Algorithms and mechanism design for multi-agent systems
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A scenario where multiple entities interact with a common environment to achieve individual and common goals either co-operatively or competitively can be classified as a Multi-Agent System. In this thesis, we concentrate on the situations where the agents exhibit selfish, competitive and strategic behaviour, giving rise to interesting game theoretic and optimization problems. From a computational point of view, the presence of multiple agents introduces strategic and temporal issues, apart from enhancing the difficulty of optimization. We study the following natural mathematical models of such multi-agent problems faced in practice: a) combinatorial optimization problems with multi-agent submodular cost functions, b) combinatorial auctions with partially public valuations and c) online vertex-weighted bipartite matching and single bid budgeted allocations. We provide approximation algorithms, online algorithms and hardness of approximation results for these problems.