  Existing settings of decentralized learning either require players to have
full information or the system to have certain special structure that may be
hard to check and hinder their applicability to practical systems. To overcome
this, we identify a structure that is simple to check for linear dynamical
system, where each player learns in a fully decentralized fashion to minimize
its cost. We first establish the existence of pure strategy Nash equilibria in
the resulting noncooperative game. We then conjecture that the Nash equilibrium
is unique provided that the system satisfies an additional requirement on its
structure. We also introduce a decentralized mechanism based on projected
gradient descent to have agents learn the Nash equilibrium. Simulations on a
$5$-player game validate our results.
