I guess it's too early to draw any conclusions as de-regulation started 24 hours ago.
AR really set the game with one way domestic tickets for as low as 500 pesos (18 USD) and a huge advertisement campaign. This forced LATAM to react with tickets for the same price with 1 checked-in bag (AR fares are hand-baggage only), and Flybondi went ultra-low-cost with tickets for 200 pesos (7 USD) one-way.
Both AR and Flybondi's websites crashed several times during the day, and according to the press all three airlines report a +400% rise on ticket sales vis-ŕ-vis any normal day.
Andes and Avianca said they would not join the price war -- understandable, since Andes is already low-cost(ish) and Avianca's routes mostly target business travelers.
This is a country where many, many people have never taken a plane because they were always told "flying is for the rich". Hopefully the de-regulation and subsequent offers show that is not the case. Today, Flybondi was selling EPA-TUC for 1,000 pesos return (36 USD) -- that is a quarter of the price of a bus ticket, and the bus takes 18 hours to Tucumán, while the plane does the journey in less than 2 hours.