Does anybody know, any (advanced/classic) textbook that combines game theory with differential equations in mathematical economics. Specifically, I an interested in asymmetric information problems.
At the intersection of differential equations and game theory one can find differential games. Arguably, the most famous applications of differential games are in warfare, e.g., the homicidal chauffeur problem. However, not all differential games are of the pursuit-evasion kind.
Whoever wants to learn differential games may wish to learn optimal control theory first. To the neophyte, I would recommend Evans's book (chapter 6 is on games):
- Lawrence C. Evans, An Introduction to Mathematical Optimal Control Theory [PDF], Department of Mathematics, University of California, Berkeley.
The next step could be the following books on applications to economics:
Engelbert J. Dockner, Steffen Jorgensen, Ngo Van Long, Gerhard Sorger, Differential Games in Economics and Management Science, Cambridge University Press, November 2000.
Luca Lambertini, Differential Games in Industrial Economics, Cambridge University Press, April 2018.
and, more on the stochastic side:
- David W. K. Yeung, Leon A. Petrosjan, Cooperative Stochastic Differential Games, Springer, May 2006.
Unlike Evans's book, I have never read these ones. My listing of these books is not an endorsement.