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Multi-agent decision problems are typically solved via distributed iterativealgorithms, where the agents only communicate between themselves on apeer-to-peer network. Each agent usually maintains a copy of each decisionvariable, while agreement among the local copies is enforced via consensusprotocols. Yet, each agent is often directly influenced by a small portion ofthe decision variables only: neglecting this sparsity results in redundancy,poor scalability with the network size, communication and memory overhead. Toaddress these challenges, we develop Estimation Network Design (END), aframework for the design and analysis of distributed algorithms, generalizingseveral recent approaches. END algorithms can be tuned to exploitproblem-specific sparsity structures, by optimally allocating copies of eachvariable only to a subset of agents, to improve efficiency and minimizeredundancy. We illustrate the END's potential by designing new algorithms forgeneralised Nash equilibrium (GNE) seeking under partial-decision information,that can leverage the sparsity in cost functions, constraints and aggregationvalues. Finally, we test numerically our methods on a unicast rate allocationproblem, revealing greatly reduced communication and memory costs.

The END: Estimation Network Design for games under partial-decision information