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Some work and some play: microscopic and macroscopic approaches to labor and leisure.

Niyogi RK, Shizgal P, Dayan P - PLoS Comput. Biol. (2014)

Bottom Line: However, averaging over the more microscopic processes that govern choices is known to pose tricky theoretical problems, and also eschews any possibility of direct contact with the neural computations involved.We develop a microscopic framework, formalized as a semi-Markov decision process with possibly stochastic choices, in which subjects approximately maximise their expected returns by making momentary commitments to one or other activity.We show macroscopic utilities that arise from microscopic ones, and demonstrate how facets such as imperfect substitutability can arise in a more straightforward microscopic manner.

View Article: PubMed Central - PubMed

Affiliation: Gatsby Computational Neuroscience Unit, University College London, London, United Kingdom.

ABSTRACT
Given the option, humans and other animals elect to distribute their time between work and leisure, rather than choosing all of one and none of the other. Traditional accounts of partial allocation have characterised behavior on a macroscopic timescale, reporting and studying the mean times spent in work or leisure. However, averaging over the more microscopic processes that govern choices is known to pose tricky theoretical problems, and also eschews any possibility of direct contact with the neural computations involved. We develop a microscopic framework, formalized as a semi-Markov decision process with possibly stochastic choices, in which subjects approximately maximise their expected returns by making momentary commitments to one or other activity. We show macroscopic utilities that arise from microscopic ones, and demonstrate how facets such as imperfect substitutability can arise in a more straightforward microscopic manner.

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Time allocation may not decrease with price for a non-linear microscopic utility of leisure.A) Upper panel: Reward rate () and lower panel: time allocation (TA) for a concave microscopic utility of leisure as a function of price. A small and a high reward intensity are shown. Reward rate decreases hyperbolically with price, eventually asymptoting. B) Leisure duration distribution as a function of price for a fixed high reward intensity (). At very long prices, as the price is increased further (eg. from 30 s to 50 s), the mode of the leisure duration distribution does not change by much although the mean does. C) Ethograms for two long prices. As price is increased, the work bouts (proportional to the price) do increase. Leisure bouts, drawn from the mode, do not change by much. Consequently, TA no longer decreases but may even increase with price (A, lower panel). This is despite the trial duration being normalised to a multiple (here 25) of the price. It is the lack of significant change in the majority of leisure durations that is critical. We normalised by the trial duration of 25  price, instead of simply normalizing by the price, to emphasise that TA is a macroscopic quantitity and to be consistent with the procedure in the example data Figure S1.
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pcbi-1003894-g007: Time allocation may not decrease with price for a non-linear microscopic utility of leisure.A) Upper panel: Reward rate () and lower panel: time allocation (TA) for a concave microscopic utility of leisure as a function of price. A small and a high reward intensity are shown. Reward rate decreases hyperbolically with price, eventually asymptoting. B) Leisure duration distribution as a function of price for a fixed high reward intensity (). At very long prices, as the price is increased further (eg. from 30 s to 50 s), the mode of the leisure duration distribution does not change by much although the mean does. C) Ethograms for two long prices. As price is increased, the work bouts (proportional to the price) do increase. Leisure bouts, drawn from the mode, do not change by much. Consequently, TA no longer decreases but may even increase with price (A, lower panel). This is despite the trial duration being normalised to a multiple (here 25) of the price. It is the lack of significant change in the majority of leisure durations that is critical. We normalised by the trial duration of 25 price, instead of simply normalizing by the price, to emphasise that TA is a macroscopic quantitity and to be consistent with the procedure in the example data Figure S1.

Mentions: However, when is non-linear, more complicated structures arise. If the price is increased while holding the reward intensity fixed, the reward rate (Eq. (2)) decreases hyperbolically and eventually asymptotes (Fig.7A). Consequently, unlike the mean, the mode of the gamma-like distribution does not substantially increase with the price (see Figs.3C and 7B). Since the mode determines the duration of the majority of leisure bouts, these do not increase substantially. If the subject continues to work for the entire price duration (Fig.7C), then, surprisingly from the macroscopic perspective of the generalized matching model, the total work time and thus the TA will increase, rather than decrease with the price (Figs.6B and 7A, lower panel). This prediction is readily amenable to experimental test.


