Has SIAI/​FHI considered putting up prizes for contributions to important problems?

Because of my interest in reducing LessWrong’s public goods problem, I’ve been reading about prizes. Prizes seem like they could be very useful for shifting the perception of the scientific and mathematical public on the importance of existential risk.

Prizes have a couple of attractive properties

  1. Shift public perception about what is important and possible

  2. Draw submissions from non-traditional sources

  3. Mobilize existing resources to work on your problem (e.g. people use grants to try to win prizes)

It seems to me that there are several open problems related to existential-risk that might be amenable to prizes. Three prizes seem immediately attractive:
  1. Reflective Decision Theory - This is an important unsolved problem, and the criteria seem like they could be fairly objective (a set of problems the decision theory must handle ‘well’, plus some judging). Of course, perhaps SIAI/​FHI do not want reflective decision theory to be public; in that case a prize would be a bad idea. This prize should probably be called The Good Prize after I.J. Good.

  2. Contributions towards a Theory of Friendliness—Shifting public opinion on this issue is very important, so I think a prize is attractive. The criteria for strong contributions are fuzzier, so you would need especially respected and trusted judges.

  3. Contributions towards understanding existential risks—Same as above.

Is my enthusiasm for this approach unwarranted? Are there other related topics amenable to prizes?
Disclosure: I have only recently read up on prizes and I think I am in fanboy mode, so take my excitement with a grain of salt.