On Phase Transitions to Cooperation in the Prisoner's Dilemma

Physical Review E, Vol. 81, 2010

CCSS Working Paper No.10-004

6 Pages Posted: 7 May 2010 Last revised: 2 Nov 2012

See all articles by Dirk Helbing

Dirk Helbing

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

Sergi Lozano

ETH Zürich

Date Written: May 4, 2010

Abstract

Game theory formalizes certain interactions between physical particles or between living beings in biology, sociology, and economics, and quantifies the outcomes by payoffs. The prisoner's dilemma (PD) describes situations in which it is profitable if everybody cooperates rather than defects (free-rides or cheats), but as cooperation is risky and defection is tempting, the expected outcome is defection. Nevertheless, some biological and social mechanisms can support cooperation by effectively transforming the payoffs. Here, we study the related phase transitions, which can be of first order (discontinous) or of second order (continuous), implying a variety of different routes to cooperation. After classifying the transitions into cases of equilibrium displacement, equilibrium selection, and equilibrium creation, we show that a transition to cooperation may take place even if the stationary states and the eigenvalues of the replicator equation for the PD stay unchanged. Our example is based on adaptive group pressure, which makes the payoffs dependent on the endogeneous dynamics in the population. The resulting bistability can invert the expected outcome in favor of cooperation.

Keywords: Evolution, Game Theory, Cooperation, Social and Economic Systems

Suggested Citation

Helbing, Dirk and Lozano, Sergi, On Phase Transitions to Cooperation in the Prisoner's Dilemma (May 4, 2010). Physical Review E, Vol. 81, 2010; CCSS Working Paper No.10-004. Available at SSRN: https://ssrn.com/abstract=1600091

Dirk Helbing (Contact Author)

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

Sergi Lozano

ETH Zürich ( email )

Zürichbergstrasse 18
8092 Zurich, CH-1015
Switzerland

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