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What happens if the stock sees almost no volume of trades, and we have a situation where the lowest sell is at $90 and highest buy at $100 (i.e. both parties are overgenerous)? Does the stock exchange make them split the difference, i.e. makes the trade at $95?

>>badpun+(OP)
I assume you mean highest buy (bid) is $90 and lowest sell (ask) is $100. In this case there would be no trade. This is also called the spread.

If you actually meant your original wording, theoretically whichever order came second would fill at the best price.

>>badpun+(OP)
If someone wants to buy at $100 and someone else wants to sell at $90 it depends on who came first. To really answer this question, you need to understand the difference between market maker and taker and you need to understand how the limit order book [1] works.

Assume there are no other orders in the order book.

Scenario 1: Seller submits a limit sell order for $90. Since there are no buyers, this order goes into the book. Then a buyer submits a limit buy order for $100. The order would be filled at $90 (the best ask) and the buyer only pays $90. Here, the seller is the maker and the buyer is the taker.

Scenario 2: Buyer submits a limit buy order for $100. Since there are no sellers, this order goes into the book. Then a seller submits a limit sell order for $90. The order will be filled at $100 (the best bid) and the seller gets $100. Here, the buyer is the maker and the seller is the taker.

Market makers are responsible for setting prices and providing liquidity. If you want to understand this in more detail, check out this post [1] I wrote up a while ago.

[1] https://www.tradientblog.com/2020/03/understanding-the-limit...