Review of EJC 35-9 (1997) 1495-1500.
This is the first paper I am aware of that uses game theory to study a problem in the field of cancer research. The paper is only from 1997 so it is easy to see that the field is ripe for further development.
The advantage of being the first to use a given tool in any area is that you can chose the problem and come with an simple and elegant study. Tomlinson has used a simple system in which tumour cells can adopt a number of strategies such as producing cytotoxic substances and cytotoxic resistance. The hypothesis is that some tumour cells attempt to gain advantage by actively harming neighbouring cells. This initial hypothesis is studied considering a number of different scenarios in which different phenotypes are combined. Initially there are three types of phenotypes or strategies: cells that can produce cytotoxic substances, cells that can produce factors that protect them from cytotoxic substances and finally cells that do none of this. Tomlinson presents a payoff table in which the interactions between the different phenotypes are presented in a parametrised way so he can hypothesise different values of the cost it represents to produce the toxin or the cost of producing the resistance or the benefit conferred to harm a player by doing so. Once the game is properly defined he goes on to study the potential equilibria by running simulations on a computer and varying the different parameters of the payoff table.
He also studies alternative strategies such as phenotypes that produce both the cytotoxic substance and its resistance and flexible strategies that behave differently according to the phenotype of the player they compete against. The conclusions he obtains are that several phenotypes can coexist simultaneously in a tumour (since there are configurations of parameters of the payoff table that lead to equilibrium), that flexible strategies are better than fixed ones (unless the cost of flexibility is too high and that therapies could be designed that could exploit the fact that tumour cells can harm other tumour cells under some circumstances (maybe promoting competition and not collaboration among them).
Of course the model is very very simple and the conclusions should be taken with some care (there are no spacial considerations, no hints of what the parameters of the payoff table could be, the results are not surprising). Still, this model gives some theoretical backing to these conclusions and suggests some ideas on how to design a therapy which is quite nice.