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Best-Response Principals. / Kolokoltsov, Vassili N.; Malafeyev, Oleg A.

Springer Series in Operations Research and Financial Engineering. Springer Nature, 2019. p. 27-70 (Springer Series in Operations Research and Financial Engineering).

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Harvard

Kolokoltsov, VN & Malafeyev, OA 2019, Best-Response Principals. in Springer Series in Operations Research and Financial Engineering. Springer Series in Operations Research and Financial Engineering, Springer Nature, pp. 27-70. https://doi.org/10.1007/978-3-030-12371-0_2

APA

Kolokoltsov, V. N., & Malafeyev, O. A. (2019). Best-Response Principals. In Springer Series in Operations Research and Financial Engineering (pp. 27-70). (Springer Series in Operations Research and Financial Engineering). Springer Nature. https://doi.org/10.1007/978-3-030-12371-0_2

Vancouver

Kolokoltsov VN, Malafeyev OA. Best-Response Principals. In Springer Series in Operations Research and Financial Engineering. Springer Nature. 2019. p. 27-70. (Springer Series in Operations Research and Financial Engineering). https://doi.org/10.1007/978-3-030-12371-0_2

Author

Kolokoltsov, Vassili N. ; Malafeyev, Oleg A. / Best-Response Principals. Springer Series in Operations Research and Financial Engineering. Springer Nature, 2019. pp. 27-70 (Springer Series in Operations Research and Financial Engineering).

BibTeX

@inbook{c5518de9ab5e49efa75ed1119f2dc4e3,
title = "Best-Response Principals",
abstract = "In this chapter our basic tool, the dynamic law of large numbers (LLN, whose descriptive explanation was given in Chapter 1 ), is set on a firm mathematical foundation. We prove several versions of this LLN, with different regularity assumptions on the coefficients, with and without major players, and finally with a distinguished (or tagged) player, the latter version being used later, in Part II. convergence is proved with rather precise estimates of the error terms, which is, of course, crucial for any practical applications. For instance, we show that in the case of smooth coefficients, the convergence rates, measuring the difference between the various bulk characteristics of the dynamics of N players and the limiting evolution (corresponding to an infinite number of players), are of order 1 / N. For example, for N=10 players, this difference is about 10%, showing that the number N does not have to be “very large” for the approximation (1.3 ) of “infinitely many players” to give reasonable predictions.",
author = "Kolokoltsov, {Vassili N.} and Malafeyev, {Oleg A.}",
note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2019",
doi = "10.1007/978-3-030-12371-0_2",
language = "English",
series = "Springer Series in Operations Research and Financial Engineering",
publisher = "Springer Nature",
pages = "27--70",
booktitle = "Springer Series in Operations Research and Financial Engineering",
address = "Germany",

}

RIS

TY - CHAP

T1 - Best-Response Principals

AU - Kolokoltsov, Vassili N.

AU - Malafeyev, Oleg A.

N1 - Publisher Copyright: © 2019, Springer Nature Switzerland AG. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2019

Y1 - 2019

N2 - In this chapter our basic tool, the dynamic law of large numbers (LLN, whose descriptive explanation was given in Chapter 1 ), is set on a firm mathematical foundation. We prove several versions of this LLN, with different regularity assumptions on the coefficients, with and without major players, and finally with a distinguished (or tagged) player, the latter version being used later, in Part II. convergence is proved with rather precise estimates of the error terms, which is, of course, crucial for any practical applications. For instance, we show that in the case of smooth coefficients, the convergence rates, measuring the difference between the various bulk characteristics of the dynamics of N players and the limiting evolution (corresponding to an infinite number of players), are of order 1 / N. For example, for N=10 players, this difference is about 10%, showing that the number N does not have to be “very large” for the approximation (1.3 ) of “infinitely many players” to give reasonable predictions.

AB - In this chapter our basic tool, the dynamic law of large numbers (LLN, whose descriptive explanation was given in Chapter 1 ), is set on a firm mathematical foundation. We prove several versions of this LLN, with different regularity assumptions on the coefficients, with and without major players, and finally with a distinguished (or tagged) player, the latter version being used later, in Part II. convergence is proved with rather precise estimates of the error terms, which is, of course, crucial for any practical applications. For instance, we show that in the case of smooth coefficients, the convergence rates, measuring the difference between the various bulk characteristics of the dynamics of N players and the limiting evolution (corresponding to an infinite number of players), are of order 1 / N. For example, for N=10 players, this difference is about 10%, showing that the number N does not have to be “very large” for the approximation (1.3 ) of “infinitely many players” to give reasonable predictions.

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U2 - 10.1007/978-3-030-12371-0_2

DO - 10.1007/978-3-030-12371-0_2

M3 - Chapter

AN - SCOPUS:85098066293

T3 - Springer Series in Operations Research and Financial Engineering

SP - 27

EP - 70

BT - Springer Series in Operations Research and Financial Engineering

PB - Springer Nature

ER -

ID: 72679018