<p>I was able to find an application of combinatorial game theory in cryptography. See the link <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.2.2928&amp;rep=rep1&amp;type=pdf" rel="nofollow">here</a></p>

CC BY-SA 3.0
2015-09-12T16:45:48.920Z
2015-09-12T16:45:48.920Z
Halbort
<p>Combinatorial game theory and topics thereof has received a lot of attention in modelling and verification of reactive systems. I would draw your attention to <a href="http://www.cs.cornell.edu/Courses/cs6860/2010fa/Handouts/thomas.pdf" rel="nofollow">this</a> nice reference for more information.</p>

CC BY-SA 3.0
2015-08-18T06:38:57.010Z
Which combinatorial games have  you got in mind?
Martin Berger
CC BY-SA 3.0
2015-08-17T08:29:51.073Z
2015-08-17T08:29:51.073Z
Star
<p>I think Kaveh's comment is the correct answer: applications? We don't need no applications.</p>

<p>But despite all that, combinatorial game theory does appear to have some applications in error correcting codes. See Conway and Sloane, "Lexicographic codes: Error-correcting codes from game theory", IEEE Trans. Inf. Th. 1986.</p>

<p>More simply, if you are willing to think of nim-addition (bitwise exclusive or) as something that came out of combinatorial game theory, then there are plenty of applications, for instance in <a href="https://en.wikipedia.org/wiki/Tabulation_hashing">tabulation hashing</a>, or as one of the components of Schieber and Vishkin's lowest common ancestors data structure, or as one of the components of some block cipher systems.</p>

CC BY-SA 3.0
2015-11-19T13:04:52.790Z
Nim-addition gives a nice definition of exclusive or that does not depend on binary representation. It is introduced only with a game involving natural numbers in mind, no binary required.
Christopher King
CC BY-SA 4.0
2018-10-24T06:42:46.117Z
But, isn't considering biwise XOR as something that came out of CGT, a bit far fetched? Anyway, I like your answer.
Cyriac Antony
CC BY-SA 3.0
2015-08-17T04:53:45.077Z
2015-08-17T05:25:51.103Z
2015-08-17T05:25:51.103Z
David Eppstein
<p>I find Combinatorial Game Theory very interesting as my primary interest is mathematics. My question is why do Computer Scientists (who tend to have a more practical approach) study it as well? Are there some applications of it? This question is similar to this <a href="https://cstheory.stackexchange.com/questions/16187/applications-of-game-theory-in-computer-science">one</a> but I am asking about combinatorial games such as nim. Could someone provide me with a reference?</p>

CC BY-SA 3.0
2015-11-19T13:02:48.273Z
Indeed, one of the first books in combinatorial game theory (*Surreal Numbers* by Knuth) explicitly *praises* its lack of applications.
Christopher King
CC BY-SA 3.0
2015-07-02T01:07:53.887Z
A vague guess is that applications are more in AI than "theory" as we usually think of it...
usul
CC BY-SA 3.0
2015-07-02T04:03:29.800Z
You seem to assume that computer scientists study a topic mainly because it has applications, which is false.
Kaveh
<ds.algorithms><reference-request><gt.game-theory><combinatorial-game-theory>
What is the application of combinatorial game theory
Halbort
# What is the application of combinatorial game theory

(Asked by: username_0 on 2015-07-01)

I find Combinatorial Game Theory very interesting as my primary interest is mathematics. My question is why do Computer Scientists (who tend to have a more practical approach) study it as well? Are there some applications of it? This question is similar to this [one](https://cstheory.stackexchange.com/questions/16187/applications-of-game-theory-in-computer-science) but I am asking about combinatorial games such as nim. Could someone provide me with a reference?

**Tags:** ds.algorithms, reference-request, gt.game-theory, combinatorial-game-theory
> **Comments:**
> **username_2**: A vague guess is that applications are more in AI than "theory" as we usually think of it...  
> **username_3**: You seem to assume that computer scientists study a topic mainly because it has applications, which is false.  
> **username_1**: Indeed, one of the first books in combinatorial game theory (*Surreal Numbers* by Knuth) explicitly *praises* its lack of applications.  

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## 3 answers

### Answer by username_6 on 2015-08-17. Score: 11 | Accepted answer

I think Kaveh's comment is the correct answer: applications? We don't need no applications.

But despite all that, combinatorial game theory does appear to have some applications in error correcting codes. See Conway and Sloane, "Lexicographic codes: Error-correcting codes from game theory", IEEE Trans. Inf. Th. 1986.

More simply, if you are willing to think of nim-addition (bitwise exclusive or) as something that came out of combinatorial game theory, then there are plenty of applications, for instance in [tabulation hashing](https://en.wikipedia.org/wiki/Tabulation_hashing), or as one of the components of Schieber and Vishkin's lowest common ancestors data structure, or as one of the components of some block cipher systems.

> **Comments:**
> **username_1**: Nim-addition gives a nice definition of exclusive or that does not depend on binary representation. It is introduced only with a game involving natural numbers in mind, no binary required.  
> **username_7**: But, isn't considering biwise XOR as something that came out of CGT, a bit far fetched? Anyway, I like your answer.  

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### Answer by username_0 on 2015-09-12. Score: 3

I was able to find an application of combinatorial game theory in cryptography. See the link [here](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.2.2928&rep=rep1&type=pdf)


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### Answer by username_4 on 2015-08-17. Score: 1

Combinatorial game theory and topics thereof has received a lot of attention in modelling and verification of reactive systems. I would draw your attention to [this](http://www.cs.cornell.edu/Courses/cs6860/2010fa/Handouts/thomas.pdf) nice reference for more information.

> **Comments:**
> **username_5**: Which combinatorial games have  you got in mind?  

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