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Hypergraph Distributed Optimization & Decentralized Control with Applications in Economic Networks and Graphical Games https://doi.org/10.17863/CAM.115409 Papastaikoudis, Ioannis Lestas, Ioannis In this thesis we present results on the subjects of applied mathematics and economics. More specifically, our applied mathematics results focus on the use of hypergraphs instead of their graph analogue, the clique expansion graphs in the settings of distributed optimization and decentralized control. In both settings we present results where the use of hypergraphs provides a scalable and a decentralized way for consistently better convergence rate. Additionally hypergraphs provide a more compact information structure compared to their respective clique expansion graphs. We conduct all the comparisons among hypergraphs and their clique expansion graphs by means of algebraic graph theory. For our economic contributions we make use of our applied mathematics results and we provide generalizations in all aspects of economic theory in the distributed optimization and decentralized control settings for the topics of consumer theory, general equilibrium, cooperative and non-cooperative game theory, oligopolistic models and microeconometrics by utilizing network theory. University of Cambridge 2024-04-02 Thesis Doctoral Doctor of Philosophy (PhD) eng Cambridge Trust https://www.repository.cam.ac.uk/handle/1810/379257 embargo 2031-01-24 https://www.repository.cam.ac.uk/bitstreams/f45251c3-ca01-4af8-8f72-5ba1c79ae565/download ce53c8b0935fbf04a8de11b2ef6bc08d https://www.repository.cam.ac.uk/bitstreams/be32734b-e97b-417d-980b-b57b30f40c8c/download 87eda9de84448d1f82354d60eee3eb5f http://purl.org/NET/rdflicense/allrightsreserved Algebraic Graph Theory Decentralized Control Distributed Optimization Economic Networks Graphical Game Theory Hypergraphs