Bifurcation in non-negotiable games: a paradigm for self-organisation in cognitive systems

The interaction between two self-organising systems, each possessing two hierarchical levels, is dealt with. The communication process is pursued as a bidirectional information transfer. The criterion for the selection of the intrasystem control algorithm(s) is based on the maximisation of the 'Joint Figure of Merit' related to the long-term average of an appropriately weighted sum of conflicting terms: Probabilities of homeostases versus adequate matching with the partner.