  In this paper we introduce a neural network model of self-organization. This
model uses a variation of Hebb rule for updating its synaptic weights, and
surely converges to the equilibrium status. The key point of the convergence is
the update rule that constrains the total synaptic weight and this seems to
make the model stable. We investigate the role of the constraint and show that
it is the constraint that makes the model stable. For analyzing this setting,
we propose a simple probabilistic game that models the neural network and the
self-organization process. Then, we investigate the characteristics of this
game, namely, the probability that the game becomes stable and the number of
the steps it takes.
