  Multi-agent decision problems are typically solved via distributed iterative
algorithms, where the agents only communicate between themselves on a
peer-to-peer network. Each agent usually maintains a copy of each decision
variable, while agreement among the local copies is enforced via consensus
protocols. Yet, each agent is often directly influenced by a small portion of
the decision variables only: neglecting this sparsity results in redundancy,
poor scalability with the network size, communication and memory overhead. To
address these challenges, we develop Estimation Network Design (END), a
framework for the design and analysis of distributed algorithms, generalizing
several recent approaches. END algorithms can be tuned to exploit
problem-specific sparsity structures, by optimally allocating copies of each
variable only to a subset of agents, to improve efficiency and minimize
redundancy. We illustrate the END's potential by designing new algorithms for
generalised Nash equilibrium (GNE) seeking under partial-decision information,
that can leverage the sparsity in cost functions, constraints and aggregation
values. Finally, we test numerically our methods on a unicast rate allocation
problem, revealing greatly reduced communication and memory costs.
