  We investigate the interior turnpike phenomenon for discrete-time multi-agent
optimal control problems. While for continuous systems the turnpike property
has been established, we focus here on first-order discretizations of such
systems. It is shown that the resulting time-discrete system inherits the
turnpike property with estimates of the same type as in the continuous case. In
particular, we prove that the discrete time optimal control problem is strictly
dissipative and the cheap control assumption holds.
