The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer

Abstract

Evolutionary game theory mathematically conceptualizes and analyzes biological interactions where one's fitness not only depends on one's own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather inherit their traits. Cancer can be framed as such an evolutionary game, as it is composed of cells of heterogeneous types undergoing frequency-dependent selection. In this article, we first summarize existing works where evolutionary game theory has been employed in modeling cancer and improving its treatment. Some of these game-theoretic models suggest how one could anticipate and steer cancer's eco-evolutionary dynamics into states more desirable for the patient via evolutionary therapies. Such therapies offer great promise for increasing patient survival and decreasing drug toxicity, as demonstrated by some recent studies and clinical trials. We discuss clinical relevance of the existing game-theoretic models of cancer and its treatment, and opportunities for future applications. Moreover, we discuss the developments in cancer biology that are needed to better utilize the full potential of game-theoretic models. Ultimately, we demonstrate that viewing tumors with evolutionary game theory has medically useful implications that can inform and create a lockstep between empirical findings and mathematical modeling. We suggest that cancer progression is an evolutionary competition between different cell types and therefore needs to be viewed as an evolutionary game.

Keywords: Competitive release; Eco-evolutionary dynamics; Evolutionary game theory; Genetics; Resistance; Stackelberg evolutionary games.

Fig. 1

Illustration of the difference between Stackelberg equilibrium, Nash equilibrium, and Maximum Tolerable Dose in the cancer treatment game. The solid line represents the best response of cancer cells (followers) to any possible scalar treatment level $m\in [0,1]$, the dotted line the best response of the physician (leader) to any possible resistance level $u\in [0,1]$. The panel on the left shows the cancer cells population at equilibrium, while the panel on the right shows the quality of life of the patient for the same situation. In the green area, the population of cancer cells goes extinct, while in the red area it grows above the survival threshold of the patient and as such, it is incompatible with life. The yellow area represents the situation in-between, with different levels of quality of life. Three different outcomes of the game are presented: ‘MTD’ corresponds to the case where the physician plays a fixed Maximum Tolerable Dose strategy, ’N’ corresponds to adjusting the dose according to the resistance rate of cancer cells, until a Nash equilibrium is reached, and ’S’ corresponds to anticipating the cancer cells’ resistance strategy. Adapted from [157] (Color figure online)