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State-dependent behavioral theory and the evolution of play

ADAPTIVE BEHAVIOR 2015年第6期23卷 362-370页

作者： Grunloh, Nicholas Mangel, Marc Univ Calif Santa Cruz Grad Program Stat & Appl Math Santa Cruz CA 95064 USA Univ Calif Santa Cruz Dept Appl Math & Stat Ctr Stock Assessment Res Santa Cruz CA 95064 USA Univ Bergen Dept Biol Bergen Norway

We show how state-dependent behavioral theory, as implemented by stochastic dynamic programming can enhance our understanding of play, assuming that play is an evolutionary adaptation rather than a non-functional consequence of other processes. We first explain in generic terms the components of a state-dependent behavioral model. We then develop a state-dependent life history model on the assumption that social play is adaptive and thus focus on play's contribution toward the development of skill and how such development affects an individual's future lifetime expected reproductive success (i.e. fitness that accounts for both survival and reproduction). Although our model is not intended to capture a specific situation, a number of commonly observed phenomena emerge from the model, including that most social play is dyadic and that animals select partners that are of similar age or skill. We discuss ways of increasing the fidelity of the model by allowing injury due to play, the role of energetic reserves, handicapping, and polyadic play.

关键词： Skill development social play stochastic dynamic programming state dependence life history

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Experimental or precautionary? Adaptive management over a range of time horizons

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JOURNAL OF APPLIED ECOLOGY 2008年第1期45卷 72-81页

作者： Hauser, Cindy E. Possingham, Hugh P. Univ Melbourne Sch Bot Australian Ctr Excellence Risk Anal Melbourne Vic 3010 Australia Univ Queensland Sch Integrat Biol Ctr Ecol St Lucia Qld 4072 Australia Univ Queensland Dept Math St Lucia Qld 4072 Australia

1. Many studies of adaptive harvest management already exist in the literature, but most (if not all) use long, sometimes infinite, time horizons. Such long-term objectives provide an opportunity to manage experimentally, so that poorly understood dynamics are learned and any returns sacrificed for experimentation are repaid by improved management over the remaining time horizon. 2. However, a manager is unlikely to weight outcomes in the distant future equally against outcomes in the present. Furthermore, the most appropriate model of system dynamics may not remain constant over the time-frame required to experiment, learn and improve management. In these cases the use of discounting and/or a finite time horizon fit the manager's assumptions and goals more effectively, and the value of experimentation is likely to be diminished. 3. In this paper we construct a simple model of a hypothetical population and compare optimal passive and active adaptive harvest strategies over a range of time horizons. This allows us to determine the optimal level of experimentation for short-, medium- and long-term goals. 4. We discover that the optimal active adaptive harvest strategy may be precautionary over short to medium time horizons, rather than experimental. That is, an action with known moderate benefits is preferred over an action with uncertain but marginally larger expected benefits. This runs counter to the widespread assumption in the adaptive management literature that incorporating learning into an optimization of management will encourage experimentation. 5. Synthesis and applications. The general results of this paper have potential application to any environmental management problem where adaptive management might be applied;for example, conservation, pest control, harvesting and management of water flows. We examine adaptive management over a range of finite time horizons to reflect a variety of possible management goals and assumptions. Our simple example demonstr

关键词： decision theory harvest optimization precautionary stochastic dynamic programming

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AVERAGE OPTIMALITY IN dynamic-programming WITH GENERAL STATE-SPACE

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MATHEMATICS OF OPERATIONS RESEARCH 1993年第1期18卷 163-172页

作者： SCHAL, M Institut Für Angewandte Mathematik Universität Bonn Wegelerstrasse 6 D-5300 Bonn Germany

A Markovian decision model with general state space, compact action space, and the average cost as criterion is considered. The existence of an optimal policy is shown via an optimality inequality in terms of the minimal average cost g and a relative value function w. The existence of some w is usually shown via relative compactness in a space of real-valued functions on the state space. Here it shall be shown that one can instead do with pointwise relative compactness in the set of real numbers if one makes use of a (generalized) lower limit of functions. An application to an inventory model is given.

