Attempts to tie CEO interests to owner interests by tying compensation to the company's performance have thus far failed, mostly because a) the fraction of compensation isn't sufficient to overcome the CEOs self-serving motivation or b) the specific tying system can be gamed to the CEO's advantage.
Furthermore, there is an asymmetry in the degree of interest between the parties: CEOs have a very large interest in maximizing their own compensation, while shareholders see CEO compensation as one expense amongst many others, and as such are less interested in it.
These issues have been known for a long time, and again: no one has come up with a viable answer. Anything anyone who is posting here thinks of has almost certainly been thought of before, tried, and seen to fail.
and/or c) extrinsic motivators aren't effective for non-mechanical work.
But the question with CEO pay is a bit different, and I don't think the studies Pink refers to say anything about it: what can you do to encourage CEOs to act in the best interests of the companies they manage?
This isn't a matter of, e.g., whether they notice opportunities to attack a previously unaddressed market -- which is the kind of thing for which Pink finds extrinsic motivation isn't good at improving. It's a matter of whether, having noticed such an opportunity, they further notice that taking it would be good for the company but bad for them personally because, e.g., it would have short-term costs that would drive down the value of the shares they were hoping to sell next year to buy a new house.
In which case, the findings Pink describes might actually be good news: the prospect of personal gain may be ineffective in making unscrupulous CEOs good at spotting opportunities to screw their company over to make a quick buck.
A CEO can always blame the economy, blame the market, blame the weather, blame their predecessors or otherwise spin things in a favorable way. They can sell a story of tough times needed to make a turnaround. Sometimes there will be some secret scratching behind the back (I'm on your board, you're on my board). There's the cognitive dissonance on the board side of things, we've selected this guy therefore he must be good. etc.
As others have said, the incentives are set in a way that a CEO looks primarly after his own interests. It's safe to assume that CEOs that make a lot of money are even better at looking after their own interests. They are also very good at convincing others that they're not looking after their own interests.