Critical transitions and Early Warning Signals in repeated Cooperation Games

Christian Hofer; Georg Jäger; Manfred Füllsack

doi:10.3934/jdg.2018014

Article Contents

2018, Volume 5, Issue 3: 223-230. Doi: 10.3934/jdg.2018014

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Critical transitions and Early Warning Signals in repeated Cooperation Games

Institute of Systems Sciences, Innovation and Sustainability Research, University of Graz, Graz, Austria

* Corresponding author: georg.jaeger@uni-graz.at
* Corresponding author: georg.jaeger@uni-graz.at

Received: October 31, 2017

Revised: January 31, 2018

Published: July 2018

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Abstract

Scanning a system's dynamics for critical transitions, i.e. sudden shifts from one system state to another, with the methodology of Early Warning Signals has been shown to yield promising results in many scientific fields. So far however, such investigations focus on aggregated system dynamics modeled with equation-based methods. In this paper the methodology of Early Warning Signals is applied to critical transitions found in the context of Cooperation Games. Since equation-based methods are not well suited to account for interactions in game theoretic settings, an agent-based model of a repeated Cooperation Game is used to generate data. We find that Early Warning Signals can be detected in agent-based simulations of such systems.

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Mathematics Subject Classification: Primary: 37M10; Secondary: 62-07, 62J10, 62M10.

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Figure 1. Time development of the rate of cooperators in a simulated Cooperation Game with a population of 1000 agents. The highlighted fraction of the time series (orange) was considered for EWS analysis.

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Figure 2. Critical transition of cooperation in a Cooperation Game. Simulated data (orange) is compared to a Hill function (blue) that is known to replicate critical transitions on an aggregated level.

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Figure 3. Results of EWS analysis for pure (left column) as well as for detrended data (right column). Apart from the kurtosis, all indicators show EWSs.

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