Introduction: what is an evolutionary model Why evolutionary models? The plan of what follows Static analysis Theoretical framework Basic model Alternative scenarios: "playing the fiels" or "pairwise contests" Evolutionarily stable strategy General definition Alternative interpretations of ESS: monomorphic vs. polymorphic opulations Examples Pairwise contestt: the hawk-dove game Playing the field: the sex-ratio game ESS and refinements of nash equilibrium The existence of an ESS Asymetric contests Introduction Ex ante symmetry with ex post asymmetries Example: the hawk-dove game revisited Extensive-form contests ESS and finite populations The "spite" of an ESS An example of oligopolistic competition Evolution and cheap talk Basic dynamic analysis Introduction The replicator dynamics The discrete-time case The continuous-time case Properties of the replicator dynamics The ESS and the replicator dynamics The implicit dynamics of a monomorphic ESS ESS conditions and polymorphic stability Evolutionary dynamics and nash refinemts Some examples The hawk-dove game revisited The rock-scissors-paper game Relicator dynamics in mixed strategies The model ESS conditions and dynamic evolutionary stability Permanence and survival Definitions Necessary conditions for persistence and permanence Sufficient conditions for permanence Average behaviour in permanent systems Population genetics The prisoner's dilemma Basic (unperturbed) model Noisy dynamics Pollination and reward: an example Preliminaries The model Evolution in social environments Introduction Theoretical framework Evolutionary growth dynamics The model Monotonicity properties Some examples Dynamics of monotomic evolutionary systems Dynamic stability and nash equilibrium Set stability Long-run regularities Evolution and pay-off dominance Evolution, iterative dominance, and rationalizability General evolutionary processes Gradient monotonicity Dynamic stability and rationality Examples Trading complementarities Risky trading A simplified ultimatum game A hierarchic model of cultural evolution Stochastic evolution Introduction A simple example Theoretical framework Analysis Large matching noise Small matching noise On the role of noise in evolutionary models Extensions Continuous-time dynamics Rate of convergence and interaction pattern Global interaction Local interaction The evolution of walrasian behaviour Evolution, expectations, and drift Introduction General theoretical framework Static expectations Simultaneous contexts Co-ordination games A simple model of bargaining Multi-stage contexts Introduction Forward induction and efficient co-ordination Dynamic expectations Introduction Admissible updating rules Equilibrium volatility On the evolution of sophistication Introduction The model Narrow sophistication range Wide sophistication range Discussion Afterword Appendix Liapunov's theorem Liouville's theorem A characterization of negative-definiteness Invariant distribution: graph characterization