论文标题
在刻板计算的马尔克·马尔克夫决策过程中，伯克 - 纳什平衡存在无限空间
On Existence of Berk-Nash Equilibria in Misspecified Markov Decision Processes with Infinite Spaces
论文作者
论文摘要
在理论和经验经济学的许多领域，模型错误指定是一个关键问题。在误指出的马尔可夫决策过程的具体情况下，Esponda和Pouzo（2021）定义了伯克 - 纳什平衡的概念，并在有限状态和行动空间的环境中确立了其存在。但是，许多实质性应用（包括Esponda和Pouzo提出的三个激励示例中的两个，以及高斯和对数正态分布，以及CARA，CRRA和均值变化的偏好）涉及持续状态或动作空间，因此并不涵盖spepa-pouzo的存在。我们将Berk-Nash平衡的存在扩展到紧凑的动作空间和Sigma-Compact状态空间，并具有无界的回报功能。出现并发症之所以出现，是因为Berk-Nash平衡概念严重取决于ra碱衍生物，后者必然在有限的情况下进行界定，但通常在错误指定的连续模型中无限。这些证据依赖于非标准分析，并且相对于非标准分析在经济理论中的先前应用，它借鉴了可追溯到第二作者在马尔可夫流程的非标准表示方面可追溯的新论点。
Model misspecification is a critical issue in many areas of theoretical and empirical economics. In the specific context of misspecified Markov Decision Processes, Esponda and Pouzo (2021) defined the notion of Berk-Nash equilibrium and established its existence in the setting of finite state and action spaces. However, many substantive applications (including two of the three motivating examples presented by Esponda and Pouzo, as well as Gaussian and log-normal distributions, and CARA, CRRA and mean-variance preferences) involve continuous state or action spaces, and are thus not covered by the Esponda-Pouzo existence theorem. We extend the existence of Berk-Nash equilibrium to compact action spaces and sigma-compact state spaces, with possibly unbounded payoff functions. A complication arises because the Berk-Nash equilibrium notion depends critically on Radon-Nikodym derivatives, which are necessarily bounded in the finite case but typically unbounded in misspecified continuous models. The proofs rely on nonstandard analysis and, relative to previous applications of nonstandard analysis in economic theory, draw on novel argumentation traceable to work of the second author on nonstandard representations of Markov processes.
