How Individuals Learn to Take Turns: Emergence of Alternating Cooperation in a Congestion Game and the Prisoner's Dilemma

Advances in Complex Systems, Vol. 8, pp. 87-116

28 Pages Posted: 15 Apr 2005  

Dirk Helbing

ETH Zürich - Department of Humanities, Social and Political Sciences (GESS)

Martin Schoenhof

Dresden University of Technology - Institute for Transport and Economics

Hans-Ulrich Stark

Dresden University of Technology - Institute for Transport and Economics

Janusz Holyst

Warsaw University of Technology - Faculty of Physics; Warsaw University of Technology - Centre of Excellence for Complex Systems Research

Abstract

In many social dilemmas, individuals tend to generate a situation with low payoffs instead of a system optimum (tragedy of the commons). Is the routing of traffic a similar problem? In order to address this question, we present experimental results on humans playing a route choice game in a computer laboratory, which allow one to study decision behavior in repeated games beyond the Prisoner's Dilemma. We will focus on whether individuals manage to find a cooperative and fair solution compatible with the system-optimal road usage. We find that individuals tend towards a user equilibrium with equal travel times in the beginning. However, after many iterations, they often establish a coherent oscillatory behavior, as taking turns performs better than applying pure or mixed strategies. The resulting behavior is fair and compatible with system-optimal road usage. In spite of the complex dynamics leading to coordinated oscillations, we have identified mathematical relationships quantifying the observed transition process. Our main experimental discoveries for 2- and 4-person games can be explained with a novel reinforcement learning model for an arbitrary number of persons, which is based on past experience and trial-and-error behavior. Gains in the average payoff seem to be an important driving force for the innovation of time-dependent response patterns, i.e. the evolution of more complex strategies. Our findings are relevant for decision support systems and routing in traffic or data networks.

Keywords: Game theory, reinforcement learning, multi-agent simulation

JEL Classification: C72, C73, C92, C91

Suggested Citation

Helbing, Dirk and Schoenhof, Martin and Stark, Hans-Ulrich and Holyst, Janusz, How Individuals Learn to Take Turns: Emergence of Alternating Cooperation in a Congestion Game and the Prisoner's Dilemma. Advances in Complex Systems, Vol. 8, pp. 87-116. Available at SSRN: https://ssrn.com/abstract=691801

Dirk Helbing

ETH Zürich - Department of Humanities, Social and Political Sciences (GESS) ( email )

ETH Zurich - Swiss Federal Institute of Technology
Clausiusstrasse 50
Zurich, 8092
Switzerland

HOME PAGE: http://www.coss.ethz.ch

Martin Schoenhof (Contact Author)

Dresden University of Technology - Institute for Transport and Economics ( email )

Mommsenstrasse 13
D-01062 Dresden
Germany
+49/0 351 463-36721 (Phone)
+49/0 351 463-36809 (Fax)

Hans-Ulrich Stark

Dresden University of Technology - Institute for Transport and Economics ( email )

Mommsenstrasse 13
D-01062 Dresden
Germany

Janusz Holyst

Warsaw University of Technology - Faculty of Physics ( email )

Koszykowa 75
Warsaw, PL-00-662
Poland

Warsaw University of Technology - Centre of Excellence for Complex Systems Research ( email )

75 Koszykowa
Warsaw, PL-00-662
Poland

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