Regensburg 2007 – scientific programme
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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme
AKSOE 13: Economic Models and Evolutionary Game Theory II
AKSOE 13.1: Talk
Thursday, March 29, 2007, 11:45–12:15, H8
Finite-size fluctuations and macroscopic equations in agent-based models: Mutations and extended number of strategies — Arne Traulsen1, •Jens Christian Claussen2, and Christoph Hauert1 — 1Program for Evolutionary Dynamics, Harvard — 2Institut f. Theoret. Physik & Astrophys., Univ. Kiel, Germany
Agent-based behavioral models of social or economic behaviour are widely investigated by Monte Carlo simulations as well as by differential equations. However, macroscopic stochastic equations can in quite general cases be derived from microscopic behavioral processes [1]. We point out three aspects: First, finite-size fluctuations in coevolutionary dynamics in general differ from additive white noise [2]. Second, it can be shown that the Moran process and a local update process can be identified as microscopic models leading to the adjusted and standard replicator equations, respectively [3]. As a consequence, the direction of evolutionary drift can reverse due to a finite-size effect [3]. Third, the approach can be extended to many strategies and including mutations [4]. Depending on mutation rate, population size, and location of the equilibrium points, the stationary distributions can be localized at the borders, or exhibit interior peaks. We illustrate some of these scenarios by considering neutral selection, the Prisoner's Dilemma, and the snowdrift game [4].
[1] D.Helbing, Physica A 181,29(1992); 193,241(1993); 196,546(1993) [2] J. C. Claussen & A. Traulsen, Phys. Rev.E 71, 025101 (R) (2005) [3] A. Traulsen, J. C. Claussen, C. Hauert, PRL 95, 238701 (2005) [4] A. Traulsen, J. C. Claussen, C. Hauert, PRE 74, 011901 (2006)