Applied by email. Was contacted 3-months later for a phone interview. Phone interview was on advanced economic theory and C++ programming.
Be sure to write a very detailed economics essay, review or paper on a topic relevant to the video game industry or Valve. Ideally this paper should be published, or at the very least reviewed by an economist, like a supervising professor. This paper should be over 20 pages in length and include advanced mathematical derivations for an economics model. As well it should include a detailed econometrics analysis of the data used in your paper. Finally your paper should include an implementation of your findings in code (ideally C++, but mine was in MATLAB). Include this essay with your resume in your initial application.
I thoroughly recommend writing some sample code beforehand. Submit it to the interviewer a day or two before your phone interview. The sample code should be for a small game written in C++. This game should have a strong UI component (like a basic first-person-shooter or a 2D platformer/puzzle game). Along with the code sample specify how many hours you spent on it. Be sure to include advanced C++ concepts in the game, like child classes, virtualization tables, pointer arithmetic, dynamic casting and memory management.