We study stochastic static teams with countably infinite number of decision makers (DMs), with the goal of obtaining (globally) optimal policies under a decentralized information structure. We present sufficient conditions to connect the concepts of team optimality and person-byperson optimality for static teams with countably infinite number of DMs. We show that under uniform integrability and uniform convergence conditions, an optimal policy for static teams with countably infinite number of DMs can be established as the limit of sequences of optimal policies for static teams with N DMs as N → ∞. Under the presence of a symmetry condition, we relax the conditions and this leads to optimal results for a large class of mean-field optimal team problems where the existing results have been limited to person-by-person optimality and not global optimality (under strict decentralization). In particular, we establish the optimality of symmetric (i.e., identical) policies for such problems. As a further condition, this optimality result leads to an existence result for mean-field teams. We consider a number of illustrative examples where the theory is applied to setups with either infinitely many DMs or an infinite-horizon stochastic control problem reduced to a static team.

中文翻译：

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无限玩家随机团队和平均场团队的最优解


我们研究具有可数无限数量的决策者（DM）的随机静态团队，其目标是在分散的信息结构下获得（全局）最优策略。我们提出了足够的条件来连接具有可数无限数量的 DM 的静态团队的团队最优性和个人最优性的概念。我们证明，在一致可积和一致收敛的条件下，具有可数无限个 DM 的静态团队的最优策略可以被建立为具有 N 个 DM 的静态团队的最优策略序列的极限，即 N → ∞。在存在对称条件的情况下，我们放宽条件，这会导致一大类平均场最优团队问题的最优结果，其中现有结果仅限于个人最优性而不是全局最优性（在严格的条件下）权力下放）。特别是，我们针对此类问题建立了对称（即相同）策略的最优性。作为进一步的条件，这种最优性结果导致平均场团队的存在结果。我们考虑了许多说明性示例，其中该理论应用于具有无限多个 DM 的设置或简化为静态团队的无限范围随机控制问题。