Several scenarios of interacting neural networks which are trained either in an identical or in a competitive way are solved analytically. In the case of identical training each perceptron receives the output of its neighbour. The symmetry of the stationary state as well as the sensitivity to the used training algorithm are investigated. Two competitive perceptrons trained on mutually exclusive learning aims and a perceptron which is trained on the opposite of its own output are examined analytically. An ensemble of competitive perceptrons is used as decision-making algorithms in a model of a closed market (El Farol Bar problem or Minority Game); each network is trained on the history of minority decisions. This ensemble of perceptrons relaxes to a stationary state whose performance can be better than random.

29 pages, 10 figures