Distributed Fictitious Play for Multi-Agent Systems with Uncertainty
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© 2016 IEEE. We consider a networked multi-agent system in which agents' actions and an unknown state of the environment affect the global well-being of the system. Agents have different and time varying beliefs on the state. As a consequence, when an agent chooses an action to execute, it is important for it to reason about what the beliefs of other agents may be and what are the consequent actions that other agents may take. We propose a decentralized solution based on the construction of empirical histograms of past actions using shared empirical histograms by neighboring agents and the use of best responses to the utility expectation with respect to the constructed histograms and the state belief. This algorithmic behavior is a variation of the fictitious play algorithm and is shown to be asymptotically optimal in the sense that if agents move towards a common belief on the state fast enough, their behavior is a Nash equilibrium of the game with the utility given by the expectation of the global objective with respect to the common belief. We numerically analyze the algorithm in a target covering game.
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