Do airlines over sell First Class seats also?

In other words, do they ever offer first class passengers compensation for giving up their seats? If so, what is the normal compensation for first class?

Sure. If they calculate that they normally get an appropriate number of F no-shows this will be done. There have been several posts on the BA forum about this happening and the resultant compensation offered.

I think some airlines never do as a matter of policy (e.g. Singapore). I think AA says they don't but several years ago I had a confirmed upgrade and they were oversold by one seat. The was just a LGA-ORD trip and I jumped at the chance to downgrade to a row by myself in coach. Compensation was a $500 travel voucher. They are probably stingier now.

Continental's policy is not to oversell FC/BF, though I'm sure there's an occasional glitch taht allows it to happen. Downgrading to a smaller aircraft sometimes causes FC oversells, too.

I don't think I buy the prevailing supposition that airlines end up bumping passengers PRIMARILY because fewer no-shows materialize than they had counted on. Rather, I think the PRIMARY reason they bump is because they're selling a ticket near to flight time at a high premium, and are able to make more money with the premium ticket price even after subtracting any compensation they may have to pay if someone gets bumped. If I'm operating the airline and someone says, "I'll pay $1000 to fly today on your oversold flight," I'll sell that ticket every time if I know the worst case is to pay a $300 compensation to someone who paid $200 for his ticket and fly him on a seat that remains unsold later in the day.

So at first blush, you might expect to find first class to be less commonly oversold than economy, since first class fares tend to start high but not rise significantly as the flight time approaches. This all changes, though, when you introduce discount, restricted first class fares that are not available close to flight time. Confirmed upgrades also make it likely, since it's a great deal to compensate the confirmed upgrade a fraction of what you'll get in return for replacing him with a full-fare F.

Just conjecture, I'll admit, but it makes more sense to me than the idea that the airline "penalizes" itself for its "mistake" in selling more tickets than there are seats on the plane.

BA routinely over-sells first class, at least on Caribbean flights.

FWIW, several US agents have told me they never oversell F. I have seen the screens that show number of physical seats, number available to sell, number actually sold, etc. Y always shows 20 or so more to sell than capacity, but F always had the same numbers.