Acyclic, or totally tight, two-person game forms: Characterization and main properties

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• 作者：Endre Boros ; Vladimir Gurvich ; Kazuhisa Makino ; Dá ; vid Papp
• 关键词：Game ; Game form ; Effectivity function ; Improvement cycle ; Acyclic ; Assignable ; Tight ; Totally tight ; Nash-solvable ; Dominance-solvable
• 刊名：Discrete Mathematics
• 出版年：2010
• 出版时间：6 April 2010
• 年：2010
• 卷：310
• 期：6-7
• 页码：1135-1151
• 全文大小：1931 K

文摘

It is known that a two-person game form g is Nash-solvable if and only if it is tight. We strengthen the concept of tightness as follows: a game form is called totally tight if each of its 2×2 subforms is tight. (It is easy to show that in this case all, not only 2×2, subforms are tight.) We characterize totally tight game forms, and derive from this characterization that they are tight, Nash-solvable, dominance-solvable, acyclic, and assignable. In particular, total tightness and acyclicity are equivalent properties of two-person game forms.