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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 6: Economic Models and Evolutionary Game Theory I

AKSOE 6.2: Vortrag

Dienstag, 28. März 2006, 10:45–11:15, BAR 205

Statistical mechanics of random replicators and matrix games — •Tobias Galla — The Abdus Salam International Centre for Theoretical Physics Trieste, Italy

An important objective of game theory consists in the static study of Nash equilibria. Popular cases are situations in which the payoffs take matrix form, the well-known prisoner’s dilemma or the rock-scissors-paper game are simple examples.

Replicator equations on the other hand describe the dynamic evolution of self-reproducing interacting species for example in population dynamics and theoretical biology. In the context of evolutionary game theory these equations correspond to matrix games which are played repeatedly by players, who then reproduce according to their success, passing on their strategies to their children.

In this talk we will apply the methods and concepts of statistical mechanics of disordered systems to study large dynamical replicator systems with random couplings. We will give an overview over their basic phenomenological behaviour and will address different ergodic/non-ergodic phase transitions exhibited by such models. The connection between ergodicity in replicator systems, their attractors and the Nash equilibria in the corresponding games will be discussed.