Bridging the Gap between Opinion Dynamics and Evolutionary Game Theory: Some Equivalence Results

Both opinion dynamics and evolutionary game theory have been receiving considerable attention in the control community in the last decade. In spite of this, they are generally regarded as two different fields and thus have been studied separately. It is proved in this paper that the voter model on the evolving network in the study of opinion dynamics and the Moran process on the complete network in evolutionary game theory are equivalent both in fixation probability and in limiting behavior, provided that the network evolves much faster than the opinions. These results bridge the gap between opinion dynamics and evolutionary game theory. With the aid of this bridge, we transform the in-group bias opinion dynamics on evolving networks, where individuals are likely to keep a steady relationship with those holding similar opinions, to the coordination game on the complete network; and the out-group bias opinion dynamics to the coexistence game. These equivalence results not only provide game-theoretical insights into opinion formation but also pave the way to understand fundamental concepts in game theory such as payoff and Nash equilibrium in the perspective of opinion dynamics.