The Nobel Prize website is a good source of information. On the economics prize page they have a link to a page for each laureate. From there you can find, in particular, a biography for each prize winner where the laureates often talk about the genesis of their interest in economics.
For example, Eric Maskin writes
I became a math major at Harvard College, where I studied algebra with Pierre Samuel and Richard Brauer and analysis with George Mackey and Lars Ahlfors − all of them inspiring, some of them amusingly eccentric. Almost by accident, I wandered at one point into a course on "information economics" taught by Kenneth Arrow, later my Ph.D. advisor. The course was a hodgepodge of topics from the frontier of economic theory, but a good part of it was devoted to Leonid Hurwicz's work in the nascent field of mechanism design. This work was a revelation to me: it had the precision, rigor, and sometimes the beauty of pure mathematics and also addressed problems of real social importance − an irresistible combination.
In fact, I ended up essentially doing an economics Ph.D. The degree was nominally in applied mathematics. But the applied math program at Harvard in those days was remarkably flexible, and allowed students to study whatever they wanted, as long as they wrote a thesis with "significant mathematical content." I took quite a few economics courses (although none, I regretted later, in macroeconomics or economic history), including Truman Bewley's general equilibrium course, where I first got to work with my classmate and later co-Laureate Roger Myerson (we sometimes tackled the rather demanding problem sets together) and Jerry Green's analytic seminar, whose student participants included Elhanan Helpman, Bob Cooter, and Jean-Jacques Laffont.
As an advisor, Ken Arrow was amazingly generous with his time; and I learned an immense amount from our many one-on-one discussions in his office.
