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The formation of continuous opinion dynamics based on a gambling mechanism and its sensitivity analysis

The formation of continuous opinion dynamics is investigated based on a virtual gambling mechanism where agents fight for a limited resource. We propose a model with agents holding opinions between −1 and 1. Agents are segregated into two cliques according to the sign of their opinions. Local communication happens only when the opinion distance between corresponding agents is no larger than a pre-defined confidence threshold. Theoretical analysis regarding special cases provides a deep understanding of the roles of both the resource allocation parameter and confidence threshold in the formation of opinion dynamics. For a sparse network, the evolution of opinion dynamics is negligible in the region of low confidence threshold when the mindless agents are absent. Numerical results also imply that, in the presence of economic agents, high confidence threshold is required for apparent clustering of agents in opinion. Moreover, a consensus state is generated only when the following three conditions are satisfied simultaneously: mindless agents are absent, the resource is concentrated in one clique, and confidence threshold tends to a critical value(=1.25+2/ka; 8/3$ ?>ka>8/3, the average number of friends of individual agents). For fixed a confidence threshold and resource allocation parameter, the most chaotic steady state of the dynamics happens when the fraction of mindless agents is about 0.7. It is also demonstrated that economic agents are more likely to win at gambling, compared to mindless ones. Finally, the importance of three involved parameters in establishing the uncertainty of model response is quantified in terms of Latin hypercube sampling-based sensitivity analysis.