Optimality of Decentralized Symmetric Policies for Stochastic Teams with Mean-Field Information Sharing

We study a class of stochastic exchangeable teams comprising a finite number of decision makers (DMs) as well as their mean-field limits involving infinite numbers of DMs. In the finite population regime, we study exchangeable teams under the centralized information structure (IS). For the infinite population setting, we study exchangeable teams under the decentralized mean-field information sharing. The paper makes the following main contributions: i) For finite population exchangeable teams, we establish the existence of a randomized optimal policy that is exchangeable (permutation invariant) and Markovian. This optimal policy is obtained via value iterations for an equivalent measure-valued controlled Markov decision problem (MDP); ii) We show that a sequence of exchangeable optimal policies for a finite population setting converges to a conditionally symmetric (identical), independent, and decentralized randomized policy for the infinite population problem. This result establishes the existence of a symmetric, independent, decentralized optimal randomized policy for the infinite population problem. Additionally, it proves the optimality of the limiting measure-valued MDP for the representative DM; iii) Finally, we show that symmetric, independent, decentralized optimal randomized policies are approximately optimal for the corresponding finite-population team with a large number of DMs under the centralized IS.