One thing to consider in the real world. Often on certain routes, an airline has a regular clientale that fills up a significant capacity on that route at fairly low prices. Examples are corporate arrangements where one or more corporate clients can have regular "commute" traffic between the two locations. For example, IBM employees can apparently fly RDU-LGA on AA for less than $60 R/T with no Sat night stayover or advance booking requirements. IBM employees take up a lot of seats on such a route.

The other example is of travel/tour consolidators that get a bloc of seats.

Any airline that has such an arrangement is not really trying to compete with the others who may not have such arrangements in those routes. In other words, their lower priced fares are already "sold out". Unless they have a lot of empty seats available there is no need to reduce the price for such routes.