This 1987 collaboration with Elvis Costello first appeared on Paul McCartney's Flowers in the Dirt LP.
The entire album reflected a strong effort on Macca's part, after a succession of rather bland projects during the decade preceding. It was released to coincided with a world tour and McCartney said that an explanation for its high quality was that he didn't want to be stuck in America promoting a bad LP.
It's one of my favorite McCartney projects, a consistently strong album from track to track. There's only one song on the entire album I don't care for.
This one, with an arrangement (and video) clearly meant to evoke memories of the Beatles, has particularly strong lyrics. McCartney and Costello worked together on several songs, some of which appeared on projects by each. Listening to them makes you wish that they would work together more. They seem to bring out the best in each other.
This song is all about the facades we create to protect ourselves from others, so as not to unveil our deepest selves to everybody. The song calls them "brave" faces. Others might call them "game" faces. Here, the narrator is lamenting the loss of his woman and talking about the fakery he engages in each day to avoid talking about how much he hurts.
Included here is the music video of the version McCartney and his band recorded for Flowers in the Dirt (the video being really stupid) and the interesting demo done by McCartney and Costello.
By the way, as alluded to in the first video, Paul McCartney really did, as of a few years ago anyway, still have the set list from the Beatles' 1966 tour taped to his Hofner.
In 1987, Macca hadn't used the bass for several years when Costello remarked on how much he loved the instrument's sound and asked McCartney to use it on the material they composed together. The album marked the return of the famous "Beatles Hofner," which has remained a staple of McCartney's recorded and live performances ever since.
[UPDATE: Actually, McCartney has had at least two Hofner basses, I've learned from this and several other articles.]