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Competitive cognition dynamics are widespread in modern society, especially with the rise of information-technology ecosystem. While previous works mainly focus on internal interactions among individuals, the impacts of the external public opinion environment remain unknown. Here, we propose a heuristic model based on co-evolutionary game theory to study the feedback-evolving dynamics of competitive cognitions and the environment. First, we show co-evolutionary trajectories of strategy-environment system under all possible circumstances. Of particular interest, we unveil the detailed dynamical patterns under the existence of an interior saddle point. In this situation, two stable states coexist in the system and both cognitions have a chance to win. We highlight the emergence of bifurcation phenomena, indicating that the final evolutionary outcome is sensitive to initial conditions. Further, the attraction basins of two stable states are not only influenced by the position of the interior saddle point but also affected by the relative speed of environmental feedbacks.

Co-evolutionary Game Dynamics of Competitive Cognitions and Public Opinion Environment