demoralized Posted October 21, 2011 Share Posted October 21, 2011 Hi all, I am wondering what is the recommended level of math required for game theory? As a business PhD student, I have to take a PhD course in game theory next winter, but my background is basically up to calc 2 and matrix algebra. I am just looking to survive the class (i.e. pass), not get an A or anything. I am also currently taking a masters economics course this semester that will expose me to game theory during the last 1/3 of the course. All in all, how hard of a time will I probably have passing the PhD game theory course given my background? Quote Link to comment Share on other sites More sharing options...
Walras Posted October 21, 2011 Share Posted October 21, 2011 Is this PhD game theory course a field course, or the 2nd part of a year long sequence in micro theory from the econ dept? For that matter is this PhD course taught by the math dept., the econ dept or the business dept. You should expect some proofs, but, so long as it's not from the Math dept or a Micro Theory II course that's named Game Theory, I wouldn't worry too much. The math may be tough, depending upon what papers are used, but it's not the type of stuff that the people who took analysis I and II have a huge advantage over you in. If you're not familiar with proofs take a glance at Fundenberg and Tirole's Game Theory book to see what sort of techniques you'll need to be picking up over the semester. For review, though, I'd try a much easier book like Gibson. Quote Link to comment Share on other sites More sharing options...
tm_member Posted October 21, 2011 Share Posted October 21, 2011 On the other hand, if it is the Micro II course taught at most schools, the math required is not awful... it only gets tough in the existence proofs. The rest are fairly simple. Have you ever seen a fixed point theorem? Quote Link to comment Share on other sites More sharing options...
Peot Posted October 21, 2011 Share Posted October 21, 2011 On the other hand, if it is the Micro II course taught at most schools, the math required is not awful... And then you get to mechanism design. Quote Link to comment Share on other sites More sharing options...
OneArmedEcon Posted October 21, 2011 Share Posted October 21, 2011 Personally, I found that the mathematical foundations of game theory was probably the most challenging math that we did all year. There were people in the class from other departments who had no idea what was going on for those 2-3 weeks, but then bounced back just fine when it came back to applications. But if you want to truly understand game theory (and honestly, I still don't), then a very solid foundation in math is required, IMHO. Quote Link to comment Share on other sites More sharing options...
EconBeach Posted October 21, 2011 Share Posted October 21, 2011 I didn't take a PhD course in Game Theory (not yet) but I have taken an upper division Game Theory course tought through the math dept at my school. We did a lot of linear programming (both algorithms and proofs) and the expected level of math was at least up to matrix theory (proofs based.) The course was pretty intense and being the only econ major in class (most students in my class were math grad students), I felt a bit behind for the whole semester. However though, I do agree with OneArmedEcon, It'll get much better when you do applications. Just make sure your matrix algebra is solid, and some linear programming too if you have a chance. Quote Link to comment Share on other sites More sharing options...
Galoisj Posted October 21, 2011 Share Posted October 21, 2011 I don't think there is any "real" prerequisite for game theory at the level of first year micro sequence. It requires some sort of math maturity (if you would call it) though. For more advanced level, one might need to know basic measure theory and functional analysis (and some other things such as Markov chains). However, one could understand most of the main ideas without those fancy knowledge. Quote Link to comment Share on other sites More sharing options...
coughka Posted October 21, 2011 Share Posted October 21, 2011 I'm curious how much math is needed in mechanism design? I haven't looked into very much but just wondering what kind of preparation would be necessary to get to that level? Quote Link to comment Share on other sites More sharing options...
Zeno Posted October 22, 2011 Share Posted October 22, 2011 I'm curious how much math is needed in mechanism design? I haven't looked into very much but just wondering what kind of preparation would be necessary to get to that level? The required mathematical background isn't particularly more advanced than in straight GT. There are just some annoying computations to wade through... Quote Link to comment Share on other sites More sharing options...
whatdoido Posted October 22, 2011 Share Posted October 22, 2011 I don't think there is any "real" prerequisite for game theory at the level of first year micro sequence. It requires some sort of math maturity (if you would call it) though. For more advanced level, one might need to know basic measure theory and functional analysis (and some other things such as Markov chains). However, one could understand most of the main ideas without those fancy knowledge. What kinds of subjects in measure theory and functional analysis are important for game theory? Quote Link to comment Share on other sites More sharing options...
