Price dispersion and incomplete learning in the long run

McLennan, Andrew

doi:10.1016/0165-1889(84)90023-x

Cited by 139 publications

(71 citation statements)

References 2 publications

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“…Transitions then follow from Bayes' rule, and, as is well known, {x t } is a martingale. Here the approximation implies the complete learning results of McLennan (1984) and Easley and Kiefer (1988). In particular, the argument proceeds counter-factually: if beliefs converge to any fixed point (interior as well as extremal) and the discount factor is high enough, then the approximation must necessarily obtain.…”

Section: Dynamic Two State Learning Problems This Follows On Work Bymentioning

confidence: 99%

“…The same techniques can be used to establish that a similar approximation must necessarily hold around any fixed point. Specifically, given an optimal policy α * (x), let x * ∈ (0, 1) That complete learning obtains for high δ in learning problems was shown in an example by McLennan (1984) and more generally by Easley and Kiefer (1988). the appendicized proof offers added intuition, as well as a computable lower bound on δ.…”

Section: Two State Learning Problemsmentioning

confidence: 99%

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Geometric Asymptotic Approximation of Value Functions

Anderson

2009

The B.E. Journal of Theoretical Economics

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This paper characterizes the behavior of value functions in dynamic stochastic discounted programming models near fixed points of the state space. When the second derivative of the flow payoff function is bounded, the value function is proportional to a linear function plus x ψ δ . A specific formula for ψ δ is provided, which implies ψ δ continuously falls in the rate of patience.If the state variable is a martingale, the second derivative of the value function is unbounded. If the state variable is instead a strict local submartingale, then the same holds for the first derivative of the value function. Thus, the proposed approximation is more accurate than Taylor series approximation.The approximation result is used to characterize locally optimal policies in several fundamental economic problems. * Thanks to Lones Smith for substantial advice and assistance throughout this project. Any errors are mine. †

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Section: Dynamic Two State Learning Problems This Follows On Work Bymentioning

confidence: 99%

Section: Two State Learning Problemsmentioning

confidence: 99%

Geometric Asymptotic Approximation of Value Functions

Anderson

2009

The B.E. Journal of Theoretical Economics

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“…This model is nothing but the multi-armed bandit problem with unknown payoffs for arms. McLennan (1984) extended the model of Rothschild (1974) by allowing the seller to choose from a continuum of prices. Azoulay-Schwartz et al (2003) and Krähmer (2003) examined the problem of experiment from the buyer's point of view where buyer can not observe the quality of products.…”

Section: Experiments and Learningmentioning

confidence: 99%

A survey on the bandit problem with switching costs

Jun

2004

De Economist

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SummaryThe paper surveys the literature on the bandit problem, focusing on its recent development in the presence of switching costs. Switching costs between arms makes not only the Gittins index policy suboptimal, but also renders the search for the optimal policy computationally infeasible. This survey will first discuss the decomposability properties of the arms that make the Gittins index policy optimal, and show how these properties break down upon the introduction of costs on switching arms. Having established the failure of the simple index policy, the survey focus on the recent efforts to overcome the difficulty of finding the optimal policy in the bandit problem with switching costs: characterization of the optimal policy, exact derivation of the optimal policy in the restricted environments, and lastly approximation of optimal policy. The advantages and disadvantages of the above approaches are discussed.

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“…If several firms were to experiment independently in the same market, they might offer different prices in the long run. Optimal experimentation may therefore lead to price dispersion in the long run, as shown formally in [13]. [4] used both the MAB and MARB to identify the best strategy for managing obsolescence in such instances wherein organizations have to deal with continuous technological evolution under uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Optimal dynamic resource allocation to prevent defaults

Ayesta

Erausquin

Ferreira

et al. 2016

Operations Research Letters

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We consider a resource allocation problem, where a rational agent has to decide how to share a limited amount of resources among different companies that might be facing financial difficulties. The objective is to minimize the total long term cost incurred by the economy due to default events. Using the framework of multiarmed restless bandits and, assuming a two-state evolution of the default risk, the optimal dynamic resource sharing policy is determined. This policy assigns an index value to each company, which orders its priority to be funded. We obtain an analytical expression for this index, which generalizes the return-on-investment (ROI) index under the static setting, and we analyse the influence of the future events on the optimal dynamic policy. A discussion about the structure of the optimal dynamic policy is provided, as well as some extensions of the model.

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Price dispersion and incomplete learning in the long run

Cited by 139 publications

References 2 publications

Geometric Asymptotic Approximation of Value Functions

Geometric Asymptotic Approximation of Value Functions

A survey on the bandit problem with switching costs

Optimal dynamic resource allocation to prevent defaults

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