MA7870 Game Dynamics

Course Details

This course aims to equip interested phd students with fundamentals of single and multipopulation game dynamics which is an active area of research with applications in Biology, Economics and Learning. The objective is to make these phd students ready to begin research in game dynamics and related areas.

N-person games: Strategy, payoff function, dominance, best response, Nash equilibrium, refinements of Nash equlibrium, symmetric two-person games.
Evolutionary stability: Evolutionarily stable strategies and characterizations, setwise evolutionary stability criteria, preplay communication, role-dependent behavior.
Replicator dynamics: Derivation and basic properties, stationary points of replicator dynamics and their stability, relations with evolutionarily stable strategy, replicator dynamics of doubly symmetric games, discrete-time version of replicator dynamics.
Other selection dynamics: General selection dynamics, replication by imitation, BNN dynamics.
Multipopulation models: Evolutionary stability criteria, standard and adjusted replicator dynamics.

Course References:

1. J. Weibull, Evolutionary Game Theory, MIT Press, 1995.
2. R. Cressman, Evolutionary Dynamics and Extensive Form Games, MIT Press, 2003.

1. W. H. Sandholm, Population Games and Evolutionary Dynamics, MIT Press, 2010.
2. J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, 1998.
3. J. Hofbauer and K. Sigmund, Evolutionary game dynamics, Bull. AMS, 40(4): 479-519, 2003.