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