  In this paper, we aim to develop distributed continuous-time algorithms over
directed graphs to seek the Nash equilibrium in a noncooperative game.
Motivated by the recent consensus-based designs, we present a distributed
algorithm with a proportional gain for weight-balanced directed graphs. By
further embedding a distributed estimator of the left eigenvector associated
with zero eigenvalue of the graph Laplacian, we extend it to the case with
arbitrary strongly connected directed graphs having possible unbalanced
weights. In both cases, the Nash equilibrium is proven to be exactly reached
with an exponential convergence rate. An example is given to illustrate the
validity of the theoretical results.
