In contrast to game-theoretic interaction models with additive payoffs, the temporal evolution of natural and artificial systems in often governed by a multiplicative process. In evolutionary biology, these systems are studied within the general framework of fluctuating environments , where the individual entities are subject to spatio-temporal fluctuations in the environmental conditions. In these environments, evolutionary behavior may emerge that essentially differs from the one observed in standard models . The study of the evolution of cooperation in fluctuating environments typically assumes a homogeneous, well mixed population, whose constituents choose between two behavioral strategies . In this paper, we generalize these results by developing a systematic study of the cooperation dynamics in fluctuating environments under the consideration of structured, heterogeneous populations with individual entities subjected to general behavioral rules.  We find that, in the presence of environmental fluctuations, the cooperation dynamics yields the creation of network components with distinct evolutionary properties.  We utilize this result to examine the applicability of a generalized reciprocity behavioral rule in a variety of settings. We thereby show that the introduced rule leads to steady state cooperative behavior that is always greater than or equal to the one predicted by the evolutionary stability analysis of unconditional cooperation. As a consequence, the implementation of our results may go beyond explaining the evolution of cooperation. In particular, they can be directly applied in domains that deal with the development of artificial systems able to adequately mimic reality, such as reinforcement learning.
Fluctuating environments are situations where the spatio-temporal stochasticity plays a significant role in the evolutionary dynamics . The study of the evolution of cooperation in these environments typically assumes a homogeneous, well mixed population, whose constituents are endowed with identical capabilities . In this paper, we generalize these results by developing a systematic study for the cooperation dynamics in fluctuating environments under the consideration of structured, heterogeneous populations with individual entities subjected to general behavioral rules. Considering complex network topologies, and a behavioral rule based on generalized reciprocity, we perform a detailed analysis of the effect of the underlying interaction structure on the evolutionary stability of cooperation. We find that, in the presence of environmental fluctuations, the cooperation dynamics can lead to the creation of multiple network components, each with distinct evolutionary properties. This is paralleled to the freezing state in the Random Energy Model. We utilize this result to examine the applicability of our generalized reciprocity behavioral rule in a variety of settings. We thereby show that the introduced rule leads to steady state cooperative behavior that is always greater than or equal to the one predicted by the evolutionary stability analysis of unconditional cooperation. As a consequence, the implementation of our results may go beyond explaining the evolution of cooperation. In particular, they can be directly applied in domains that deal with the development of artificial systems able to adequately mimic reality, such as reinforcement learning.
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In contrast to game-theoretic interaction models with additive payoffs, the temporal evolution of natural and artificial systems in often governed by a multiplicative process. In evolutionary biology, these systems are studied within the general framework of fluctuating environments , where the individual entities are subject to
Fluctuating environments are situations where the
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fluctuations in the environmental conditions. In these environments, evolutionary behavior may emerge that essentially differs from the one observed in standard models
stochasticity plays a significant role in the evolutionary dynamics
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fluctuating
these
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choose between two behavioral strategies
are endowed with identical capabilities
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of
for
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Considering complex network topologies, and a behavioral rule based on generalized reciprocity, we perform a detailed analysis of the effect of the underlying interaction structure on the evolutionary stability of cooperation.
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yields
can lead to
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network components
multiple network components, each
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This is paralleled to the freezing state in the Random Energy Model.
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a
our