关键词： stochastic dynamic programming MARKOV DECISION PROCESSES AVERAGE COST DISCRETE TIME MODEL UNBOUNDED COSTS INVENTORY CONTROL MODEL

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Hierarchical production control in a stochastic N-machine flowshop with long-run average cost

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2000年第1期251卷 285-309页

作者： Sethi, SP Zhang, HQ Zhang, Q Univ Texas Sch Management Richardson TX 75083 USA Acad Sinica Inst Appl Math Beijing 100080 Peoples R China Univ Georgia Dept Math Athens GA 30602 USA

This paper presents an asymptotic analysis of stochastic manufacturing systems consisting of machines in tandem subject to breakdown and repair and facing a constant demand, as the sates of change of the machine states approach infinity. This situation gives rise to a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem converges to the long-run average cost of the limiting problem. A method of "shrinking" and "entire lifting" is introduced in order to construct the near optimal controls for the original problem by using near optimal controls of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem is established. This helps in providing an error estimate for the constructed open-loop asymptotic optimal control. (C) 2000 Academic Press.

关键词： hierarchical control manufacturing systems stochastic dynamic programming optimal control long-run average cost

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Optimizing Inventory Replenishment of Retail Fashion Products

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Manufacturing and Service Operations Management 2001年第3期3卷 230-241页

作者： Fisher, Marshall Rajaram, Kumar Raman, Ananth

We consider the problem of determining (for a short lifecycle) retail product initial and replenishment order quantities that minimize the cost of lost sales, back orders, and obsolete inventory. We model this problem as a two-stage stochastic dynamic program, propose a heuristic, establish conditions under which the heuristic finds an optimal solution, and report results of the application of our procedure at a catalog retailer. Our procedure improves on the existing method by enough to double profits. In addition, our method can be used to choose the optimal reorder time, to quantify the benefit of leadtime reduction, and to choose the best replenishment contract.

关键词： Retailing Inventory Replenishment stochastic dynamic programming Heuristics

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stochastic bycatch, informational asymmetry, and discarding

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JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT 2005年第3期49卷 463-483页

作者： Herrera, GE Bowdoin Coll Dept Econ Brunswick ME 04011 USA Woods Hole Oceanog Inst Marine Policy Ctr Woods Hole MA 02543 USA

The existing literature (i) examines bycatch and discard behavior in a static framework and (ii) treats bycatch as a deterministic process uniform across vessels. Using a dynamic representative agent model in a two-stock resource, this paper explores strategic interactions between a social planner and two groups of harvesters, one of which imposes a stochastic '' technological externality '' (bycatch) on the other. In addition to limitations on entry and the number of trips taken in each industry, three bycatch control instruments are compared to the unconstrained case: taxes, trip limits, and value-based quotas. Implementation and enforcement costs aside, taxes dominate both types of quota, and value limits outperform trip limits by eliminating one type of discarding. In simulations, relative performance depends upon variance in the bycatch process, differences in the ex vessel prices of stocks, relative efficiency of the harvester types, and fixed costs on the trip and industry margins. (c) 2004 Elsevier Inc. All rights reserved.

关键词： bioeconomic model fishery bycatch discarding instrument choice trip limits value quotas taxes stochastic dynamic programming

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Optimal eradication: when to stop looking for an invasive plant

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ECOLOGY LETTERS 2006年第7期9卷 759-766页

作者： Regan, TJ McCarthy, MA Baxter, PWJ Panetta, FD Possingham, HP Univ Queensland Ctr Ecol Sch Integrat Biol St Lucia Qld 4072 Australia Univ Melbourne Australian Res Ctr Urban Ecol Royal Bot Gardens Melbourne cl Sch Bot Melbourne Vic 3010 Australia Univ Melbourne Sch Bot Melbourne Vic 3010 Australia Dept Nat Resources & Mines Sherwood Qld 4075 Australia CRC Australian Weed Management Glen Osmond SA 5064 Australia

