Abstract
We investigate how people make choices when they are unsure about the value of the options they face and have to decide whether to choose now or wait and acquire more information first. In an experiment, we find that participants deviate from optimal information acquisition in a systematic manner. They acquire too much information (when they should only collect little) or not enough (when they should collect a lot). We show that this pattern can be explained as naturally emerging from Fechner cognitive errors. Over time participants tend to learn to approximate the optimal strategy when information is relatively costly.
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Notes
This is clearly the case when the DM can access new external information when waiting to make a choice. The framework we describe can also be used in situations where no new external information is available. In such situations, taking more time to engage in cognitive introspection can help reduce the uncertainty about the values of the different choices by matching previous memories with perceived features of the available choices (Ratcliff et al. 2016).
That is \(U(d_{t}=a;\pi _t) = \pi _{t} U_0 + (1- \pi _{t}) U_1\) if \(d_{t} = a\) and \(U(d_{t}=b;\pi _t) = \pi _{t} U_1 + (1- \pi _{t}) U_0\) if \(d_{t} = b\).
Among all the possible choices of urn compositions, we chose this one to have signals which are moderately informative. We can therefore study participants facing a flow of moderately informative signals and deciding when to stop.
Ideally, one could prefer a constant optimal threshold, but it would require an infinite horizon. Since the participants have to pay to sample signals, we provide them with a budget to do so. This budget is finite and, as a consequence, the experiment has a finite horizon and an optimal threshold which is not constant. Our analyses rely on the identification assumption that participants are not influenced by the length of the horizon as such (e.g. via some heuristic using a proportion of the horizon to decide when to stop). Note that an alternative solution would have been to vary the budget of participants across treatments to provide the same horizon. But such design implies potential wealth effect issues as a major drawback.
This choice is identical to choosing an action \(d_t \in \{a,b\}\) mirroring the state of the world.
All amounts are in Australian dollars.
It is enough to reach the expected stopping time in each treatment. Time horizons were the following: \(T=100\) in the $0.10 condition, \(T=20\) in the $0.50 condition and \(T=10\) in the $1 condition.
In the loss frame we inform the participants that they are all given $20 at the start of the session, and that correctly guessing the nature of the urn will allow them to keep this money. On the other hand, in the gain frame we tell them that if they make the right guess, they will get $20.
According to the optimal sequential sampling model, framing the payoffs as gains or losses should not matter. However, there is extensive evidence that individual behaviour substantially changes depending on whether a prospect is framed as leading to possible gains or losses (Kahneman and Tversky 1979; Wakker 2010). A simple way to introduce the idea that “losses loom larger than gains”, is to consider that when the DM faces a potential loss, the payoff V is subjectively transformed in \(\mu V\), with \(\mu >1\). Mechanically, the higher stakes push the optimal frontier outwards and make the marginal incentive to sample greater. We did not find any effect of framing. We report these analyses in “Framing effects” section of Appendix in Electronic Supplementary Material.
The results of the CRT are provided in “CRT” section of Appendix in Electronic Supplementary Material.
This has been shown to be an efficient way to allocate payment in experiments with repeated choices, see Baltussen et al. (2012).
All the Wilcoxon signed-rank tests reported are performed on subject-wise moments and bootstrapped 10,000 times
The previous analyses only made comparison between average optimal strategy and average behaviour over all the rounds.
In the $0.1, $0.50, and $1 treatments, this is equivalent to increasing the size of the sampling set by 10%, 25% and 100% respectively.
All regressions are clustered at the individual level.
The slope of the regression line is neither statistically significant for the average stopping time (\(p=0.21\)) nor for the signal intensity (\(p=0.54\)).
We did not find any significant difference in individual characteristics such as gender or CRT score on their tendency to make mistakes.
We thank a reviewer for making this very useful suggestion.
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Acknowledgements
For detailed and constructive comments we gratefully thank Martijn van den Assem, Aurélien Baillon, Sebastian Ebert, Drew Fudenberg, Changxia Ke, Martin Kocher, Morten Lau, Philipp Strack, Susan Thorp, Peter Wakker, Joel van der Weele and Leonard Wolk. We also benefited from comments by seminar and conference participants at the Economic Science Association World Meetings (Sydney), Erasmus School of Economics in Rotterdam, Monash University, University of Technology of Sydney, University of Sydney, University of Melbourne, VU Amsterdam, Griffith University, Australian Meeting of the Econometric Society (Sydney), Australian Conference of Economists (Adelaide), Econometric Society Summer School (Kyoto), Asian Meeting of the Econometric Society (Kyoto). The final version of the paper greatly benefited from insights and suggestions from two reviewers which led us to improve the main interpretation of the results. Harriet Smith provided excellent research assistance. For S. Massoni, the project has been conducted in the framework of the program FUTURE LEADER of Lorraine Université d’Excellence within the program Investissements Avenir (ANR-15-IDEX-04-LUE) operated by the French National Research Agency (ANR). The views expressed in this article are those of the authors alone.
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Descamps, A., Massoni, S. & Page, L. Learning to hesitate. Exp Econ 25, 359–383 (2022). https://doi.org/10.1007/s10683-021-09718-7
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DOI: https://doi.org/10.1007/s10683-021-09718-7