Risk of collective failure provides an escape from the tragedy of the commons, Francisco C. Santos & Jorge M. Pacheco, PNAS,

Proceedings of the National Academy of Sciences, 108(26) (2011) 10421-10425; published online before print June 9, 2011; doi: 10.1073/pnas.1015648108

Risk of collective failure provides an escape from the tragedy of the commons

1. Francisco C. Santos^a,^b and 
2. Jorge M. Pacheco^b,^c,¹

1. ^aDepartamento de Informática and Centro de Inteligência Artificial, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal;
2. ^bApplications of Theoretical Physics Group, Centro de Matemática e Aplicações Fundamentais, Instituto de Investigação Interdisciplinar, P-1649-003 Lisbon Codex, Portugal; and
3. ^cDepartamento de Matemática e Aplicações, Universidade do Minho, 4710-057 Braga, Portugal

1. Edited by Simon A. Levin, Princeton University, Princeton, NJ, and approved May 11, 2011 (received for review October 18, 2010)

Abstract

From group hunting to global warming, how to deal with collective action may be formulated in terms of a public goods game of cooperation. In most cases, contributions depend on the risk of future losses. Here, we introduce an evolutionary dynamics approach to a broad class of cooperation problems in which attempting to minimize future losses turns the risk of failure into a central issue in individual decisions. We find that decisions within small groups under high risk and stringent requirements to success significantly raise the chances of coordinating actions and escaping the tragedy of the commons. We also offer insights on the scale at which public goods problems of cooperation are best solved. Instead of large-scale endeavors involving most of the population, which as we argue, may be counterproductive to achieve cooperation, the joint combination of local agreements within groups that are small compared with the population at risk is prone to significantly raise the probability of success. In addition, our model predicts that, if one takes into consideration that groups of different sizes are interwoven in complex networks of contacts, the chances for global coordination in an overall cooperating state are further enhanced.

http://www.pnas.org/content/108/26/10421.abstract