Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. Wh...

We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant one, where players are averse to risks. We assume that individuals play with randomly chosen opponents (they do not play against average strategies as in the s...

Evolutionary game theory has grown into an active area of research that bridges concepts from biology, evolution, nonlinear dynamics, and game theory. The mechanisms necessary to conduct an evolutionary analysis of games are presented. Relations between evolutionary stable strategies and Nash equilibria are considered. Replicator dynamics are developed and applied to three relevant games. The a...

We consider a version of the N-player snowdrift game in which payoffs obtained by players are delayed. The delay is shown to lead Hopf bifurcation with an associated critical value time replicator dynamics. For delays larger than delay, dynamics oscillate around equilibrium instead asymptotically approaching it. dependence this on parameters determined. After developing analysis for 2-player ga...

The purpose of the course is to study several dynamics generated by strategic interactions in games. Among the topics are adaptive dynamics in evolutionary game theory, robust procedures for on-line algorithms and stochastic approximation. 1. Fictitious play Discrete time Continuous time and best reply dynamics 2. Replicator dynamics n populations One population Evolutionary Stable Strategies 3...