Strict Descriptions of Some Typical 2×2 Games and Negative Games
Volume 4, Issue 3-1, June 2015, Pages: 6-13
Received: Dec. 23, 2014; Accepted: Dec. 28, 2014; Published: Jan. 23, 2015
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Dianyu Jiang, Institute of Game Theory with Applications, Huaihai Institute of Technology, No.59 Cangwu Road, Lianyungang, China
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In this paper, we shall give the strict description of some typical 2×2 games such as stag hunt, game of chicken, battle of the sexes, prisoner’s dilemma (briefly PD) and Rasumsen’s boxed pigs and we shall invent three new game stories, game of musicians, game of ruffians and negative Rasumsen boxed pigs. Every game is not necessarily symmetrical. We shall divide battle of the sexes into two forms and introduce the concept of weak PD. A game is said to be negative game of another one if the sum of their payoff functions is equal zero. The following main results will be obtained. (1) A negative game of chicken is a stage hunt. (2) A negative non-weak PD is a non-weak PD, where defection and cooperation of the original non-weak PD are corresponding to cooperation and defection of the negative non-weak PD respectively. The negative game of a weak PD is not a PD. (3) The negative first battle of the sexes is the game of musicians and the negative second one is the game of ruffians. (4) The negative Rasmusen boxed pigs is a weak PD and so is asymmetrical. (5) The guilt game as a negative Rasmusen boxed pigs is not a non-weak PD; it is a weak PD if and only if the small pig is conscienceless.
Stag Hunt, Game of Chicken, Battle of the Sexes, Prisoner’s Dilemma, Rasumsen’s Boxed Pigs, Game of Musicians, Game of Ruffians, Negative Game
To cite this article
Dianyu Jiang, Strict Descriptions of Some Typical 2×2 Games and Negative Games, Economics. Special Issue: Axiomatic Theory of Boxed Pigs. Vol. 4, No. 3-1, 2015, pp. 6-13. doi: 10.11648/
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