Introduction: Adami, Schossau, and Hintze  present a review of evolutionary game theory where they apply agent based modeling, which goes beyond the conventional approach that is based on game theoretical analysis of Maynard–Smith games or on the dynamical systems approach of game dynamics. In the focus of evolutionary games are binary contests: Two players invest in a contest and receive payoffs depending on the strategies they were choosing. Whereas human players in traditional game theory are commonly assumed to be free in their choice of strategies, a genetic component of animal behavior is the link between animal contests and evolution in Maynard–Smith games. The players choose from inherited or at least partially inherited distributions of strategies. Game dynamics converts the discrete investment versus payoff relations into dynamical systems, in particular into differential equation, which resemble the conventional equations of population genetics and accordingly refer to infinite populations. The equations of game dynamics provide a useful link between evolutionary games in the game theoretic context and theoretical population genetics as developed by Fisher, Haldane, and Wright. Emphasis is laid here on mutation that is understood as the ultimate long-time driving force of evolution and an attempt is made to shed light on the origin of mutations in Maynard–Smith games, in population genetics, and in molecular evolution. Problems are highlighted that prevent from success of the analytical approach in case of models combining frequency dependent fitness and mutation.