Swarm intelligence inspired cooperation promotion and symmetry breaking in interdependent networked game

Abstract

The evolution of a cooperative strategy on multilayer networks is arousing increasing concern. Most of the previous studies assumed that agents can only choose cooperation or defection when interacting with their partners, whereas the actual provisions in real world scenarios might not be discrete, but rather continuous. Furthermore, in evolutionary game, agents often make use of their memory which keeps the most successful strategy in the past, as well as the best current strategy gained by their directed neighbors, to find the best available strategies. Inspired by these observations, we study the impact of the particle swarm optimization (PSO) algorithm on the evolution of cooperation on interdependent networks in the continuous version of spatial prisoner’s dilemma games. Following extensive simulations of this setup, we can observe that the introduction of the PSO mechanism on the interdependent networks can promote cooperation strongly, regardless of the network coupling strength. In addition, we find that the increment of coupling strength is more suitable for the propagation of cooperation. More interestingly, we find that when the coupling strength is relatively large, a spontaneous symmetry breaking phenomenon of cooperation occurs between the interdependent networks. To interpret the symmetry breaking phenomenon, we investigate the asynchronous expansion of heterogeneous strategy couples between different networks. Since this work takes cooperation from a more elaborate perspective, we believe that it may provide a deep understanding of the evolution of cooperation in social networks.

Gradual learning supports cooperation in spatial prisoner’s dilemma game

“…In this way a strategy-neutral microscopic rule has a biased impact on the competition of strategies. We note that this observation fits nicely to the general concept when there is a non-trivial consequence of a neutral intervention on strategy evolution [46,12,47,48,49,50,51].…”

Symmetry breaking in the prisoner's dilemma on two-layer dynamic multiplex networks

“…Fixed networks also show asymmetric results with some parameter values. Previous studies have also reported symmetry breaking on static networks [40][41][42]. However, as Figure 2 shows, this result occurs only with a limited combination of parameter values and the effects are small compared to those observed with link updating.…”

“…Moreover, such disparity over networks appears not only at the individual level but also at the macroscopic level; interdependent networks show symmetry breaking by which the overall cooperation levels in each layer diverge. Thus, although the same rules may be applied across the network, the extent of cooperation enhancement can differ across layers [40][41][42].…”

Exploitation by asymmetry of information reference in coevolutionary learning in prisoner's dilemma game

“…Evolution of strategy in a single population [12][13][14][15][16][17][18][19][20][21][22][23] does not generate the difference in payoffs among the players in principle, where the strategy is selected within the same group. Evolution in multi-population [24][25][26][27][28][29] (i.e., intra-group selection of strategies by the inter-group game) and learning among multi-agent [30][31][32][33][34][35][36][37] can generate the exploitation, but so far most studies have focused only on the emergence of cooperation. Recently, the exploitation has been studied as to "symmetry" breaking of the payoffs of players [26,34], where only the game between the same class of strategies is assumed.…”