[murbard2]

And no, you don't assume that every strategy is equally likely. You assume that the opponent plays optimally with full knowledge of your own strategy, which means you're looking for a Nash equilibrium http://en.wikipedia.org/wiki/Nash_equilibrium

[foldr]

That's fine if you already know game theory, but then the problem is not quite as accessible as you made out. You can't expect someone to just invent the concept of a Nash Equilibrium on the spot from the words "best strategy". (Although I understand that you may expect your interviewees to already be familiar with game theory.)

[murbard2]

In this case, the candidate's thesis work explicitly dealt with game theory. In addition, this doesn't require much knowledge of game theory... if you think about the problem for a bit, you can re-derive the concept fairly easily.

Nash's brilliance was in proving that under reasonable conditions, a mixed equilibrium always exists, which is far less obvious.

[foldr]

The issue isn't the difficulty of the concept but the ambiguity of "best strategy".

[murbard2]

Fine, best strategy given a perfectly rational opponent. There, ambiguity removed.

[foldr]

Well not quite, you also need to specify that the opponent assumes that you are perfectly rational, and that he assumes that you assume that he is, and that he assumes that you assume that he assumes that you are, and so on. A perfectly rational opponent would not assume that you are perfectly rational in the absence of any relevant information. Rather, he would assume that his opponent was equally likely to be using any strategy.

[megrimlock]

Makes sense. I didn't realize the problem description was for a game that would be played repeatedly with the same opponent -- i.e. one where you can gather information. If we were doing this in person instead of on a internet forum and async post/response we'd probably iron that out quickly. Thanks for elaborating.