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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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Microscopic choices yield macroscopic partial allocation even with independent marginal utilities.To compare directly with labor supply theory, we derive macroscopic utility functions consistent with our assumed microscopic utiities. Curves show indifference curves of the derived macroscopic utility function. Cool colours show order of increasing macroscopic utility. Solid black lines show different budget constraints  as  is changed. Dashed black line denotes the path through theoretically predicted optimal leisure and work combinations as  is increased. A), B) Stochastic, approximately optimal microscopic choices with linear  yields partial allocation (A) high and B) medium payoffs are shown). Inverse temperature . C) Deterministic, optimal microscopic choices with linear  yield all-or-none allocation–work all the time if . Inverse temperature . , Reward intensity,  in A),  in B) and C), price s in A-C. D) Deterministic, optimal choices with non-linear  also yields partial allocation. , ,  and price s.
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pcbi-1003894-g004: Microscopic choices yield macroscopic partial allocation even with independent marginal utilities.To compare directly with labor supply theory, we derive macroscopic utility functions consistent with our assumed microscopic utiities. Curves show indifference curves of the derived macroscopic utility function. Cool colours show order of increasing macroscopic utility. Solid black lines show different budget constraints as is changed. Dashed black line denotes the path through theoretically predicted optimal leisure and work combinations as is increased. A), B) Stochastic, approximately optimal microscopic choices with linear yields partial allocation (A) high and B) medium payoffs are shown). Inverse temperature . C) Deterministic, optimal microscopic choices with linear yield all-or-none allocation–work all the time if . Inverse temperature . , Reward intensity, in A), in B) and C), price s in A-C. D) Deterministic, optimal choices with non-linear also yields partial allocation. , , and price s.

Mentions: Its ICs have negative slopes, which, for stochastic choices (), are not constant. These changes in slope generate partial time allocations (Fig.4A,B), when a budget constraint (BC; solid black lines) is tangent to an IC. Including an appropriate (Eq. (A-14) in Text S1) enables the optimal macroscopic combination of cumulative work and leisure times to be consistent with the microscopic mean leisure duration. At the optimum, as long as , and otherwise (Eqs. (A-9), (A-10) in Text S1). Thus stochasticity replaces substitutability in generating partial allocation.


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

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

Microscopic choices yield macroscopic partial allocation even with independent marginal utilities.To compare directly with labor supply theory, we derive macroscopic utility functions consistent with our assumed microscopic utiities. Curves show indifference curves of the derived macroscopic utility function. Cool colours show order of increasing macroscopic utility. Solid black lines show different budget constraints  as  is changed. Dashed black line denotes the path through theoretically predicted optimal leisure and work combinations as  is increased. A), B) Stochastic, approximately optimal microscopic choices with linear  yields partial allocation (A) high and B) medium payoffs are shown). Inverse temperature . C) Deterministic, optimal microscopic choices with linear  yield all-or-none allocation–work all the time if . Inverse temperature . , Reward intensity,  in A),  in B) and C), price s in A-C. D) Deterministic, optimal choices with non-linear  also yields partial allocation. , ,  and price s.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003894-g004: Microscopic choices yield macroscopic partial allocation even with independent marginal utilities.To compare directly with labor supply theory, we derive macroscopic utility functions consistent with our assumed microscopic utiities. Curves show indifference curves of the derived macroscopic utility function. Cool colours show order of increasing macroscopic utility. Solid black lines show different budget constraints as is changed. Dashed black line denotes the path through theoretically predicted optimal leisure and work combinations as is increased. A), B) Stochastic, approximately optimal microscopic choices with linear yields partial allocation (A) high and B) medium payoffs are shown). Inverse temperature . C) Deterministic, optimal microscopic choices with linear yield all-or-none allocation–work all the time if . Inverse temperature . , Reward intensity, in A), in B) and C), price s in A-C. D) Deterministic, optimal choices with non-linear also yields partial allocation. , , and price s.
Mentions: Its ICs have negative slopes, which, for stochastic choices (), are not constant. These changes in slope generate partial time allocations (Fig.4A,B), when a budget constraint (BC; solid black lines) is tangent to an IC. Including an appropriate (Eq. (A-14) in Text S1) enables the optimal macroscopic combination of cumulative work and leisure times to be consistent with the microscopic mean leisure duration. At the optimum, as long as , and otherwise (Eqs. (A-9), (A-10) in Text S1). Thus stochasticity replaces substitutability in generating partial allocation.

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
Related in: MedlinePlus