Econ Papers Daily / 期刊论文
计算与学习低维交互下的平稳平均场均衡：算法与应用
Computing and Learning Stationary Mean Field Equilibria with Low-Dimensional Interactions: Algorithms and Applications
摘要
Mean field equilibrium (MFE) has emerged as a computationally tractable solution concept for large dynamic games. However, computing MFE remains challenging due to nonlinearities and the absence of contraction properties, limiting its reliability for counterfactual analysis and comparative statics. This paper studies dynamic models in which agents interact through a small number of functions of the population distribution, with particular emphasis on the scalar case. Such low-dimensional interactions naturally arise in a wide range of applications in economics and operations. The main contribution of this paper is to introduce iterative algorithms that leverage this structure and have provide global convergence guarantees for computing and learning MFE under mild assumptions. Unlike existing approaches, our algorithms do not require monotonicity or contraction properties. We also provide model-free algorithms that learn an approximate MFE from simulation using reinforcement learning methods, without requiring prior knowledge of payoff or transition functions. Beyond computation, we establish existence of stationary MFE for non-compact state spaces. For scalar interactions, we also derive analytical comparative statics without requiring monotonicity of the equilibrium mapping. We apply our methods to classical models of dynamic competition, including capacity competition; to heterogeneous-agent macroeconomic models; and to models motivated by online marketplaces and learning, including inventory competition, ridesharing, and social learning. The applications illustrate how changes in market parameters affect equilibrium outcomes and how the algorithms can be used for reliable counterfactual analysis.
中文摘要
平均场均衡（MFE）已成为大型动态博弈中一种计算上可行的解概念。然而，由于非线性性质以及缺乏收缩性质，计算MFE仍然具有挑战性，这限制了其在反事实分析和比较静态分析中的可靠性。本文研究一类动态模型，其中主体通过 population distribution 的少数几个函数进行交互，并特别关注标量情形。这种低维交互自然出现在经济学和运筹学中的广泛应用中。本文的主要贡献是引入迭代算法，这些算法利用该结构，并在温和假设下为计算和学习MFE提供全局收敛保证。与现有方法不同，我们的算法不需要单调性或收缩性质。我们还提供了无模型算法，这些算法使用强化学习方法从模拟中学习近似MFE，而不需要关于收益函数或转移函数的先验知识。除计算之外，我们还建立了非紧状态空间下平稳MFE的存在性。对于标量交互，我们还推导了解析比较静态，而不需要均衡映射的单调性。我们将我们的方法应用于动态竞争的经典模型，包括产能竞争；应用于异质性主体宏观经济模型；以及应用于受在线市场和在线学习启发的模型，包括库存竞争、网约车和社会学习。这些应用说明了市场参数的变化如何影响均衡结果，以及这些算法如何用于可靠的反事实分析。