The communication process between two hierarchical systems each possessing two levels is dealt with. The dynamics at all levels are modelled- as finite state parametrized Markov chains. For the lower levelsQ,Q′the transitions are parametrized on control variables stemming from an underlying game, which simulates collectively all hierarchical levels belowQ, andQ′respectively. The higher levelsW, Ware modelled by semi-Markov chains with holding times following a geometrical distribution. The control parameters upon which the transition probabilities at the levolsW, W′depend are :