In this paper, we address the challenge of Nash equilibrium (NE) seeking in
non-cooperative convex games with partial-decision information. We propose a
distributed algorithm, where each agent refines its strategy through
projected-gradient steps and an averaging procedure. Each agent uses estimates
of competitors' actions obtained solely from local neighbor interactions, in a
directed communication network. Unlike previous approaches that rely on
(strong) monotonicity assumptions, this work establishes the convergence
towards a NE under a diagonal dominance property of the pseudo-gradient
mapping, that can be checked locally by the agents. Further, this condition is
physically interpretable and of relevance for many applications, as it suggests
that an agent's objective function is primarily influenced by its individual
strategic decisions, rather than by the actions of its competitors. In virtue
of a novel block-infinity norm convergence argument, we provide explicit bounds
for constant step-size that are independent of the communication structure, and
can be computed in a totally decentralized way. Numerical simulations on an
optical network's power control problem validate the algorithm's effectiveness