  In this paper, we investigate the problem of the empirical coordination in a
triangular multiterminal network. A triangular multiterminal network consists
of three terminals where two terminals observe two external i.i.d correlated
sequences. The third terminal wishes to generate a sequence with desired
empirical joint distribution. For this problem, we derive inner and outer
bounds on the empirical coordination capacity region. It is shown that the
capacity region of the degraded source network and the inner and outer bounds
on the capacity region of the cascade multiterminal network can be directly
obtained from our inner and outer bounds. For a cipher system, we establish key
distribution over a network with a reliable terminal, using the results of the
empirical coordination. As another example, the problem of rate distortion in
the triangular multiterminal network is investigated in which a distributed
doubly symmetric binary source is available.
