3 problems

Bi-SP Conjecture. If $G$ has an $(s,V_T)$-path, then $P_1$ and $P_2$ have such a path in common, that is,

Terminal Nash equilibrium conjecture. Every finite positive two-person shortest path game has a terminal Nash equilibrium provided it has at least one terminal play.

Let $G=(V,E)$ be a finite directed graph with distinct vertices $s,t\in V$, where every vertex in $V\setminus\{t\}$ has an outgoing edge, $t$ has none, $G$ contains a directed path…