A Game-Theoretic Approach to Team Formation in The Voice Show

Ivashko, Anna A.; Мазалов, Владимир; Mazurov, Alexander Yurievich

doi:10.1007/978-3-030-58657-7_19

Cited by 1 publication

(6 citation statements)

References 9 publications

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“…As k is large in the limit N → ∞, we may use the asymptotic approximation for v n in the large n limit for each term in the product. Consequently, if v n satisfies the requirements for (11) to hold, we find that…”

Section: Calculating Optimal Stopping Statistics 41 Calculating the E...mentioning

confidence: 99%

“…The assumptions required for (11) to be valid hold for all distributions considered in the present study. Therefore, this relationship is used to simplify a later result for a collection of common distributions.…”

Section: Asymptotics Of V N As N → ∞mentioning

confidence: 99%

“…It is straightforward to show, using (11), that large-n asymptotics of h(v n ) are independent of α and β to leading order, giving h(v n ) ∼ 1/n in the limit n → ∞.…”

Section: Example 2 the Pareto Distribution Is Given Bymentioning

confidence: 99%

“…In fact, for many distributions, this may be further simplified, using the large-n asymptotics for v n and its derivatives. For the distributions in Examples 1-4, as well as each distribution from Table 1, it is straightforward to show, by direct calculation using (11), that…”

Section: Calculating Optimal Stopping Statistics 41 Calculating the E...mentioning

confidence: 99%

“…Related analyses may be found in [8,9]. Optimal stopping also features in financial and economic applications, such as in the pricing of American options [10], games [11], operational risk insurance [12], dynamic pricing [13] and more complicated buying-selling problems [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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On Asymptotics of Optimal Stopping Times

Entwistle¹,

Lustri²,

Sofronov³

2022

Mathematics

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We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward. In this analysis, we obtained asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables became large. In the case of distributions with infinite upper bound, the asymptotic behaviour of these statistics depends solely on the algebraic power of the probability distribution decay rate in the upper limit. In the case of densities with finite upper bound, the asymptotic behaviour of these statistics depends on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.

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Section: Calculating Optimal Stopping Statistics 41 Calculating the E...mentioning

confidence: 99%

Section: Asymptotics Of V N As N → ∞mentioning

confidence: 99%

“…It is straightforward to show, using (11), that large-n asymptotics of h(v n ) are independent of α and β to leading order, giving h(v n ) ∼ 1/n in the limit n → ∞.…”

Section: Example 2 the Pareto Distribution Is Given Bymentioning

confidence: 99%

Section: Calculating Optimal Stopping Statistics 41 Calculating the E...mentioning

confidence: 99%