<p>This is probably an old question. However there is a book on PDE's and game theory.</p>
<p>Game Theory and Partial Differential Equations, Pablo Blanc and Julio Daniel Rossi.</p>
<p>If you found other books on this matter, I would like to know as well.</p>

CC BY-SA 4.0
2021-04-19T22:33:23.243Z
2021-04-19T22:33:23.243Z
Ramesh Kadambi
<p>At the intersection of differential equations and game theory one can find <a href="https://en.wikipedia.org/wiki/Differential_game" rel="noreferrer">differential games</a>. Arguably, the most famous applications of differential games are in warfare, e.g., the <a href="https://en.wikipedia.org/wiki/Homicidal_chauffeur_problem" rel="noreferrer">homicidal chauffeur problem</a>. However, not all differential games are of the <a href="https://en.wikipedia.org/wiki/Pursuit-evasion" rel="noreferrer">pursuit-evasion</a> kind.</p>
<p>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):</p>
<ul>
<li>Lawrence C. Evans, <a href="https://math.berkeley.edu/%7Eevans/control.course.pdf" rel="noreferrer">An Introduction to Mathematical Optimal Control Theory</a> [PDF], Department of Mathematics, University of California, Berkeley.</li>
</ul>
<p>The next step could be the following books on applications to economics:</p>
<ul>
<li><p>Engelbert J. Dockner, Steffen Jorgensen, Ngo Van Long, Gerhard Sorger, <a href="https://books.google.com/books?id=TMJWWMsE1_AC" rel="noreferrer">Differential Games in Economics and Management Science</a>, Cambridge University Press, November 2000.</p>
</li>
<li><p>Luca Lambertini, <a href="https://books.google.com/books?id=aU9TDwAAQBAJ" rel="noreferrer">Differential Games in Industrial Economics</a>, Cambridge University Press, April 2018.</p>
</li>
</ul>
<p>and, more on the stochastic side:</p>
<ul>
<li>David W. K. Yeung, Leon A. Petrosjan, <a href="https://books.google.com/books?id=F8NNYgv7FKAC" rel="noreferrer">Cooperative Stochastic Differential Games</a>, Springer, May 2006.</li>
</ul>
<p>Unlike Evans's book, I have never read these ones. My listing of these books is not an endorsement.</p>

CC BY-SA 4.0
2020-07-12T19:30:27.597Z
2020-07-12T19:30:27.597Z
Rodrigo de Azevedo
<p>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.</p>

CC BY-SA 4.0
2020-07-12T14:36:54.320Z
Why do you think ODEs are relevant to games with asymmetric information?
Michael Greinecker
CC BY-SA 4.0
2020-07-12T14:47:44.017Z
@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
Hunger Learn
CC BY-SA 4.0
2020-07-12T14:49:11.220Z
@Rodrigo de Azevedo, it is a field that i am eager to leran!
Hunger Learn
CC BY-SA 4.0
2020-07-12T18:07:51.080Z
Weibull's [*Evolutionary Game Theory*](https://books.google.ca/books/about/Evolutionary_Game_Theory.html?id=m98ed0_Na1sC&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=false) has a chapter (Ch. 6) on ODE and its applications in evolutionary games.
Herr K.
CC BY-SA 4.0
2020-07-12T19:29:10.500Z
If evolutionary game theory is an option then use https://mitpress.mit.edu/books/population-games-and-evolutionary-dynamics#preview-drawer.
VARulle
<microeconomics><game-theory><mathematical-economics><ode>
Game theory and differential equations
Hunger Learn
# Game theory and differential equations

(Asked by: username_0 on 2020-07-12)

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.

**Tags:** microeconomics, game-theory, mathematical-economics, ode
> **Comments:**
> **username_1**: Why do you think ODEs are relevant to games with asymmetric information?  
> **username_0**: @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  
> **username_0**: @Rodrigo de Azevedo, it is a field that i am eager to leran!  
> **username_2**: Weibull's [*Evolutionary Game Theory*](https://books.google.ca/books/about/Evolutionary_Game_Theory.html?id=m98ed0_Na1sC&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=false) has a chapter (Ch. 6) on ODE and its applications in evolutionary games.  
> **username_3**: If evolutionary game theory is an option then use https://mitpress.mit.edu/books/population-games-and-evolutionary-dynamics#preview-drawer.  

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## 2 answers

### Answer by username_5 on 2020-07-12. Score: 5 | Accepted answer

At the intersection of differential equations and game theory one can find [differential games](https://en.wikipedia.org/wiki/Differential_game). Arguably, the most famous applications of differential games are in warfare, e.g., the [homicidal chauffeur problem](https://en.wikipedia.org/wiki/Homicidal_chauffeur_problem). However, not all differential games are of the [pursuit-evasion](https://en.wikipedia.org/wiki/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](https://math.berkeley.edu/%7Eevans/control.course.pdf) [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](https://books.google.com/books?id=TMJWWMsE1_AC), Cambridge University Press, November 2000.
* Luca Lambertini, [Differential Games in Industrial Economics](https://books.google.com/books?id=aU9TDwAAQBAJ), Cambridge University Press, April 2018.

and, more on the stochastic side:

* David W. K. Yeung, Leon A. Petrosjan, [Cooperative Stochastic Differential Games](https://books.google.com/books?id=F8NNYgv7FKAC), 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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### Answer by username_4 on 2021-04-19. Score: 1

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.


---

