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

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.