Distributed control and game design: From strategic agents to programmable machines
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Large scale systems are forecasted to greatly impact our future lives thanks to their wide ranging applications including cooperative robotics, mobility on demand, resource allocation, supply chain management. While technological developments have paved the way for the realization of such futuristic systems, we have a limited grasp on how to coordinate the individual components to achieve the desired global objective. This thesis deals with the analysis and coordination of large scale systems without the need of a centralized authority. In the first part of this thesis, we consider non-cooperative decision making problems where each agent's objective is a function of the aggregate behavior of the population. First, we compare the performance of an equilibrium allocation with that of an optimal allocation and propose conditions under which all equilibrium allocations are efficient. Towards this goal, we prove a novel result bounding the distance between the strategies at a Nash and Wardrop equilibrium that might be of independent interest. Second, we show how to derive scalable algorithms that guide agents towards an equilibrium allocation. In the second part of this thesis, we consider large-scale cooperative problems, where a number of agents need to be allocated to a set of resources with the goal of jointly maximizing a given submodular or supermodular set function. Since this class of problems is computationally intractable, we aim at deriving tractable algorithms for attaining approximate solutions. We approach the problem from a game-theoretic perspective and ask the following: how should we design agents' utilities so that any equilibrium configuration is almost optimal? To answer this question we introduce a novel framework that allows to characterize and optimize the system performance as a function of the chosen utilities by means of a tractable linear program.
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