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

2009; Elsevier BV; Volume: 310; Issue: 6-7 Linguagem: Inglês

10.1016/j.disc.2009.11.009

1872-681X

Endre Boros, Vladimir Gurvich, Kazuhisa Makino, Dávid Papp,

Game Theory and Voting Systems

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.