In the pooling and sharing mechanism of multiplicatively grown individual resources, the evolution of cooperation is uniquely determined by the physical traits of the population. If the entities in the population exhibit homogeneous traits, cooperation is always favored. However, if there is heterogeneity within the population, the evolution of cooperation is dependent on both the interaction structure and the decision making rules implemented by the entities. Here, we perform a detailed analysis on the role of the interaction structures in the evolutionary stability of cooperation in heterogeneous multiplicative environments. We utilize this analysis to examine the applicability of a simple state-based decision making 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  evolutionary stability analysis and discuss relevant implications to natural and artificial systems .
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 .
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the pooling and sharing mechanism of multiplicatively grown individual resources, the evolution of cooperation is uniquely determined by
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
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physical traits of the population. If the entities in the population exhibit homogeneous traits, cooperation is always favored. However, if there is heterogeneity within the population, the
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is dependent on both the interaction structure and the decision making rules implemented by the entities. Here, we perform a detailed analysis on the role of the interaction structures in the evolutionary stability of cooperation in heterogeneous multiplicative environments. We utilize this analysis
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
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simple state-based decision making
generalized reciprocity behavioral
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the
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and discuss relevant implications to natural and artificial systems
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