Games and the Treatment Convexity of Cancer

Evolutionary game theory has been highly valuable in studying frequency-dependent selection and growth between competing cancer phenotypes. We study the connection between the type of competition as defined by the properties of the game, and the convexity of the treatment response. Convexity is predictive of differences in the tumor's response to treatments with identical cumulative doses delivered with different variances. We rely on a classification of 2 x 2 games based on the signs of "gains of switching," containing information about the kind of selection through the game's equilibrium structure. With the disease starting in one game class, we map the type of effects treatment may have on the game depending on dosage and the implications of treatment convexity. Treatment response is a linear function of dose if the game is a Prisoner's Dilemma, Coordination, or Harmony game and does not change game class, but may be convex or concave for Anti-Coordination games. If the game changes class, there is a rich variety in response types including convex-concave and concave-convex responses for transitions involving Anti-Coordination games, response discontinuity in case of a transition out of Coordination games, and hysteresis in case of a transition through Coordination games.