel the 'fake' order and the traders would turn around and short the stock. Source: https://www.justice.gov/opa/pr/eight-individuals-charged-deceptive-trading-practices-executed-us-commodities-markets
Edit 2: removed paywall FT link and provided citation from DoJ
For publicly traded shares, the exchange is what prevents this from happening. At any given time for any reasonably liquid stock there will be a list of buyers with bids to buy a number of shares at a given price and a list of sellers with offers to sell their stocks at a given price.
If you stop the clock here, you will observe that no shares are trading hands and there are a large number of shares sitting out on offer to either buy or sell at a range of prices. It will always be the case at any given time that the highest bid price to buy any of these shares will be lower than the lowest offer price - otherwise a transaction would be taking place and the share price would move.
So the last traded share was done at $20/share and the market then might look something like this
Offers to sell
STOCK TICKER PRICE $20.00
Bids to buy
So when your sly friend goes to the exchange to offer to sell his share for $100 he simply goes into the offers list way up the chain behind everyone else who is willing to sell their shares for a lower price.
When a buyer goes to the exchange to buy a share they can't choose which they will buy - they can choose to either post a bid at a price of their selection and wait for a seller to come along willing to sell at that price, OR, they buy at the market price.
In this case, let's take our spread of bids and offers above as example, and let's say our buyer enters the market willing to buy 7000 shares at market prices. The exchange will negotiate the transaction from the available share pool as:
After this transaction the exchange will list the stock price as the last transaction price - this buyer, in buying these shares, will have moved the stock price up to $21.25.
If no other buyers or sellers act during this time the bid-ask spread will have increased from $0.47 to $1.45 and other buyers and sellers may adjust their positions in reaction to this.
This is the whole point of the market - a single individual with a single transaction cannot materially affect the price of a stock without engaging in such a significant purchase or sale of stock that they consume all of the outstanding bids and/or offers between the current share price and their "target" price. If you want to move a stock from $20 to $100 you have to buy a LOT of shares. Furthermore, you can't move a stock price UP by selling shares at market prices and you can't move it DOWN by buying shares at market prices.
Honestly, most of the time Market Makers will widen the spread to change investor sentiment and this usually will be enough to slow it down and correct itself.
As well as the other answers, it seems worth pointing out that there’s generally no point to doing this. Companies want a high share price for the benefit of their shareholders, so that they will get more money when they sell their shares. A spoofed price at which no real transactions can occur doesn’t achieve this.
