Volume 4, Issue 3-1, June 2015, Page: 6-13
Strict Descriptions of Some Typical 2×2 Games and Negative Games
Dianyu Jiang, Institute of Game Theory with Applications, Huaihai Institute of Technology, No.59 Cangwu Road, Lianyungang, China
Received: Dec. 23, 2014;       Accepted: Dec. 28, 2014;       Published: Jan. 23, 2015
DOI: 10.11648/j.eco.s.2015040301.12      View  2976      Downloads  95
Abstract
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.
Keywords
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/j.eco.s.2015040301.12
Reference
[1]
Ahn TK., Lee M., Ruttan L.,and Walker J.(2007). Asymmetric payoffs in simultaneous and sequential prisoner’s dilemma games. Public Choose, 132:354-366.
[2]
Ahn TK., Ostrom E., and Walker J.(2003). Heterogeneous preferences and collective action. Public Choose, 117:295-315.
[3]
Ahn TK., Ostrom E., Schmidt D., Shupp R., and Walker J.(2001). Cooperation in PD games: Fear, greed, and history of play. Public Choose, 106(1/2): 137-155.
[4]
Jiang D.Y.(2010), Situation Analysis of Double Action Games with Entropy, Science Press, Science Press USA Inc.
[5]
Jiang D.Y.(2012a), Most probable situations in strong Rasmusen axiom system for boxed pigs, Systems Engineering.30(5):96-100. (in Chinese).
[6]
Jiang D.Y.(2012b), Possbilities of situations of boxed pigs based on peace-strong cost assumption, Journal of Systems science and mathematical sciences. 32(9):1145-1155. (in Chinese).
[7]
Jiang D.Y.(2012c), Situation Analysis and Trick Theory on Games with Entropy, Science Press. (in Chinese).
[8]
Jiang D.Y.(2013), Axiom system for Rasmuusen boxed pigs and a game of technology innovations, Journal of Systems Engineering. 28(2):180-186. (in Chinese).
[9]
Jiang D.Y.(2015). L-system of Boxed Pigs and its Deductive Sub-systems. Columbia: Columbia International Publishing.
[10]
Jiang D.Y., Shao Y.B., Zhu X.Y., Matsuhisa T.(2014). Adjustment of the small pig alone abdicating in a mathematical system of rational pigs. Journal of Advanced Computing. 3(2):83-97.
[11]
Jiang D.Y.,et al. (2013), Labor activist problems about axiomatic system on boxed pigs under background of time-consuming technology developments, Operations Research and Management Science, 22(5):146-152.
[12]
Luce R.D., and Raiffa H.(1957), Games and Decisions. New York: John Wiley and Sons.
[13]
Maynard Smith, J. and G. R. Price (1973): The logic of animal conflicts. Nature. 246, 15-18.
[14]
Rapoport A., Guyer M., and Gordon D. (1976), The 2×2 Game, Ann Arbor, MI: The University of Michigan Press.
[15]
Raporport A., and Chammah, AM.(1965). Prisoner’s Dilemma: A study in conflict and cooperation. Ann Arbor: University of Michigan Press.
[16]
Rasmusen E.(2001).Games and Information: An Introduction to Game Theory (3rd ed.). New York: Wiley- Blackwell.
[17]
Roger A. McCain.(2004). Game Theory: A Non-Technical Introduction to the Analysis of Strategy. New York: Thomson Learning Press.
[18]
Rousseau, Jean-Jacques, Rosenblatt, Helena (1755), Discourse on the origin and foundations of inequality among men. (in French, Its English edition has been published by St Martin's Press in 2011).
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