Kate Upton in the Game of War Super Bowl commercial (Youtube)

Two mobile game developers paid big bucks to get big names to sell their apps during the Super Bowl on Sunday. Actor Liam Neeson did a riff on his role in the "Taken" film series for Clash of Clans, while model Kate Upton was featured in an ad for "Game of War: Fire Age."

Getting those celebrities on board and paying for airtime, which was a cool $4.5 million for a 30-second national spot, was likely not cheap. So how could a pair of "free to play" fantasy games afford such glitzy campaigns?

Both Clash of Clans and Game of War are fantasy games that rely on a "freemium" model -- the basic game is free, but players pay for in-game extras, such as another life or power-ups. They are consistently among the most popular games on iTunes and have been downloaded millions of times.

They use the same strategy that underlies other popular titles such as Candy Crush, and it's a super lucrative one, even if it leaves some industry watchers worried that "free to play" means "pay to win." Supercell, the company behind Clash of Clans, reportedly reaps millions of dollars per day from its three titles. Two of Supercell's Finnish founders became Finland's largest individual taxpayers for a single year in 2014, according to the Wall Street Journal.

Machine Zone, the company behind Game of War, is doing an entire ad campaign with Upton. The Super Bowl spot was part of a roughly $40 million campaign that included inserting the model's likeness into the game as the character of Athena.

But who exactly subsidizes these multimillion-dollar campaigns? A very small minority of players, research suggests.

Only 1.5 percent of "freemium" players made in-app purchases during January 2014, according to research about app gaming monetization by mobile advertising company Swrve. And 50 percent of revenues came from just the top 10 percent of payers -- meaning that 0.15 percent of total players accounted for half of the money brought in by the freemium model.

These big spenders are often colloquially called "whales" by some in the industry -- a reference to a high-rolling gambler. And some worry that the most committed paying players actually exhibit the sort of compulsive behavior associated with drug or gambling addiction. In fact, that was the plot of a "South Park" episode that aired last year.

You can watch both ads here:

Supercell's "Clash of Clans" Super Bowl ad stars Liam Neeson. (Supercell)