AI 中文总结
该研究以Hebert等提出的Fisher信息成本为基础，用变分方法分析二元选择问题，得出智能体最优响应为状态S型函数的结论，契合心理测量曲线特征。
AI 中文摘要
我们研究一个二元选择问题，其中智能体在两个行动之间进行选择，其收益取决于连续状态。智能体选择投入多少精力来了解该状态，等价地，可将状态视为刺激强度，智能体付出成本以更灵敏地响应刺激。以Hebert和Woodford（2021）提出的Fisher信息成本为给定条件，我们采用变分方法分析最优的状态依赖选择规则。主要结果是，在温和条件下，智能体的最优响应是状态的S型函数，该预测与心理学和经济学实验文献中广泛记录的心理测量曲线响应特征一致。
英文摘要
We study a binary choice problem in which an agent chooses between two actions whose payoff depends on a continuous state. The agent chooses how much effort to invest in learning about the state. Equivalently, we can think of the state as the strength of a stimulus, with the agent exerting costly effort to be more responsive to it. Taking as given the Fisher information cost introduced by Hebert and Woodford (2021), we analyze the optimal state-dependent choice rule using a variational approach. The main result is that agents' optimal response is an S-shaped function of the state under mild conditions. This prediction is aligned with the widely documented psychometric curve response profile observed in the experimental literature in psychology and economics.
