Abstract
We study the coevolution of quantum and classical strategies on weighted and directed random networks in the realm of the prisoner’s dilemma game. During the evolution, agents can break and rewire their links with the aim of maximizing payoffs, and they can also adjust the weights to indicate preferences, either positive or negative, towards their neighbors. The network structure itself is thus also subject to evolution. Importantly, the directionality of links does not affect the accumulation of payoffs nor the strategy transfers, but serves only to designate the owner of each particular link and with it the right to adjust the link as needed. We show that quantum strategies outperform classical strategies, and that the critical temptation to defect at which cooperative behavior can be maintained rises, if the network structure is updated frequently. Punishing neighbors by reducing the weights of their links also plays an important role in maintaining cooperation under adverse conditions. We find that the self-organization of the initially random network structure, driven by the evolutionary competition between quantum and classical strategies, leads to the spontaneous emergence of small average path length and a large clustering coefficient.
Highlights
Evolutionary games on graphs and networks as well as coevolutionary games have recently received significant attention [1,2,3,4]
If strategies evolve on a static network, a quantum strategy becomes the dominant strategy in the population from the outset, when a Prisoner’s Dilemma (PD) game is employed
How the probability of a structural update event occurring influences the evolution of quantum and classical strategies is studied first, and the results are explained in detail
Summary
Evolutionary games on graphs and networks as well as coevolutionary games have recently received significant attention [1,2,3,4]. Since the strong heterogeneity of the degree distribution of scale-free networks was identified as a key driving force behind flourishing cooperative states [31,32,33,34,35], some alternative sources of heterogeneity were investigated as potential promoters of cooperation with noticeable success (see [36]). Examples of such approaches include the introduction of preferential selection [37], asymmetry of connections [38], different teaching capabilities [39], heterogeneous influences [40], social diversity [41] as well as diversity of reproduction time scales [42]. Coevolutionary games [3] have been extensively studied, for example in the study of the coevolution of strategy and structure [43], games on networks subject to random or intentional rewiring procedures [14,44,45,46,47,48,49,50,51], prompt reactions to adverse ties [52,53], games on growing networks [54,55], and many more [49,56,57,58,59,60,61,62,63,64,65,65,66]
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