Even if you are not planning to fly on any of the airlines mentioned above, you should check the fares from other airlines as all the major airlines usually match competitor fares on their competitive city pairs.
Note that there are many exclusions on these sales when it comes to excluded dates and time of the week when the travel is allowed. Remember to read the fine print.
Airlines tend not to advertise that they have matched competitors’ fares but they usually do from their most important markets. You just have to keep eye on Southwest’s and other’s fare sales and then check the prices on your favorite airlines.