Present and the Future of Axiomatic Theory of Boxed Pigs
Issue:
Volume 4, Issue 3-1, June 2015
Pages:
1-5
Received:
23 December 2014
Accepted:
28 December 2014
Published:
23 January 2015
Abstract: Boxed pigs or rational pigs are well-known stories with many editions of game theory. In order to promote these to a systematic and scientific theory, an axiomatic theory, called L-system of boxed pigs, is established and some special subsystems are deduced from it. In this article, we introduce the background, the main results and the future research plan of axiomatic theory of boxed pigs. This introduction is divided into the following five aspects: appearance of boxed pigs, development and actualities of boxed pigs or rational pigs, boxed pigs in China, L-system of axiomatic theory of boxed pigs, and future research------non L-systems of axiomatic theory of boxed pigs.
Abstract: Boxed pigs or rational pigs are well-known stories with many editions of game theory. In order to promote these to a systematic and scientific theory, an axiomatic theory, called L-system of boxed pigs, is established and some special subsystems are deduced from it. In this article, we introduce the background, the main results and the future resea...
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Strict Descriptions of Some Typical 2×2 Games and Negative Games
Issue:
Volume 4, Issue 3-1, June 2015
Pages:
6-13
Received:
23 December 2014
Accepted:
28 December 2014
Published:
23 January 2015
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.
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. ...
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A Game of Boxed Pigs to Allow Robbing Food
Qichen Li,
Dianyu Jiang,
Takashi Matsuhisa,
Yabin Shao,
Xiaoyang Zhu
Issue:
Volume 4, Issue 3-1, June 2015
Pages:
14-16
Received:
5 January 2015
Accepted:
8 January 2015
Published:
27 January 2015
Abstract: In this short paper, a new simple system of boxed pigs with three troughs, three dispensers and two panels is given. The main result is that each pig will enjoy his own labor if the pressing cost is lower; the big one will enjoy his own labor but his food has to be robbed by the small one if the pressing cost is higher but the big pig’s labor can bring profit for him; and none presses his own panel if the big pig’s labor brings loss for him. Finally, an example shows an application of the theory in technology development.
Abstract: In this short paper, a new simple system of boxed pigs with three troughs, three dispensers and two panels is given. The main result is that each pig will enjoy his own labor if the pressing cost is lower; the big one will enjoy his own labor but his food has to be robbed by the small one if the pressing cost is higher but the big pig’s labor can b...
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