Do prizewinners use prize money for academic purposes? Suppose Alice wins the Nobel Prize and $1 million. Does the prize money go entirely to personal matters, or is she likely to use some (most/all?) of it for academic pursuits? If the latter, how does she go about it? Does she just "award herself" a grant similar to grants that academics apply for?

I'm particularly curious about the Fields Medal since it has a stated purpose to encourage awardees for further achievement, which can be interpreted as saying that awardees should use the prize money for academic purposes.
I suspect awardees do not use the award money to do research in the majority of instances. My opinion is not judgemental: in most cases, it would not make much sense to spend that money for research purpose. 

In fact, the average Nobel (or Fundamental Physics Prize, probably the largest sum awarded as prize to scientists) is shared among several people, and amounts to a few hundred of thousands of US dollars each. While that is a large sum for personal purpose, it is not necessarily a large sum for research purpose. 

More importantly, a Nobel medalist is certainly in the league, and with much better prospects of success, to obtain research grants that range in the millions (European research council grant for  example). If you can fetch millions of research money every 5 - 10 years, what difference your ten times smaller, once-in-a lifetime Nobel prize sum would make? Of course the argument above is even stronger for the Fields medal, given its relatively low monetary value.