Optimal Learning Before Choice

Ke, T. Tony; Villas-Boas, J. Miguel

doi:10.2139/ssrn.2844417

Cited by 14 publications

(17 citation statements)

References 42 publications

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“…While the analysis above applies for exogenously fixed stopping beliefs, similar results hold in a related setting in which the stopping region is chosen optimally when the DM is patient. Ke and Villas‐Boas (2019) examine a continuous‐time model with exponential discounting and show that the analogue of the strategy

α^{*}

(together with a stopping region they characterize) is optimal. Despite the differences between these models, they both converge to the same demands in the limit as learning becomes arbitrarily precise, that is, in the limit as

\underline{p} \to 0

and

\overset{p}{true} \to 1

in our model, and as the discount factor tends to 1 in the model of Ke and Villas‐Boas.…”

Section: Manipulation Of One‐shot Choicementioning

confidence: 99%

“…Our model builds on a long tradition in statistics and economic theory originating with Wald (1945), who proposed a theory of optimal sequential learning about a single binary state. A growing literature studies optimal sequential learning about several options when attention must focus on one item at a time (Mandelbaum, Shepp, and Vanderbei (1990), Ke, Shen, and Villas‐Boas (2016), Ke and Villas‐Boas (2019), Nikandrova and Pancs (2018), Austen‐Smith and Martinelli (2018)). The structure of the optimal learning strategy varies depending on the costs and information structure.…”

Section: Introductionmentioning

confidence: 99%

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Attention Please!

Gossner

Steiner

Stewart

2021

ECTA

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We study the impact of manipulating the attention of a decision‐maker who learns sequentially about a number of items before making a choice. Under natural assumptions on the decision‐maker's strategy, directing attention toward one item increases its likelihood of being chosen regardless of its value. This result applies when the decision‐maker can reject all items in favor of an outside option with known value; if no outside option is available, the direction of the effect of manipulation depends on the value of the item. A similar result applies to manipulation of choices in bandit problems.

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α^{*}

\underline{p} \to 0

and

\overset{p}{true} \to 1

in our model, and as the discount factor tends to 1 in the model of Ke and Villas‐Boas.…”

Section: Manipulation Of One‐shot Choicementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Attention Please!

Gossner

Steiner

Stewart

2021

ECTA

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show abstract

“…Thus, if the agent finds it optimal to stop, he takes max iPU μ i . 6 In particular, if he has only one box, then by Proposition 0, it is optimal to take it without inspection. When there is more than one box left to inspect, Proposition 2 below provides necessary conditions for the optimality of stopping and taking a box without inspection.…”

Section: Then Weitzman's Policy Is Optimal In All Continuation Histomentioning

confidence: 99%

Whether or not to open Pandora's box

Doval

2018

Journal of Economic Theory

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I study a single-agent sequential search problem as in Weitzman [13].Contrary to Weitzman, conditional on stopping, the agent may take any uninspected box without first inspecting its contents. This introduces a new trade-off. By taking a box without inspection, the agent saves on its inspection costs. However, by inspecting it, he may discover that its contents are lower than he anticipated. I identify sufficient conditions on the parameters of the environment under which I characterize the optimal policy. Both the order in which boxes are inspected and the stopping rule may differ from that in Weitzman's model. Moreover, I provide additional results that partially characterize the optimal policy when these conditions fail.

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“…It is discovered that the decision-maker is indifferent to search an alternative arm which does not have the highest reservation price. When a Bayesian decision-maker makes a selection from multiple arms with uncertain payoffs and an outside arm with known payoff, maximizing his expected profit is studied in Ke et al [16]. For other optimal strategies and control approaches, the reader is referred to [17,18] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Differential Equation Driven by Poisson Random Measure and Its Application in a Duopoly Market

Wang

Liang

2020

Mathematical Problems in Engineering

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We investigate a stochastic differential equation driven by Poisson random measure and its application in a duopoly market for a finite number of consumers with two unknown preferences. The scopes of pricing for two monopolistic vendors are illustrated when the prices of items are determined by the number of buyers in the market. The quantity of buyers is proved to obey a stochastic differential equation (SDE) driven by Poisson random measure which exists a unique solution. We derive the Hamilton-Jacobi-Bellman (HJB) about vendors’ profits and provide a verification theorem about the problem. When all consumers believe a vendor’s guidance about their preferences, the conditions that the other vendor’s profit is zero are obtained. We give an example of this problem and acquire approximate solutions about the profits of the two vendors.

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Optimal Learning Before Choice

Cited by 14 publications

References 42 publications

Attention Please!

Attention Please!

Whether or not to open Pandora's box

A Stochastic Differential Equation Driven by Poisson Random Measure and Its Application in a Duopoly Market

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