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Erschienen in:
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2020 | OriginalPaper | Buchkapitel

4. The Nash Equilibrium

verfasst von : Manfred J. Holler, Barbara Klose-Ullmann

Erschienen in: Scissors and Rock

Verlag: Springer International Publishing

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Abstract

Here a definition of the Nash equilibrium is presented, regarded as the most prominent solution concept for non-cooperative games. Information requirements such as common knowledge of rationality (CKR) and consistent-aligned beliefs (CAB) are discussed. A historical note on Nash and his equilibrium concept accompanies the definition, including a reference to the movie “Beautiful Mind.” For illustration, the concept is applied to the QWERTY-DSK game of standardization—and to the Kama Sutra.

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Vorheriges Kapitel The Prisoners’ Dilemma, but Who Are the Players?
Nächstes Kapitel Sequence of Moves and the Extensive Form
Fußnoten
1
Nash (1950a, 1951) contains two versions of the proof.
 
2
Chapter 10 describes at length the concept ofmixed strategies. As we will see, a mixed strategy means that a player selects apure strategy with a probability smaller than 1.
 
3
For Historical Note I, see Sect. 2.​1.
 
4
In the movie, the braggart Buzz provokes his rival Jim (James Dean) to a test of courage: The two drive at high speed toward a cliff. The one who gets out first is a chicken. Buzz crashes down and is dead. Jim survives. We find driving toward each other is more compelling as a duel.
 
5
See Chap. 9 below.
 
6
Vatsyayana’s Kamasutra is a Sanskrit text, written down in the third or fourth century CE. The text is well known for its frank treatment of erotic love and sexual practices also explaining the “art of love making.” The translation referred to by Vikas Kumaris Doniger and Kakar (2002). As Kumar (2011: 482) noticed, neither of the translators is a game theorist.
 
7
Matrix 4.5 derives from Fig. 4.2 in Kumar (2011), but has been adjusted to the present text.
 
8
Kumar (2011: 494) pointed out that “Vatsyayana thinks that if the man accepts his mistake wholeheartedly (for instance, ‘by falling at her feet,’ …), then the lady accepts him back because ‘even a bashful or very angry woman cannot resist a man falling at her feet; this is a universal rule’”.
 
9
For an extended analysis of secrets and secrecy in strategic situations, see Holler (2018: 121–229).
 
Literatur
David, P. A. (1985). Clio and the economics of QWERTY, papers and proceedings. American Economic Review,75, 332–337.
Doniger, W., & Kakar, S. (2002). Kamasutra. Oxford: Oxford University Press.
Holler, M. J. (2018). The economics of the good, the bad, and the ugly: Secrets, desires, and second-mover advantages. London and New York: Routledge.CrossRef
Kumar, V. (2011). Scheming lovers and their secrets: Strategy-making in the Kamasutra. Homo Oeconomicus,28, 479–498.
Liebowitz, S. J., & Margolis, S. E. (1990). The fable of the keys. Journal of Law and Economics,33, 1–25.CrossRef
Nash, J. F. (1950a). Equilibrium points in N-person games. Proceedings of the National Academy of Sciences,36, 48–49.CrossRef
Nash, J. F. (1950b). The bargaining problem. Econometrica,18, 155–162.CrossRef
Nash, J. F. (1951). Non-cooperative games. Annals of Mathematics,54, 286–295.CrossRef
Nash, J. F. (1953). Two-person cooperative games. Econometrica,21, 128–140.CrossRef
Wilde, O. (1997[1890]). Collected work if Oscar Wilde. Ware: Wordsworth Edition.
Metadaten
Titel
The Nash Equilibrium
verfasst von
Manfred J. Holler
Barbara Klose-Ullmann
Copyright-Jahr
2020
Verlag
Springer International Publishing
Buch
Scissors and Rock

Print ISBN: 978-3-030-44822-6

Electronic ISBN: 978-3-030-44823-3

Copyright-Jahr: 2020

DOI
https://doi.org/10.1007/978-3-030-44823-3_4

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