Dresden 2009 – scientific programme

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AGSOE: Arbeitsgruppe Physik sozio-ökonomischer Systeme

AGSOE 12: Economic Models and Evolutionary Game Theory IV

AGSOE 12.4: Talk

Wednesday, March 25, 2009, 15:30–16:00, BAR 205

Cycles of cooperation and defection in imperfect learning — •Tobias Galla — Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M139PL, UK

In this talk we discuss the dynamics of agents learning to play a two-player game while subject to memory-loss. If players make an infinite number of observations (actions of their opponent) between adaptation events, the dynamics is deterministic and described by so-called Sato-Crutchfield equations, a modification of the standard replicator dynamics. In case of a finite number N of observations between two adaptation events, the learning dynamics becomes stochastic as the opponent's mixed strategy profile can no longer be sampled accurately.

We discuss the effects of the batch size N and the memory-loss rate for the specific example of the iterated prisoner's dilemma. The deterministic learning dynamics at non-zero memory-loss does here in general not converge to the Nash equilibrium describing full defection, but instead limit cycles or reactive fixed points can be found. The dynamics at finite batch sizes is seen to exhibit sustained stochastic oscillations between co-operation and defection, and the spectrum of these oscillations is obtained analytically within an expansion in the inverse batch size.