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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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Micro SMDP model, microscopic utilities of leisure and policies.A) The infinite horizon Micro semi-Markov decision process (Micro-SMDP). States are characterised by whether they are pre- or post-reward. Subjects choose not only whether to work or to engage in leisure, but also for how long to do so. For simplicity, we assume that a subject pre-commits to working for the entire price duration when it works. Then it receives a reward of reward intensity  and transitions to the post-reward state. In the post-reward state, by choosing to engage in leisure for a duration , it gains a microscopic benefit of leisure  and then returns to pre-reward state; this cycle repeats. B) Left: canonical microscopic utility of leisure functions , right: the marginal microscopic utility of leisure. For simplicity we considered linear  (blue); whose marginal utility is constant and concave (here logarithmic)  (red) whose marginal utility is always decreasing. C) -values and policies for engaging in leisure for low, medium and high payoffs. In upper panels, dashed, dotted and solid curves show: , AFR and -values, respectively.
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pcbi-1003894-g003: Micro SMDP model, microscopic utilities of leisure and policies.A) The infinite horizon Micro semi-Markov decision process (Micro-SMDP). States are characterised by whether they are pre- or post-reward. Subjects choose not only whether to work or to engage in leisure, but also for how long to do so. For simplicity, we assume that a subject pre-commits to working for the entire price duration when it works. Then it receives a reward of reward intensity and transitions to the post-reward state. In the post-reward state, by choosing to engage in leisure for a duration , it gains a microscopic benefit of leisure and then returns to pre-reward state; this cycle repeats. B) Left: canonical microscopic utility of leisure functions , right: the marginal microscopic utility of leisure. For simplicity we considered linear (blue); whose marginal utility is constant and concave (here logarithmic) (red) whose marginal utility is always decreasing. C) -values and policies for engaging in leisure for low, medium and high payoffs. In upper panels, dashed, dotted and solid curves show: , AFR and -values, respectively.

Mentions: Labor supply theory and generalized matching average over the temporal topography shown in Fig.S1C). By contrast, we follow [10], [18], [19] in formulating a so-called micro Semi-Markov Decision Process (SMDP) [20], [21] (Fig. 3A) with actions, states, and utilities, for which policies (i.e., the stochastic choices of actions at states) are quantified by the average reward per unit time accrued over the long run. We formulated the general normative, microscopic theoretical framework in [10]. Here we delineate a simplified model pertinent to the partial allocation problem.


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

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

Micro SMDP model, microscopic utilities of leisure and policies.A) The infinite horizon Micro semi-Markov decision process (Micro-SMDP). States are characterised by whether they are pre- or post-reward. Subjects choose not only whether to work or to engage in leisure, but also for how long to do so. For simplicity, we assume that a subject pre-commits to working for the entire price duration when it works. Then it receives a reward of reward intensity  and transitions to the post-reward state. In the post-reward state, by choosing to engage in leisure for a duration , it gains a microscopic benefit of leisure  and then returns to pre-reward state; this cycle repeats. B) Left: canonical microscopic utility of leisure functions , right: the marginal microscopic utility of leisure. For simplicity we considered linear  (blue); whose marginal utility is constant and concave (here logarithmic)  (red) whose marginal utility is always decreasing. C) -values and policies for engaging in leisure for low, medium and high payoffs. In upper panels, dashed, dotted and solid curves show: , AFR and -values, respectively.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4256012&req=5

pcbi-1003894-g003: Micro SMDP model, microscopic utilities of leisure and policies.A) The infinite horizon Micro semi-Markov decision process (Micro-SMDP). States are characterised by whether they are pre- or post-reward. Subjects choose not only whether to work or to engage in leisure, but also for how long to do so. For simplicity, we assume that a subject pre-commits to working for the entire price duration when it works. Then it receives a reward of reward intensity and transitions to the post-reward state. In the post-reward state, by choosing to engage in leisure for a duration , it gains a microscopic benefit of leisure and then returns to pre-reward state; this cycle repeats. B) Left: canonical microscopic utility of leisure functions , right: the marginal microscopic utility of leisure. For simplicity we considered linear (blue); whose marginal utility is constant and concave (here logarithmic) (red) whose marginal utility is always decreasing. C) -values and policies for engaging in leisure for low, medium and high payoffs. In upper panels, dashed, dotted and solid curves show: , AFR and -values, respectively.
Mentions: Labor supply theory and generalized matching average over the temporal topography shown in Fig.S1C). By contrast, we follow [10], [18], [19] in formulating a so-called micro Semi-Markov Decision Process (SMDP) [20], [21] (Fig. 3A) with actions, states, and utilities, for which policies (i.e., the stochastic choices of actions at states) are quantified by the average reward per unit time accrued over the long run. We formulated the general normative, microscopic theoretical framework in [10]. Here we delineate a simplified model pertinent to the partial allocation problem.

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