We consider decentralized control of Markov decision processes and give complexity bounds on the worst-case running time for algorithms that nd optimal solutions. Generalizations of both the fullyobservable case and the partially-observable case that allow for decentralized control are described. For even two agents, the nite-horizon problems corresponding to both of these models are hard for nondeterministic exponential time. These complexity results illustrate a fundamental dierence between centralized and decentralized control of Markov decision processes. In contrast to the problems involving centralized control, the problems we consider provably do not admit polynomial-time algorithms. Furthermore, assuming EXP
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