Article

Opinion formation and cyclic dominance in adaptive networks

11/2010;
Source: arXiv

ABSTRACT 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.

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    ABSTRACT: The dynamics of opinion formation in a society has been lately explored by statistical physicists using different agent based models. Voter and threshold mod-els, used to investigate the competition between two equivalent opinions, are among the most studied. In voter models, individuals adopt the opinion of a random part-ner, while in threshold models an opinion update occurs only when the number of partners with the opposite opinion overcomes a given threshold. In this chapter, we give a brief overview of some variants of these models on coevolving or adaptive networks, recently studied in the literature. We describe how the coupled evolution of opinions and network (coevolution) induces new macroscopic patterns, unseen in static networks, such as stable or metastable coexistence of opinions, or the frag-mentation of the network in communities. The likelihood of each of these outcomes depends on the relative speed of the opinion-spreading and network-adaptation pro-cesses. In this way, consensus of a single opinion is usually achieved when opinions spread faster than the evolution of the network, while for fast adaptation the network splits into static or sometimes dynamic communities of same-opinion individuals. We briefly report on known mean-field approaches used to describe the dynamics of these systems, and discuss about their performance and limitations.
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