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.
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1$\begingroup$ Why do you think ODEs are relevant to games with asymmetric information? $\endgroup$– Michael GreineckerCommented Jul 12, 2020 at 14:36
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$\begingroup$ @Michael Greinecker, neither I know that, nor I think that they are relevant...I am still searching and I am asking if there is some textbook that mat contain also asymmetric information. If there is not then I am not going to paint it black $\endgroup$– Hunger LearnCommented Jul 12, 2020 at 14:47
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$\begingroup$ @Rodrigo de Azevedo, it is a field that i am eager to leran! $\endgroup$– Hunger LearnCommented Jul 12, 2020 at 14:49
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1$\begingroup$ Weibull's Evolutionary Game Theory has a chapter (Ch. 6) on ODE and its applications in evolutionary games. $\endgroup$– Herr K.Commented Jul 12, 2020 at 18:07
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$\begingroup$ If evolutionary game theory is an option then use mitpress.mit.edu/books/…. $\endgroup$– VARulleCommented Jul 12, 2020 at 19:29
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2 Answers
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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.
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This is probably an old question. However there is a book on PDE's and game theory.
Game Theory and Partial Differential Equations, Pablo Blanc and Julio Daniel Rossi.
If you found other books on this matter, I would like to know as well.
