  The generalization of the problem of adaptive competition, known as the
minority game, to the case of $K$ possible choices for each player is
addressed, and applied to a system of interacting perceptrons with input and
output units of the type of $K$-states Potts-spins. An optimal solution of this
minority game as well as the dynamic evolution of the adaptive strategies of
the players are solved analytically for a general $K$ and compared with
numerical simulations.
