  Sensor network localization (SNL) problems require determining the physical
coordinates of all sensors in a network. This process relies on the global
coordinates of anchors and the available measurements between non-anchor and
anchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally
optimal solution to SNL is challenging, as well as implementing corresponding
algorithms. In this paper, we formulate a non-convex multi-player potential
game for a generic SNL problem to investigate the identification condition of
the global Nash equilibrium (NE) therein, where the global NE represents the
global solution of SNL. We employ canonical duality theory to transform the
non-convex game into a complementary dual problem. Then we develop a
conjugation-based algorithm to compute the stationary points of the
complementary dual problem. On this basis, we show an identification condition
of the global NE: the stationary point of the proposed algorithm satisfies a
duality relation. Finally, simulation results are provided to validate the
effectiveness of the theoretical results.
