  We propose genuine ($k$, $m$)-threshold controlling schemes for controlled
teleportation via multi-particle entangled states, where the teleportation of a
quantum state from a sender (Alice) to a receiver (Bob) is under the control of
$m$ supervisors such that $k$ ($k\leq m$) or more of these supervisors can help
Bob recover the transferred state. By construction, anyone of our quantum
channels is a genuine multipartite entangled state of which any two parts are
inseparable. Their properties are compared and contrasted with those of the
well-known Greenberger-Horne-Zeilinger, W, and linear cluster states, and also
several other genuine multipartite entangled states recently introduced in
literature. We show that our schemes are secure against both Bob's dishonesty
and supervisors' treacheries. For the latter case, the game theory is utilized
to prove that supervisors' cheats can be well prevented. In addition to their
practical importance, our schemes are also useful in seeking and exploring
genuine multipartite entangled states and opening another perspective for the
applications of the game theory in quantum information science.
