Learning to coordinate in a complex and non-stationary world

Details Learning to coordinate in a complex and non-stationary world Learning to coordinate in a complex and non-stationary world

2001-05-17

arxiv.org/abs/cond-mat/0105345v1

Phys. Rev. Lett 87, 208701 (2001)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.87.208701

We study analytically and by computer simulations a complex system of adaptive agents with finite memory. Borrowing the framework of the Minority Game and using the replica formalism we show the existence of an equilibrium phase transition as a function of the ratio between the memory $\lambda$ and the learning rates $\Gamma$ of the agents. We show that, starting from a random configuration, a dynamic phase transition also exists, which prevents the system from reaching any Nash equilibria. Furthermore, in a non-stationary environment, we show by numerical simulations that agents with infinite memory play worst than others with less memory and that the dynamic transition naturally arises independently from the initial conditions.

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