Abstract
In the previous chapter, we modeled and studied the process of natural selection between all possible mixed strategies in classical two-player two-strategy games. In this chapter, we describe a mathematical framework for analyzing natural selection not only between strategies but also between games. We provide theoretical analysis of natural selection between the games of prisoner's dilemma (PD) and Hawk-Dove (HD) and demonstrate that while the dynamics of cooperators and defectors within their respective games are 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 compositions. 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. This Chapter is based on (Kareva and Karev, 2019).
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