The impact of peer incentives that integrate node similarity on the evolution of cooperation in complex networks

In the natural world and human society, incentives, as an important means to maintain and promote cooperation, hold indispensable significance. In this work, based on the Prisoner’s Dilemma (PD) game, we propose a new peer incentive mechanism by integrating node similarity, and conduct simulation analyses mainly in two typical complex networks, the Watts–Strogatz (WS) and Barabási–Albert (BA) networks. Considering real-world scenarios, we examine two cases in simulations where cooperators and defectors have the same incentive intensity (βC=βD) and different incentive intensities (βC≠βD). Overall, compared with the traditional model: the new mechanism has a significantly higher effect on enhancing cooperation when βC≠βD than when βC=βD; even if βC<βD, it still has the potential to enhance cooperation; the degree to which the new mechanism enhances cooperation in WS networks is higher than in BA networks. Under this new mechanism in WS networks, the range of temptation b that allows cooperators to exist continuously can reach b≤1.9, while in BA networks it can reach b<2.9, both significantly better than the ranges of b<1.3 and b<2.2 under the traditional model. Additionally, when studying the impact of βC and βD on the evolutionary results of the new model in WS networks, linear boundaries for the combination (βC,βD) are found under larger incentive sensitivity α values. When the value of (βC,βD) lies below the corresponding boundary, the new model is more likely to promote cooperation. Our study of the peer incentive mechanism can provide a strong explanation for the emergence and stability of cooperative behaviors in team cooperation, while offering a scientific basis and effective methodological guidance for solving cooperation dilemmas in real society.