This may not be an appropriate question for this platform, but I couldn't think of any place that it fits. My concern is understanding about game theory papers. Whenever I read classical papers of Harsanyi, Aumann etc. I start to feel lost with unknown math. This happens a lot. I studied many of these classical concepts on a textbook level and I had no problem at all, but when it comes to the original paper I can easily lost the track because of mathematical sophistication. I know a little bit of real analysis (Baby Rudin first $4$ chapters), I have studied a little bit of topology (Munkres) I have also some background in set theory, statistics etc. So I am not a complete beginner. What I want is to understand, at least on a reasonable level, a technical game theory paper such as Harsanyi (1973a) and Harsanyi (1973b). Can anyone suggest me a study plan with books and such? It can start from zero level I have time and patience. Any advice will be greatly appreciated!
3$\begingroup$ Classic papers/results of game theory are usually written up in easily-digestible form in standard textbooks. For example, Osborne and Rubinstein is a good first year graduate level introduction to game theory. For a more in-depth treatment, Fudenberg and Tirole is the one to go. I sometimes find the New Palgrave Dictionary of Economics useful for understanding certain topics, for example, Harsanyi's purification theorem. $\endgroup$– Herr K.Apr 25, 2016 at 16:57
2$\begingroup$ @HerrK. The thing is I have checked and have been checking those books from time to time. They are generally do not talk about the math you need to know. For instance purification paper in Palgrave is just giving UG level explanation but the actual theorem talks about atomless distribution, polyhedra etc. I want to learn these concepts too not just simplified explanations of the actual material. $\endgroup$– user64066Apr 25, 2016 at 17:31
1$\begingroup$ I suppose it would be very hard, if not impossible, to come up with a "narrow" set of books/references that encompass all the mathematical tools used in game theory. This time you might be stuck on measure theory and geometry with Harsanyi, and next time on fixed point theorems with Nash, and on differential equations with Aumann in yet another occasion. To get a solid and systematic understanding of these concepts is already the work of 3-4 courses. If you really have the time, get a math major. Otherwise, you'd have to make do with the less systematic way of Googling/looking up Wikipedia. $\endgroup$– Herr K.Apr 25, 2016 at 19:42
$\begingroup$ Probably it would not hurt to learn various fixed point theorems. $\endgroup$– HRSEApr 28, 2016 at 8:48
$\begingroup$ A good starting point is Gibbons's Game Theory for Applied Economists. It's an easy read, then you can step up to more advanced books like the ones mentioned in the comments. $\endgroup$– dv_bnMay 1, 2016 at 19:03
Probably a more general response than you're hoping for, but I recently asked a (well-published) econ prof at my university which classes he'd recommend prior to doing research. He said he usually recommends to the PhD students he advises that they take real analysis and probability at a graduate level.
Game Theory is not quite pure math, but not quite applied math either. A lot of areas within mathematics converge in game theory as well- real analysis and topology, linear programming and polyhedral theory, linear algebra, and graph theory amongst others.
I would suggest a senior undergraduate sequence in real analysis, a course in optimization (linear or integer programming), and a graduate course in linear algebra. Some bonus courses are graph theory, a course in algorithm design with an emphasis on complexity, and graduate real analysis (measure theory). Optimization courses generally touch upon polyhedral theory, especially integer programming courses. Granted, economics models tend to be more continuous. Game theorists have become increasingly interested in networks, so graph theory is very nice to have. There are papers in the last ten years that have adopted spectral techniques in networks which makes linear algebra at the graduate level very important.
Really, the advice to major in math is spot on. Econ grad students either have the math background or continually struggle with it. The latter is a bad position in which to be.