The notion of being sure that you have completely eradicated an invasive species is fanciful because of imperfect detection and persistent seed banks. Eradication is commonly declared either on an ad hoc basis, on notions of seed bank longevity, or on setting arbitrary thresholds of 1% or 5% confidence that the species is not present. Rather than declaring eradication at some arbitrary level of confidence, we take an economic approach in which we stop looking when the expected costs outweigh the expected benefits. We develop theory that determines the number of years of absent surveys required to minimize the net expected cost. Given detection of a species is imperfect, the optimal stopping time is a trade-off between the cost of continued surveying and the cost of escape and damage if eradication is declared too soon. A simple rule of thumb compares well to the exact optimal solution using stochastic dynamic programming. Application of the approach to the eradication programme of Helenium amarum reveals that the actual stopping time was a precautionary one given the ranges for each parameter.

关键词： decision theory detectability economic costs eradication invasive plants stochastic dynamic programming rule of thumb weed

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Optimal management of an ecosystem with an unknown threshold

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ECOLOGICAL ECONOMICS 2011年第4期70卷 627-640页

作者： Brozovic, Nicholas Schlenker, Wolfram Columbia Univ New York NY 10027 USA Univ Illinois Urbana IL 61801 USA NBER New York NY 10027 USA

We consider an ecosystem with two distinct equations of motion that are separated by a threshold value of the state variable. We find that increasing uncertainty (both uncertainty embedded in the natural system and uncertainty of the decisionmaker about the location of the threshold) can lead to nonmonotonic changes in precaution: a reduction in uncertainty can first increase and then decrease optimal precautionary activity. This nonmonotonicity can help to explain why regulators often give conflicting arguments about optimal abatement policies in the face of uncertainty. For example, some regulators argue for an immediate reduction in pollutant loading until uncertainty about the underlying process is reduced while others call for no costly reductions in pollutant loading until the same uncertainty is reduced. These statements can be consistent even if both sides agree on both economic objectives and the system dynamics, but have different priors on the uncertainty involved. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Ecosystem management Threshold stochastic dynamic programming

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A nonlinear stochastic growth model on discrete time domains

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JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS 2016年第11期22卷 1732-1746页

作者： Atici, Ferhan M. Cheng, Gang Lebedinsky, Alex Western Kentucky Univ Dept Math Bowling Green KY 42101 USA Western Kentucky Univ Dept Econ Bowling Green KY 42101 USA

In this paper, we introduce nonlinear stochastic dynamic problems on discrete time domains where events may occur at unevenly spaced time points. We define Euler equation and transversality condition for the problem. We prove that the Euler equation and the transversality condition are sufficient for the existence of the optimal solution. Next we generalize discrete time Cagan type rational expectation model to multivariate case. As an application of the main results, we obtain an explicit solution to a log-linearized nonlinear stochastic growth model.

关键词： Optimization stochastic dynamic programming rational expectations

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Soft and hard price collars in a cap-and-trade system: A comparative analysis

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JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT 2012年第2期64卷 183-198页

作者： Fell, Harrison Burtraw, Dallas Morgenstern, Richard D. Palmer, Karen L. Colorado Sch Mines Div Econ & Business Golden CO 80401 USA RFF Ctr Climate & Elect Policy Washington DC 20036 USA

We use a stochastic dynamic framework to compare price collars (price ceilings and floors) in a cap-and-trade system with uncertainty in the level of baseline emissions and costs. We consider soft collars, which provide limited volume of additional emission allowances (a reserve) at the price ceiling, and hard collars, which provide an unlimited supply of additional allowances, thereby preventing allowance prices from exceeding the price ceiling. Conversely, allowances are removed from the market if prices fall to the floor. We find that increasing the size of the reserve strictly lowers expected net present values of compliance costs;however, there is a diminishing effect as the allowance reserve is expanded. Most of the expected cost savings are achieved with a modest reserve. Consequently, a rather limited soft price collar could provide considerable assurance about cost while preventing the possibility that emissions could spiral out of control. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Climate change Cap-and-trade Price collars stochastic dynamic programming

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