Population games provide a general model of strategic interactions among large numbers of agents; highway congestion, multilateral externalities, and natural selection are among their many applications. To model the dynamics of behavior in population games, we introduce decision protocols, which provide explicit stochastic descriptions of how individual agents make decisions. When the number of agents is large enough, the evolution of aggregate behavior can be described by solutions to ordinary differential equations. We discuss classes of population games in which these evolutionary dynamics lead to equilibrium play, we consider simple examples in which cycling and chaos can arise, and we explain how natural decision protocols can generate potent equilibrium selection results. Finally, we discuss computational experiments whose aim is to estimate the frequency of cycling and chaos in randomly chosen games.