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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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    $\begingroup$ Why do you think ODEs are relevant to games with asymmetric information? $\endgroup$ – Michael Greinecker Jul 12 at 14:36
  • $\begingroup$ @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 Learn Jul 12 at 14:47
  • $\begingroup$ @Rodrigo de Azevedo, it is a field that i am eager to leran! $\endgroup$ – Hunger Learn Jul 12 at 14:49
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    $\begingroup$ Weibull's Evolutionary Game Theory has a chapter (Ch. 6) on ODE and its applications in evolutionary games. $\endgroup$ – Herr K. Jul 12 at 18:07
  • $\begingroup$ If evolutionary game theory is an option then use mitpress.mit.edu/books/…. $\endgroup$ – VARulle Jul 12 at 19:29
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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):

The next step could be the following books on applications to economics:

and, more on the stochastic side:

Unlike Evans's book, I have never read these ones. My listing of these books is not an endorsement.

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