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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Notes
- 1.
- 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.
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.
- 4.
See Chap. 9 below.
- 5.
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.
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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’”.
- 8.
For an extended analysis of secrets and secrecy in strategic situations, see Holler (2018: 121–229).
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Holler, M.J., Klose-Ullmann, B. (2020). The Nash Equilibrium. In: Scissors and Rock. Springer, Cham. https://doi.org/10.1007/978-3-030-44823-3_4
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