General stopping behaviors of naïve and non-committed sophisticated agents, with application to probability distortion

Yu-Jui Huang, Adrien Nguyen-Huu and Xun Yu Zhou
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Yu-Jui Huang: University of Colorado - Department of Applied Mathematics - University of Colorado [Boulder]
Xun Yu Zhou: Columbia University [New York]

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Abstract: We consider the problem of stopping a diffusion process with a payoff functional that renders the problem time-inconsistent. We study stopping decisions of naıve agents who reoptimize continuously in time, as well as equilibrium strategies of sophisticated agents who anticipate but lack control over their future selves' behaviors. When the state process is one dimensional and the payoff functional satisfies some regularity conditions, we prove that any equilibrium can be obtained as a fixed point of an operator. This operator represents strategic reasoning that takes the future selves' behaviors into account. We then apply the general results to the case when the agents distort probability and the diffusion process is a geometric Brownian motion. The problem is inherently time-inconsistent as the level of distortion of a same event changes over time. We show how the strategic reasoning may turn a na¨ıve agent into a sophisticated one. Moreover, we derive stopping strategies of the two types of agent for various parameter specifications of the problem, illustrating rich behaviors beyond the extreme ones such as "neverstopping" or "never-starting".

Keywords: equilibrium stopping law; naïve and sophisticated agents; probability distortion; time inconsistency; Optimal stopping; na¨ıvena¨ıve and sophisti-cated agents (search for similar items in EconPapers)
Date: 2018
New Economics Papers: this item is included in nep-gth
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Related works:
Journal Article: General stopping behaviors of naïve and noncommitted sophisticated agents, with application to probability distortion (2020)
Working Paper: General Stopping Behaviors of Naive and Non-Committed Sophisticated Agents, with Application to Probability Distortion (2019)
Working Paper: General stopping behaviors of naive and non-committed sophisticated agents, with application to probability distortion (2019)
Working Paper: General stopping behaviors of naïve and non-committed sophisticated agents, with application to probability distortion (2018)
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