Dilemma solving by the coevolution of networks and strategy in a 2×2 game

A 2×2 game model implemented by a coevolution mechanism of both networks and strategy, inspired by the work of Zimmermann and Eguiluz [Phys. Rev. E72, 056118 (2005)] is established. Network adaptation is the manner in which an existing link between two agents is destroyed and how a new one is established to replace it. The strategy is defined as whether an agent offers cooperation (C) or defection (D). Both the networks and strategy are synchronously renovated in a simulation time step. A series of numerical experiments, considering various 2×2 game structures, reveals that the proposed coevolution mechanism can solve dilemmas in several game classes. The effect of solving a dilemma means mutual-cooperation reciprocity (R reciprocity), which is brought about by emerging several cooperative hub agents who have plenty of links. This effect can be primarily observed in game classes of the prisoner's dilemma and stag hunt. The coevolution mechanism, however, seems counterproductive for game classes of leader and hero, where the alternating reciprocity (ST reciprocity) is meaningful.