> Individual lowering of prices makes sense if and only if your competitor is capable of saturating the market.

Individual lowering of prices makes sense if you are capable of producing some amount more than you currently do.

Suppose there are 10 suppliers, your production cost is $1 and the current market price is $2. You each sell 100 widgets and you yourself make $100, the other 9 providers also sell an average of 100 widgets, so there are 1000 total purchases.

If you can produce 200 widgets and you lower your price to $1.90, you're now making $180 instead of $100, because people prefer to pay $1.90 to $2 until you run out of capacity. Moreover, the other suppliers have now collectively lost 100 sales to you unless they match your price reduction and maybe some of them have higher costs than you and can't, which means you get to keep their share of the market. The other participants who have lower costs like you, even if they don't have any excess capacity, would rather make the ones who can't lower prices eat the loss in sales because it's better to lower margins by 10% than take an 11% reduction in sales. And lowering prices might also increase sales if customers buy more market-wide at the lower price.

> Yet, if the rest of the market does not react to the signal, the one lowering their prices hurts their profits and possibly kicks themselves out of the market.

How would the one lowering the price kick themselves out of the market? Their sales would only go up, or if consumers are completely insensitive to price, stay the same. As long as the lower price is still yielding them a net profit, they're still in the market. The theory isn't expected to cause them to lower prices below their own costs, because of course they weren't going to do that.

If consumers are completely price insensitive and they didn't know that until they tried it, they might end up raising the price again because it didn't do any good, but that's also pretty uncommon. If you can get the exact same thing for less money, do you pay more for no reason?

> Turns out the probability of either move being the winning move is dependent on probability of other market participants colluding/defecting.

Collusion is something else entirely. If all of the participants are getting together in a back room to fix prices then none of this applies, but that's also why there's a law against that.

It's also why the theory doesn't work when the number of participants is very small.

Suppose there are only two providers and they each have unlimited capacity. They each have a $1 cost, sell 500 widgets for $2 and make $500 each. If one of them lowers prices to $1.90, they'll sell 1000 widgets and make $900. Except that the other one will just match their price and then they'll each make $450 instead, which they both know so they both don't do it. And that's on top of explicit collusion being much easier to hold together and harder to detect when there are fewer sellers.

That isn't what happens when there are 100 sellers, because then 99 of them are trying to hold together a cartel and the last one is laughing at them all because they can increase their sales by 10,000% by lowering prices by 5% and none of the others are matching them.

The game theory of how algorithms can drive up prices