  We consider finite two-person normal form games. The following four
properties of their game forms are equivalent: (i) Nash-solvability, (ii)
zero-sum-solvability, (iii) win-lose-solvability, and (iv) tightness. For (ii,
iii, iv) this was shown by Edmonds and Fulkerson in 1970. Then, in 1975, (i)
was added to this list and it was also shown that these results cannot be
generalized for $n$-person case with $n > 2$. In 1990, tightness was extended
to vector game forms ($v$-forms) and it was shown that such $v$-tightness and
zero-sum-solvability are still equivalent, yet, do not imply Nash-solvability.
These results are applicable to several classes of stochastic games with
perfect information. Here we suggest one more extension of tightness
introducing $v^+$-tight vector game forms ($v^+$-forms). We show that such
$v^+$-tightness and Nash-solvability are equivalent in case of weakly
rectangular game forms and positive cost functions. This result allows us to
reduce the so-called bi-shortest path conjecture to $v^+$-tightness of
$v^+$-forms. However, both (equivalent) statements remain open.
