My background: Multivariate analysis (Factor Analysis, ICA), Time Series analysis, Probability and Statistics, Linear Algebra and also Signal Processing. (amateur in all)
Goal: To learn the mathematics behind game theory along with hints of applications.
I want the book to be framed such that it could be read without prior knowledge of anything. Any basics to be included in the book (at least in the appendix). Needs to be introductory as well as thorough as much as possible.
Fun to read with all the math necessary. (being too wordy will be a bore).
Applications to various scenarios would be an added benefit.
If just one book will not be able to cover it, suggest two books that will satiate.
Some of the Good books in other topics that satiate all mandate stated above:
Independent Component Analysis
Aapo Hyvärinen, Juha Karhunen, Erkki Oja
ISBN: 978-0-471-40540-5
http://as.wiley.com/WileyCDA/WileyTitle/productCd-047140540X.html
Linear Algebra:
Matrix Analysis and Applied Linear Algebra (Carl D. Meyer)
http://www.matrixanalysis.com/
Some standard books on game theory are
- Gibbons "Game theory for applied economist"
- Osborne & Rubinstein "A course in game theory", MIT press
but they are quite colloquial
Given your skills I guess that you can look at
- Fudenberg-Tirole "Game theory", MIT Press
- Hans Peters, "Game Theory -A Multi-Leveled Approach", Springer
The first book ever I read on game theory was The Compleat Strategyst. Here it is, for free ! http://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB113-1.pdf
Thanks, The free ebook is well written, but quite wordy. I'll probably go through it last... Game Theory - A multilevel Approach looks like exactly what the doctor ordered... but Meh... it's costly! Damn costly!. was able to get the Fudenberg one though (pdf from MIT press). Thanks. I'll get back once I read them. (gonna take a few months though). I'll try for the Hans Peters one through library. Thanks a lot.
In my opinion you can start from an advanced Microeconomics book, for example:
Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic theory, New York: Oxford university press.
This book is very comprehensive of the developments of the Microeconomic Theory at an Advanced Level. As well a good text on Mathematical Economics can be useful in order to consider the techniques in the context (for example Fundamental Methods of Mathematical Economics by Kevin Wainwright and Alpha Chiang). At this point with these foundations is possible to explore the Game Theoretical approaches with sound analytical basis:
1) Maschler M., Solan E. , Zamir S. (2013) "Game Theory" Cambridge University Press
2) Fudenberg, D., & Tirole, J. (1991). "Game Theory" MIT Press
3) Tadelis S. (2012) "Game Theory: An Introduction" Princeton University Press.
Hi,
adding to the above, one more suggestion. I will recommend you to read "Multi agent system" by Soham.
I read this book to learn game theory with mathematics concepts. I hope this will satisfy your requirements..
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