Based at the Moffitt Cancer Center, Florida, Cancer Ecology is a small research group led by David Basanta. We are mathematical modellers who work with biologists and clinicians, trying to understand the ecology of tumors and the evolutionary dynamics of cancer progression and resistance to treatment.

Mobility and the rock-paper-scissors game

This is (almost certainly) my last post about game theory research in 2007. Collecting information for my lecture on the topic this afternoon I found and read an article (relatively) recently published in Nature by Reichenbach, Mobilias and Frey (Ludwig Maximilians Universität München).

The authors take a very well known game rock-paper-scissors, widely known in game theory. Now, imagine that you place the players in a space that is divided in a way similar to a chess board. Imagine that the players play with their immediate neighbours and that the collected points can be used to determine which players are removed from the board and which ones are allowed to stay and even colonise recently emptied places. In this situation and given that no strategy dominates the other two you should expect a constant shuffle of strategies. If you give each strategy a colour then you could imagine patterns of colours moving in different directions, never settling in a permanent position.

Things seem to change if you allow an addition to a game. Once in a while we could allow two players to switch positions or a player to take an unoccupied slot and giving his old place up. According to these research, the more you allow this to happen (about a certain threshold the effects are more dramatic) the more that this coexistence of three different strategies becomes impossible. Thus motility could have a huge impact in the conservation of biodiversity. This is an interesting result and one is left just wishing that the had explained not only what happened but also (if even tentatively and with due care) why does it happen that way.

Although the work is, for the time being, computational, the authors describe how research done with E.coli in petri dishes could be used to validate experimentally their conclusions.

 

Comments

December 2007

Thursday 20
Zhijian Wang

it is so interesting to find that we two focus on similar references. After I read Mobility and the rock-paper-sicssors game, I repeat their work at once in September, try it at dopping lattice and then report it as draft. You could just have a look on the figures of the draft. 
I program evolutionary game theory with Netlogo.
:)

Thursday 27
David Basanta

Nice reference, I´ll take a look during these days. Hope you get it in a nice journal.

I guess Netlogo is a nice environment in which to place agents in space but I am not sure is that common for most other game theoretical modelling?

Monday 31
Zhijian Wang

You can have a look on Netlogo — before you download it, you can try a tumor model or you can try an evolutionary game theory model.

You are right, Netlogo is not commom today. Usually, I program & model in Netlogo, then check the result in C or Visual Basic. However, netlogo is good for it is visual at the agent-level, instead of probing with data charts. It might be helpful to directly inspecting the individual behaviors, in my view.

My English is poor, please do not pay much too much attention to that rough draft.

Yes, best wishes for your 2008
:)

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