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The Rock-Paper-Scissors(RPS) game is a paradigmatic model for cyclicdominance in biological systems. Here we consider this game in the socialcontext of competition between opinions in a networked society. In our model,every agent has an opinion which is drawn from the three choices: rock, paperor scissors. In every timestep a link is selected randomly and the game isplayed between the nodes connected by the link. The loser either adopts theopinion of the winner or rewires the link. These rules define an adaptivenetwork on which the agent's opinions coevolve with the network topology ofsocial contacts. We show analytically and numerically that nonequilibrium phasetransitions occur as a function of the rewiring strength. The transitionsseparate four distinct phases which differ in the observed dynamics of opinionsand topology. In particular, there is one phase where the population settles toan arbitrary consensus opinion. We present a detailed analysis of thecorresponding transitions revealing an apparently paradoxial behavior. Thesystem approaches consensus states where they are unstable, whereas otherdynamics prevail when the consensus states are stable.

Opinion formation and cyclic dominance in adaptive networks