Abstract
The public goods game is one of the most famous models for studying the evolution of cooperation in sizable groups. The multiplication factor in this game can characterize the investment return from the public good, which may be variable depending on the interactive environment in realistic situations. Instead of using the same universal value, here we consider that the multiplication factor in each group is updated based on the differences between the local and global interactive environments in the spatial public goods game, but meanwhile limited to within a certain range. We find that the adaptive and bounded investment returns can significantly promote cooperation. In particular, full cooperation can be achieved for high feedback strength when appropriate limitation is set for the investment return. Also, we show that the fraction of cooperators in the whole population can become larger if the lower and upper limits of the multiplication factor are increased. Furthermore, in comparison to the traditionally spatial public goods game where the multiplication factor in each group is identical and fixed, we find that cooperation can be better promoted if the multiplication factor is constrained to adjust between one and the group size in our model. Our results highlight the importance of the locally adaptive and bounded investment returns for the emergence and dominance of cooperative behavior in structured populations.
Highlights
The emergence of cooperation among selfish individuals is an intensively studied problem [1,2]
We find that this public goods game (PGG) model with the adaptive and bounded investment returns can effectively enhance cooperation in spatially structured populations, and that appropriately bounded limitations of the multiplication factor can result in the best cooperation level
We start by presenting the results as obtained when the lower limit of the multiplication factor Rl is equal to the opposite number of the upper limit Ru, i.e., Ru~{Rl~Rw1
Summary
The emergence of cooperation among selfish individuals is an intensively studied problem [1,2]. The problem of cooperation is investigated by means of the game theoretical models of the prisoner’s dilemma for pairwise interactions, and more generally public goods game for groups of interacting individuals. In the classical public goods game (PGG), individuals engage in multiplayer interactions and decide simultaneously whether to contribute (cooperate) or not (defect) to a common pool. The accumulated contributions by cooperators are multiplied by a factor large than one, i.e., the so-called multiplication factor, and the resulting assets are shared among all group members irrespective of their initial decision. The group is most successful if everybody cooperates, and the dilemma is caused by the selfishness of individual players
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