Estimating Private Beliefs of Bayesian Agents Based on Observed Decisions
Estimating Private Beliefs of Bayesian Agents Based on Observed Decisions
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DOI：
10.1109/lcsys.2019.2911802
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发表时间：
2019-04
影响因子：
3
通讯作者：
Robert Mattila;Inês Lourenço;C. Rojas;V. Krishnamurthy;B. Wahlberg
中科院分区：
文献类型：
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作者：
Robert Mattila;Inês Lourenço;C. Rojas;V. Krishnamurthy;B. Wahlberg
我们考虑顺序随机决策问题，在每一个时刻，代理优化其本地效用解决随机程序，随后，宣布其决定的世界。给定这个动作，我们研究估计代理人的私人信念的问题（即，基于其私人观察，其在自然状态集合上的后验分布）。我们证明，这是可能的，以确定一组私人的信念，是一致的公共数据，利用逆优化技术。我们进一步给出了这个集合的一些有用的特征;例如，通过求解一组线性规划（在凹效用下）的紧边界。作为一个说明性的例子，我们考虑估计投资者在制度转换投资组合配置的私人信念。最后，我们的理论结果进行了说明和评估的数值模拟。
We consider sequential stochastic decision problems in which, at each time instant, an agent optimizes its local utility by solving a stochastic program and, subsequently, announces its decision to the world. Given this action, we study the problem of estimating the agent’s private belief (i.e., its posterior distribution over the set of states of nature based on its private observations). We demonstrate that it is possible to determine the set of private beliefs that are consistent with public data by leveraging techniques from inverse optimization. We further give a number of useful characterizations of this set; for example, tight bounds by solving a set of linear programs (under concave utility). As an illustrative example, we consider estimating the private belief of an investor in regime-switching portfolio allocation. Finally, our theoretical results are illustrated and evaluated in numerical simulations.