Neural Networks realization of searching models for Nash Equilibrium points and their application to associative memories

We propose a new mutually coupled plural Neural Networks (N.N.) modules and its application to associative memories from the view point of noncooperative game theory. First, We propose a new dynamical searching model named Parallel Steepest Descent Method with Braking operators (PSDMB) which searches the Nash Equilibrium (NE) points under [0, 1]-interval or nonnegative constraints. Second, we propose a new mutually coupled plural N.N. modules named Game Neural Networks (GNN) to realize the proposed PSDMB with quadratic objective functions. In Addition, we indicate relations between the PSDMB, the GNN and the Lotka-Volterra equation. Last, for an application of the proposed GNN, we propose two kinds of multi modular associative memories which can associate the combined patterns composed of plural partial patterns: (1) the combined patterns are stored as the NE points and robust for noisy inputs; (2) the circulative sequence of the combined patterns are stored as saddles of a heteroclinic cycle.