Natural Selection Between Two Games with Applications to Game Theoretical Models of Cancer

Evolutionary game theory has been used extensively to study single games as applied to cancer, including in the context of metabolism, development of resistance, and even games between tumor and treatment. However, the situation when several games are being played against each other at the same time has not yet been investigated. Here, we describe a mathematical framework for analyzing natural selection not just between strategies, but between games. We provide theoretical analysis of situations of natural selection between the games of Prisoner's dilemma and Hawk-Dove, and demonstrate that while the dynamics of cooperators and defectors within their respective games is as expected, the distribution of games changes over time due to natural selection. We also investigate the question of mutual invasibility of games with respect to different strategies and different initial population composition. We conclude with a discussion of how the proposed approach can be applied to other games in cancer, such as motility versus stability strategies that underlie the process of metastatic invasion.