Optimal foraging theory has been criticized for underestimating patch exploitation time. However, proper modeling of costs not only answers these criticisms, but it also explains apparently irrational behaviors like the sunk-cost effect. When a forager is sure to experience high initial costs repeatedly, the forager should devote more time to exploitation than searching in order to minimize the accumulation of said costs. Thus, increased recognition or reconnaissance costs lead to increased exploitation times in order to reduce the frequency of future costs, and this result can be used to explain paradoxical human preference for higher costs. In fact, this result also provides an explanation for how continuing a very costly task indefinitely provides the optimal long-term rate of gain; the entry cost of each new task is so great that the forager avoids ever returning to search. In general, apparently irrational decisions may be optimal when considering the lifetime of a forager within a larger system.
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Here, to be consistent with Arkes and Blumer (1985), we do not allow encounters to be ignored, and so initial costs are forced and the pure patch model predicts the optimal behavior. The combined prey–patch model better fits reality as ticket purchasing opportunities can be ignored.
If the experimenters allowed for encounters to be ignored (i.e., if participants could choose to not purchase a ticket), movies with zero commitment times would also have zero ticket sales.
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We thank Thomas A. Waite for his helpful insights and instruction and Ian M. Hamilton for his comments on this paper. We also thank two anonymous referees for their help in improving this paper. Additionally, the comments of three anonymous reviewers on a related submission have also been influential in the presentation of this work.
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Pavlic, T.P., Passino, K.M. The Sunk-cost Effect as an Optimal Rate-maximizing Behavior. Acta Biotheor 59, 53–66 (2011). https://doi.org/10.1007/s10441-010-9107-8