  Competitive dynamics are thought to occur in many processes of learning
involving synaptic plasticity. Here we show, in a game theory-inspired model of
synaptic interactions, that the competition between synapses in their weak and
strong states gives rise to a natural framework of learning, with the
prediction of memory inherent in a timescale for `forgetting' a learned signal.
Among our main results is the prediction that memory is optimized if the weak
synapses are really weak, and the strong synapses are really strong. Our work
admits of many extensions and possible experiments to test its validity, and in
particular might complement an existing model of reaching, which has strong
experimental support.