Some work and some play: microscopic and macroscopic approaches to labor and leisure.

Niyogi RK, Shizgal P, Dayan P - PLoS Comput. Biol. (2014)

Time allocation may not decrease with price for a non-linear microscopic utility of leisure.A) Upper panel: Reward rate () and lower panel: time allocation (TA) for a concave microscopic utility of leisure as a function of price. A small and a high reward intensity are shown. Reward rate decreases hyperbolically with price, eventually asymptoting. B) Leisure duration distribution as a function of price for a fixed high reward intensity (). At very long prices, as the price is increased further (eg. from 30 s to 50 s), the mode of the leisure duration distribution does not change by much although the mean does. C) Ethograms for two long prices. As price is increased, the work bouts (proportional to the price) do increase. Leisure bouts, drawn from the mode, do not change by much. Consequently, TA no longer decreases but may even increase with price (A, lower panel). This is despite the trial duration being normalised to a multiple (here 25) of the price. It is the lack of significant change in the majority of leisure durations that is critical. We normalised by the trial duration of 25  price, instead of simply normalizing by the price, to emphasise that TA is a macroscopic quantitity and to be consistent with the procedure in the example data Figure S1.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4256012&req=5

pcbi-1003894-g007: Time allocation may not decrease with price for a non-linear microscopic utility of leisure.A) Upper panel: Reward rate () and lower panel: time allocation (TA) for a concave microscopic utility of leisure as a function of price. A small and a high reward intensity are shown. Reward rate decreases hyperbolically with price, eventually asymptoting. B) Leisure duration distribution as a function of price for a fixed high reward intensity (). At very long prices, as the price is increased further (eg. from 30 s to 50 s), the mode of the leisure duration distribution does not change by much although the mean does. C) Ethograms for two long prices. As price is increased, the work bouts (proportional to the price) do increase. Leisure bouts, drawn from the mode, do not change by much. Consequently, TA no longer decreases but may even increase with price (A, lower panel). This is despite the trial duration being normalised to a multiple (here 25) of the price. It is the lack of significant change in the majority of leisure durations that is critical. We normalised by the trial duration of 25 price, instead of simply normalizing by the price, to emphasise that TA is a macroscopic quantitity and to be consistent with the procedure in the example data Figure S1.
Mentions: However, when is non-linear, more complicated structures arise. If the price is increased while holding the reward intensity fixed, the reward rate (Eq. (2)) decreases hyperbolically and eventually asymptotes (Fig.7A). Consequently, unlike the mean, the mode of the gamma-like distribution does not substantially increase with the price (see Figs.3C and 7B). Since the mode determines the duration of the majority of leisure bouts, these do not increase substantially. If the subject continues to work for the entire price duration (Fig.7C), then, surprisingly from the macroscopic perspective of the generalized matching model, the total work time and thus the TA will increase, rather than decrease with the price (Figs.6B and 7A, lower panel). This prediction is readily amenable to experimental test.

Bottom Line: However, averaging over the more microscopic processes that govern choices is known to pose tricky theoretical problems, and also eschews any possibility of direct contact with the neural computations involved.We develop a microscopic framework, formalized as a semi-Markov decision process with possibly stochastic choices, in which subjects approximately maximise their expected returns by making momentary commitments to one or other activity.We show macroscopic utilities that arise from microscopic ones, and demonstrate how facets such as imperfect substitutability can arise in a more straightforward microscopic manner.

View Article: PubMed Central - PubMed

Affiliation: Gatsby Computational Neuroscience Unit, University College London, London, United Kingdom.

ABSTRACT
Given the option, humans and other animals elect to distribute their time between work and leisure, rather than choosing all of one and none of the other. Traditional accounts of partial allocation have characterised behavior on a macroscopic timescale, reporting and studying the mean times spent in work or leisure. However, averaging over the more microscopic processes that govern choices is known to pose tricky theoretical problems, and also eschews any possibility of direct contact with the neural computations involved. We develop a microscopic framework, formalized as a semi-Markov decision process with possibly stochastic choices, in which subjects approximately maximise their expected returns by making momentary commitments to one or other activity. We show macroscopic utilities that arise from microscopic ones, and demonstrate how facets such as imperfect substitutability can arise in a more straightforward microscopic manner.

Show MeSH