Abstract
Many socio-economic and biological processes can be modeled as systems of interacting individuals.
The behaviour of such systems can be often described within game-theoretic models.
In these lecture notes, we introduce fundamental concepts of evolutionary game theory
and review basic properties of deterministic replicator dynamics and stochastic dynamics
of finite populations. We discuss stability of equilibria in deterministic dynamics with migration,
time-delay, and in stochastic dynamics of well-mixed populations and spatial games with local interactions.
We analyze the dependence of the long-run behaviour of a population on various parameters
such as the time delay, the noise level, and the size of the population.
Key Words : evolutionary game theory, Nash equilibria,
replicator dynamics, time-delay, stochastic dynamics,
spatial games, equilibrium selection, long-run behavior,
stochastic stability, ensemble stability.
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