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

It is known that a two-person game form g is Nash-solvable if and only if it is tight [12, 13]. We strengthen the concept of tightness as follows: game form is called totally tight if every its 2 × 2 subform 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, Nashsolvable, dominance-solvable, acyclic, and assignable. In particular, total tightness and acyclicity are equivalent properties of two-person game forms.