Zeno Posted October 22, 2011 Share Posted October 22, 2011 What kinds of subjects in measure theory and functional analysis are important for game theory? Approximately: -Anytime you want to talk about anything infinite, measure theory is the rigorous way of talking about mixed strategies. You can often still follow arguments (at the level of a course) intuitively without knowing any measure theory. If people start talking about "beliefs about beliefs about beliefs," then you may actually need to know a course's worth of measure. -Anytime the words "Farkas" or "hyperplane" come up, it means that a treatment of the infinite case will involve basic functional analysis. The only functional analysis that comes up early in econ is the stuff that falls under the broad heading of convexity. If you have a class in linear optimization, or a really good proof-based linear algebra, you'd pick up the right intuition for this stuff. Quote Link to comment Share on other sites More sharing options...
tm_member Posted October 22, 2011 Share Posted October 22, 2011 And then you get to mechanism design. True, but for me Mechanism Design was hard on a conceptual level, the math was not the problem... :-/ Quote Link to comment Share on other sites More sharing options...
demoralized Posted October 23, 2011 Author Share Posted October 23, 2011 Sorry for the late reply. To clarify on my original question: the game theory course is taught by the economics department. It is the 2nd part of a year long micro series. Our program allowed me to take micro 1 at the masters level, but they are requiring me to take micro 2 (game theory) at the phd level. In the masters level micro course, we focus on game theory during the second half of the semester, so I am hoping that it will help get me some exposure. But nonetheless, I am worried about math. No, I don't know what a fixed point theorem is. Like I said, my math is pretty basic, with only some matrix algebra (basically simple matrix operations) and up to calc 2. Quote Link to comment Share on other sites More sharing options...
OneArmedEcon Posted October 23, 2011 Share Posted October 23, 2011 Sorry for the late reply. To clarify on my original question: the game theory course is taught by the economics department. It is the 2nd part of a year long micro series. Our program allowed me to take micro 1 at the masters level, but they are requiring me to take micro 2 (game theory) at the phd level. In the masters level micro course, we focus on game theory during the second half of the semester, so I am hoping that it will help get me some exposure. But nonetheless, I am worried about math. What's the textbook being used for the PhD level Micro II Game Theory course? Quote Link to comment Share on other sites More sharing options...
demoralized Posted October 24, 2011 Author Share Posted October 24, 2011 What's the textbook being used for the PhD level Micro II Game Theory course? I'm not sure about the text yet actually.. but it might be Osborne's "A Course on Game Theory" Quote Link to comment Share on other sites More sharing options...
OneArmedEcon Posted October 24, 2011 Share Posted October 24, 2011 I'm not sure about the text yet actually.. but it might be Osborne's "A Course on Game Theory" If that's the text, then you're probably fine. Quote Link to comment Share on other sites More sharing options...
TomRod Posted October 24, 2011 Share Posted October 24, 2011 Do you remember the hole Alice fell into when she first goes to Wonderland in Disney's adaptation? PhD level game theory is like that. I don't know that anyone ever fully understands it. Hence the need for continuing research. I've seen differential equations, topology, graduate level real analysis, and functional analysis show up both in explanations and proofs. Did I need to sit in those advanced mathematics classes and have a full and complete understanding before I was able to use the principles of game theory? Absolutely not. This is why coauthorship is typically a dominant strategy for publication! That being said, even if you can't identify what field of mathematics game theoretic concepts come from, being very clever with algebra and calculus will always help. Best of luck. Quote Link to comment Share on other sites More sharing options...
treblekicker Posted October 24, 2011 Share Posted October 24, 2011 first year game theory isn't too bad. most people stumble on the conceptual material more so than the mathematical. the proofs tend to be quite easy, especially compared to some you might see in the first semester course. a basic understanding of metric spaces and constrained optimization is more than sufficient. Quote Link to comment Share on other sites More sharing options...
JRav Posted October 25, 2011 Share Posted October 25, 2011 I did some mechanism design briefly as an undergrad in the PhD sequence and U agree with the poster above who said that concepts are tougher than math. If I could ever set up a mechanism design problem, solving was not a problem, the setup was the hard part. Quote Link to comment Share on other sites More sharing options...
tm_member Posted October 26, 2011 Share Posted October 26, 2011 I did some mechanism design briefly as an undergrad in the PhD sequence and U agree with the poster above who said that concepts are tougher than math. If I could ever set up a mechanism design problem, solving was not a problem, the setup was the hard part. Exactly my problem too... Quote Link to comment Share on other sites More sharing options...
dreck Posted October 26, 2011 Share Posted October 26, 2011 For a first year course in game theory basic optimization and probability should be enough. You might need to pick up some hardcore analysis on the fly if you really want to understand the existence proofs but most of the focus of the course will be on finding equilibria, which relies on optimization, some probability, and understanding the equilibrium concepts to begin with. Quote Link to comment Share on other sites More sharing options...
SlowLearner38 Posted October 26, 2011 Share Posted October 26, 2011 Designing a mechanism, contract, auction or an entire market is a task where math isn't going to be the most challenging section of the puzzle. Humans are the hard part. I don't think game theory, as it's used by most economists, has to involve math more complicated than algebra, a little calculus and a little probability to really get a style of incentive based thinking to sink in. From my experience, the people who struggle in game theory courses do so because they have a hard time setting up the models -- that is, taking a real story about agents who face personal decisions and problems regarding strategy, timing, information and uncertainty, and then building a model of the story using economic theory. For economists, "solving" the model is rarely the hard part, it's the building part. Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.