A Game Theoretical Perspective on the Somatic Evolution of Cancer

1.1 Introduction Environmental and genetic mutations can transform the cells in a cooperating healthy tissue into an ecosystem of individualistic tumour cells that compete for space and resources [1, 2, 3]. If we consider a tumour as an ecosystem it is possible to utilise tools traditionally used by ecologists to study the evolution of a population in which there is some degree of phenotypical diversity. One such tool is evolutionary game theory (EGT) which merges traditional game theory with population biology [4]. It allows the prediction of successful phenotypes and their adaptation to environmental selection forces. EGT is considered as a promising tool in which to frame oncological problems [5] and has been recently made more relevant by phenotypic studies of carcinogenesis such as the ones by Hanahan, Weinberg and colleagues [6, 7]. Game theory (GT) was introduced by von Neumann and Morgenstern as an instrument to study human behaviour [8, 9]. A game describes the interactions of two or more players that follow two or more well defined strategies in which the benefit of each player (payoff) results from these interactions [10]. GT can be employed to study situations in which several players make decisions in order to maximise their own benefit. GT was initially introduced to model problems in economics, social and behavioural sciences and is used as a formal way to analyse interactions between agents that behave strategically. Evolutionary game theory is the application of conventional GT as used by economists and sociologists to study evolution and population ecology [4]. As opposed to conventional GT, in EGT the behaviour of the players is not assumed to be based on rational payoff maximisation but it is thought to have been shaped by trial and error-adaptation through natural selection or individual learning [11]. In the context of the evolution of populations there are two GT concepts that have to be interpreted in a different light. First, a strategy is not a deliberate course of action but a phenotypic trait. The payoff is Darwinian fitness, that is, average reproductive success. Secondly,