See my paper "On mRJ reachability in Trees" . It is problem related to pebble movement in graphs.

Dear Diego,

I attach a few pages from Berge's 1962 book that will get you started on Games and Graphs. Hope it helps.

There is a computer game called Planarity. A graph is

generated which is guaranteed to be planar (I

assume with Kuratowski's theorem), and you have

to move vertices (find a layout) until no lines cross.

Another game is Go. It can be defined

for general graphs but it can sometimes be

difficult to craft a wooden board or

attach the stones.

Regards,

Joachim

You should check the profile of Matthias Dehmer. You should find quite a lot there!

Dear all,

Thanks for all your answers. Personal acknoledgement comes below.

Just a few comments that may help to clarify what I have in my head:

I am thinking of a kind of interdiction game in a network, one of the players been a defender and the other an intruder. What I am looking for is existence theorems for equilibria in competitive games (e.g. Nash equilibrium, etc.) or sufficient conditions for such equilibria to exist when the game is played in a graph.

I have working knowledge of both, graph and game theory, but have never work on their interactions and am looking for an starting point.

Bests!

Biswajit Deb. Thanks for the paper, very appreciated, I will have a look at it.

Lall B. Ramrattan. Thanks for the pages, I knew about the Nim example from Lin Thomas' book on Game Theory. It's a good starting point. Cheers/

Joachim Pimiskern. Thanks for your ideas but I think that you are pointing to a different direction (maybe not and I am not really able to see the link, in which case I will appreciate if you can give me some more directions).

Martin Zsifkovits. Thanks for the reference, I will check at Matthias' page.