This works while there are four food chains and they all completely independently decide that prices should be a little higher.
Even without cooperation that isn’t allowed, let’s say 5Guys comes in and see that the market will bear higher prices. Why wouldn’t they take advantage of that?
But if the prices are way higher, then 5Guys sees that by setting prices a bit lower it can capture 90% of the market, rather than 50%. Which is way more total profit.
That's how downwards price pressure in capitalism works -- by reducing price you gain market share and increase profit overall. Otherwise, under capitalism, all our prices would be sky-high!
This assumes that Five Guys is in direct competition with those other chains and that people are directly comparing prices when choosing where to eat. People are not the perfect rational actors economists like to pretend they are, and they tend to make assumptions about prices and have personal preferences (e.g. the last time I went to BK it was so bad you would have to pay me to go back).
Even without cooperation that isn’t allowed, let’s say 5Guys comes in and see that the market will bear higher prices. Why wouldn’t they take advantage of that?