The paper by J. Maynard Smith discusses the evolution of behavior patterns in animal conflicts using game theory models. It extends the arguments from Maynard Smith & Price (1973) that ritualized behavior can evolve through individual selection. The concept of an evolutionarily stable strategy (ESS) is introduced, and two types of ritualized contests—“tournaments” and “displays”—are distinguished. Displays, where victory goes to the contestant who continues longer, are analyzed in detail. The paper draws three main conclusions: the duration of contests should vary, individuals should display with constant intensity, and initial asymmetry in contests can be used to settle them, even if it is irrelevant to the outcome of a prolonged conflict. The introduction highlights the limitations of traditional models of evolution, which often assume constant fitnesses or environmental changes. The paper focuses on characteristics that affect survival or reproduction of relatives, or fitness depends on the presence of other genotypes. Hamilton (1964) and Trivers (1972) proposed group selection and kin selection, while Maynard Smith & Price (1973) introduced frequency-dependent selection. Game theory is applied to animal contests, where the utility of outcomes is measured by their contribution to reproductive success. An ESS is defined as a strategy that, when played against itself, has a higher expected utility than any other strategy played against it. The paper demonstrates that no pure strategy is an ESS but identifies a mixed strategy that is stable. This strategy involves a random distribution of display durations, which is shown to be evolutionarily stable. The paper also explores whether contestants should convey information about their intentions. It concludes that conveying information is not advantageous, as it would be easier for opponents to predict and counter these signals. The paper suggests that contests with initial asymmetries, such as first arrival, can be settled using these asymmetries, even if they do not influence the outcome. Finally, the appendix by John Haigh discusses the existence of ESSs in games with multiple pure strategies, proving that no ESS exists for certain non-trivial matrices and providing conditions under which an ESS can be found.The paper by J. Maynard Smith discusses the evolution of behavior patterns in animal conflicts using game theory models. It extends the arguments from Maynard Smith & Price (1973) that ritualized behavior can evolve through individual selection. The concept of an evolutionarily stable strategy (ESS) is introduced, and two types of ritualized contests—“tournaments” and “displays”—are distinguished. Displays, where victory goes to the contestant who continues longer, are analyzed in detail. The paper draws three main conclusions: the duration of contests should vary, individuals should display with constant intensity, and initial asymmetry in contests can be used to settle them, even if it is irrelevant to the outcome of a prolonged conflict. The introduction highlights the limitations of traditional models of evolution, which often assume constant fitnesses or environmental changes. The paper focuses on characteristics that affect survival or reproduction of relatives, or fitness depends on the presence of other genotypes. Hamilton (1964) and Trivers (1972) proposed group selection and kin selection, while Maynard Smith & Price (1973) introduced frequency-dependent selection. Game theory is applied to animal contests, where the utility of outcomes is measured by their contribution to reproductive success. An ESS is defined as a strategy that, when played against itself, has a higher expected utility than any other strategy played against it. The paper demonstrates that no pure strategy is an ESS but identifies a mixed strategy that is stable. This strategy involves a random distribution of display durations, which is shown to be evolutionarily stable. The paper also explores whether contestants should convey information about their intentions. It concludes that conveying information is not advantageous, as it would be easier for opponents to predict and counter these signals. The paper suggests that contests with initial asymmetries, such as first arrival, can be settled using these asymmetries, even if they do not influence the outcome. Finally, the appendix by John Haigh discusses the existence of ESSs in games with multiple pure strategies, proving that no ESS exists for certain non-trivial matrices and providing conditions under which an ESS can be found.