  The so-called internal shock model aims to explain the light-curves and
spectra produced by non-thermal processes originated in the flow of blazars and
gamma-ray bursts. A long standing question is whether the tenuous collisionless
shocks, driven inside a relativistic flow, are efficient enough to explain the
amount of energy observed as compared with the expected kinetic power of the
outflow. In this work we study the dynamic efficiency of conversion of
kinetic-to- thermal/magnetic energy of internal shocks in relativistic
magnetized outflows. We find that the collision between shells with a non-zero
relative velocity can yield either two oppositely moving shocks (in the frame
where the contact surface is at rest), or a reverse shock and a forward
rarefaction. For moderately magnetized shocks (magnetization {\sigma} ~ 0.1),
the dynamic efficiency in a single two-shell interaction can be as large as
40%. Hence, the dynamic efficiency of moderately magnetized shocks is larger
than in the corresponding unmagnetized two-shell interaction. We find that the
efficiency is only weakly dependent on the Lorentz factor of the shells and,
thus internal shocks in the magnetized flow of blazars and gamma-ray bursts are
approximately equally efficient.
