Format

Send to

Choose Destination
Proc Natl Acad Sci U S A. 2016 Nov 22;113(47):E7518-E7525. Epub 2016 Nov 8.

An oscillating tragedy of the commons in replicator dynamics with game-environment feedback.

Author information

1
School of Biological Sciences, Georgia Institute of Technology, Atlanta, GA 30332; jsweitz@gatech.edu.
2
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332.
3
School of Biological Sciences, Georgia Institute of Technology, Atlanta, GA 30332.
4
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332.

Abstract

A tragedy of the commons occurs when individuals take actions to maximize their payoffs even as their combined payoff is less than the global maximum had the players coordinated. The originating example is that of overgrazing of common pasture lands. In game-theoretic treatments of this example, there is rarely consideration of how individual behavior subsequently modifies the commons and associated payoffs. Here, we generalize evolutionary game theory by proposing a class of replicator dynamics with feedback-evolving games in which environment-dependent payoffs and strategies coevolve. We initially apply our formulation to a system in which the payoffs favor unilateral defection and cooperation, given replete and depleted environments, respectively. Using this approach, we identify and characterize a class of dynamics: an oscillatory tragedy of the commons in which the system cycles between deplete and replete environmental states and cooperation and defection behavior states. We generalize the approach to consider outcomes given all possible rational choices of individual behavior in the depleted state when defection is favored in the replete state. In so doing, we find that incentivizing cooperation when others defect in the depleted state is necessary to avert the tragedy of the commons. In closing, we propose directions for the study of control and influence in games in which individual actions exert a substantive effect on the environmental state.

KEYWORDS:

cooperation; environmental dynamics; evolutionary games; game theory; nonlinear dynamics

PMID:
27830651
PMCID:
PMC5127343
DOI:
10.1073/pnas.1604096113
[Indexed for MEDLINE]
Free PMC Article

Supplemental Content

Full text links

Icon for HighWire Icon for PubMed Central
Loading ...
Support Center