## Prisoner’s dilemma in an RNA virus

This is a rather old article but I particularly like it for the novelty of the idea of applying game theory to small entities. It is also mathematically non-rigorous, but the game theoretical ideas presented are very accurate.

Game theory has been conventionally used in the behavioral sciences, economics, and the evolution of animal populations. However, recently it has migrated toward smaller and smaller entities including viruses (which I discuss here) and cancer cells. (See this blog for a more expansive coverage of recent research on evolutionary game theory in cancer research.)

The main idea behind Turner and Chao’s “Prisoner’s dilemma in an RNA virus” is that viruses are born competitors. They exploit the host cells which they inhabit as well as each other. Specifically, a virus may cooperate or compete through the sharing of diffusible products. Viruses which produce a large amount of these products are deemed cooperators, while viruses which do not produce a large amount but instead utilize the products produced by other viruses are named defectors. The authors used the framework of the Prisoner’s Dilemma to describe the competition between these “cooperators” and “defectors.” To read more about the Prisoner’s Dilemma itself, please visit here.

Mathematically speaking, assume that the population consists of cooperator and defector viruses. Two cooperators interacting would give both a fitness of $1$. The interaction between a cooperator and a defector would result in a decrease in the fitness of the cooperator by a value of $s_1$ while the defector increases its fitness by a value of $s_2$. When two defectors interact, they both decrease their fitness by $c$. If $(1-c)\textless (1-s_1)$, a polymorphic population composed of cooperators and defectors would evolve. If $(1-c)\textgreater(1-s_1)$, the population will evolve to be completely composed of defectors, hence representing a Prisoner’s Dilemma. (In the Prisoner’s Dilemma, the Nash Equilibrium is to defect. Thus, the population should naturally evolve towards defectors.) Through various experimental methods described in more detail in the paper itself, a higher payoff is afforded to a defector in an interaction between defectors (a mutant clone named $\phi$H2) than to the cooperator in an interaction between a defector and the cooperator (the ancestor to the mutant clone, named $\phi$6).

Thus, a conclusion drawn by the study is that natural selection does not always lead to a fitness increase. (A population of cooperators would obviously have greater fitness, but the phage population evolves towards defectors.)