I'm studying measure theoretic stochastic calculus, and I was hoping to pick up some knowledge of decision theory along the way.
I'm very happy with Rudin or Karatzas in level of rigor, and I was hoping to find a game theory or decision theory (mainly decision theory) reference at this level as well (with good exercises, if possible). I want this because 1) I feel I need to build my math ability by working on reasonably tough books, and 2) I might get bored if it's too easy, although I like to think I'm a patient person.
Also, if it's not too much trouble, supposing I finish my introduction and am interested in learning more, could I also have a suggestion for a followup book.
I have a couple of suggestions. I'm a big fan of Osborne and Rubinstien's A Course in Game Theory, but that may not have enough decision theory. You might also try The Economics of Risk and Time By Christian Gollier. More hardcore is work by Peter Fishburn.