In this paper, we consider a class of infinite-horizon discrete-time linear quadratic N-person games, in which one of the players lacks complete information about the game. With the assumptions of a perfect state information pattern and steady state feedback strategies, we convert the original game problem into a multivariable adaptive control problem by making use of the concept of fictitious play and the scheme of adaptive control. For the proposed adjustment procedure, we prove that each element of the estimates converges to its corresponding true value under the condition of persistent excitation. We also carry out a sensitivity analysis of performance indices with respect to the embedded unknowns by using multiple models.