  We study the trade-off relations satisfied by the genuine tripartite
nonlocality in multipartite quantum systems. From the reduced three-qubit
density matrices of the four-qubit generalized Greenberger-Horne-Zeilinger
(GHZ) states and W states (4-qubit entangled state), we find that there exists
a trade-off relation among the mean values of the Svetlichny operators
associated with these reduced states. Namely, the genuine three-qubit
nonlocalities are not independent. For four-qubit generalized GHZ states and W
states, the summation of all their three-qubit maximal (squared) mean values of
the Svetlichny operator has an upper bound. This bound is better than the one
derived from the upper bounds of individual three-qubit mean values of the
Svetlichny operator. Detailed examples are presented to illustrate the
trade-off relation among the three-qubit nonlocalities.
