Effect of reputation-based heterogeneous investment on cooperation in spatial public goods game

Cooperation that emerges in the situation of multi-person social dilemma has attracted intensive interest and been analyzed under the widely used public goods game (PGG) model within the framework of evolutionary game theory. Different from the original version of spatial PGG that investments are even for all the groups, in this work, a heterogeneous investment model is present by the real observation that an individual would make a rigorous judgment on to what extent they will cooperate based on the reputation condition among the group. In the model, the investors’ investment amounts to different groups are non-uniform and dynamically modified. Once all of the remaining members’ reputation values inside the group reach the corresponding threshold, the investor will completely invest one unit to the group without hesitation; otherwise, the incomplete amounts involving the basic part and the extra part will instead of the complete one. Considering that different reputation evaluation criteria exist in reality, two different threshold situations including the subjective and objective reputation threshold are considered. Simulation results show that the heterogeneous investments based on the two situations are efficient for the promotion of cooperation as well as the improvement of the whole system's average payoffs. Moreover, compared with the simple subjective threshold or the fixed objective threshold, the cooperation level can be enhanced in the mixed rule, in which cooperators can utilize the maximum value among the two kinds of reputation threshold as the judgment basis for their investment decisions. The current work is conducive to better understand the effect of reputation-based heterogeneity investment on the persistence and emergence of cooperation in real-world systems.