Evolutionary games are introduced as models for repeated anonymous strategic interaction. The basic idea is that actions (or behaviors) which are more "fit," given the current distribution of behaviors, tend over time to displace less fit behaviors. The paper introduces the concept of fitness functions and compatible dynamics, and illustrates their relation to previous biological models. Cone fields are used to characterize the continuous-time dynamical processes compatible with a given fitness function. The analysis focuses on dynamic steady state equilibria and their relation to the static equilibria known as NE (Nash equilibrium) and ESS (evolutionary stable state). For large classes of dynamics it is shown that all stable dynamic steady states are NE and that all NE are dynamic steady states. The biologists' ESS condition is less closely related to the dynamic equilibria. The paper concludes with a brief survey of economic applications. The paper proposes a tractable framework for evolutionary games that incorporates previous work by John Maynard Smith and his collaborators. It derives substantive results on the relation between evolutionary steady states and static equilibria of the payoff or fitness function. The paper shows that all NE are compatible dynamic equilibria and that all compatible dynamic stable equilibria are NE. The ESS are always a subset of the NE, so to the extent that Maynard Smith correctly identifies the dynamically stable equilibria in terms of his ESS criteria, he provides game theorists with an appealing refinement of NE. However, in general ESS is neither necessary nor sufficient for compatible dynamic stability. The paper discusses the differences between evolutionary games and supergames and differential games. Evolutionary games focus on the distribution of behaviors in populations rather than on the behavior of rational individuals. The paper also discusses the relationship between evolutionary games and other economic applications, such as migration processes and the analysis of bimatrix games. The paper concludes with a discussion of the implications of the results for economic applications and the need for further research.Evolutionary games are introduced as models for repeated anonymous strategic interaction. The basic idea is that actions (or behaviors) which are more "fit," given the current distribution of behaviors, tend over time to displace less fit behaviors. The paper introduces the concept of fitness functions and compatible dynamics, and illustrates their relation to previous biological models. Cone fields are used to characterize the continuous-time dynamical processes compatible with a given fitness function. The analysis focuses on dynamic steady state equilibria and their relation to the static equilibria known as NE (Nash equilibrium) and ESS (evolutionary stable state). For large classes of dynamics it is shown that all stable dynamic steady states are NE and that all NE are dynamic steady states. The biologists' ESS condition is less closely related to the dynamic equilibria. The paper concludes with a brief survey of economic applications. The paper proposes a tractable framework for evolutionary games that incorporates previous work by John Maynard Smith and his collaborators. It derives substantive results on the relation between evolutionary steady states and static equilibria of the payoff or fitness function. The paper shows that all NE are compatible dynamic equilibria and that all compatible dynamic stable equilibria are NE. The ESS are always a subset of the NE, so to the extent that Maynard Smith correctly identifies the dynamically stable equilibria in terms of his ESS criteria, he provides game theorists with an appealing refinement of NE. However, in general ESS is neither necessary nor sufficient for compatible dynamic stability. The paper discusses the differences between evolutionary games and supergames and differential games. Evolutionary games focus on the distribution of behaviors in populations rather than on the behavior of rational individuals. The paper also discusses the relationship between evolutionary games and other economic applications, such as migration processes and the analysis of bimatrix games. The paper concludes with a discussion of the implications of the results for economic applications and the need for further research.