Evolutionary game dynamics for collective decision making in structured and unstructured environments

For a large population of players we consider a collective decision making process with three possible choices: option A or B or no option. The more popular option is more likely to be chosen by uncommitted players and cross-inhibitory signals can be sent to attract players committed to a different option. This model originates in the context of honeybees swarms, and we generalise it to accommodate other applications such as duopolistic competition and opinion dynamics. The first contribution is an evolutionary game model and a corresponding new game dynamics called expected gain pairwise comparison dynamics explaining how the strategic behaviour of the players may lead to deadlocks or consensus. The second contribution is the study of equilibrium points and stability in the case of symmetric or asymmetric cross-inhibitory signals. The third contribution is the extension of the results to the case of structured environment in which the players are modelled via a complex network with heterogeneous connectivity.