In the literature, existence of mean-field equilibria has been established for discrete-time mean field games under both the discounted cost and the average cost optimality criteria. In this paper, we provide a value iteration algorithm to compute mean-field equilibrium for both the discounted cost and the average cost criteria, whose existence proved previously. We establish that the value iteration algorithm converges to the fixed point of a mean-field equilibrium operator. Then, using this fixed point, we construct a mean-field equilibrium. In our value iteration algorithm, we use $Q$-functions instead of value functions.

中文翻译：

---

平均场博弈的值迭代算法

在文献中，已经为离散时间平均场博弈在贴现成本和平均成本最优标准下建立了平均场均衡的存在性。在本文中，我们提供了一种值迭代算法来计算贴现成本和平均成本标准的平均场均衡，其存在性先前已证明。我们确定值迭代算法收敛到平均场平衡算子的不动点。然后，使用这个不动点，我们构建了一个平均场平衡。在我们的价值迭代算法中，我们使用 $Q$-functions 而不是价值函数。