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

It is known that a two-person game form gg 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.