  This paper concerns value functions of time-dependent tug-of-war games. We
first prove the existence and uniqueness of value functions and verify that
these game values satisfy a dynamic programming principle. Using the arguments
in the proof of existence of game values, we can also deduce asymptotic
behavior of game values when $T \to \infty$. Furthermore, we investigate
boundary regularity for game values. Thereafter, based on the regularity
results for value functions, we deduce that game values converge to viscosity
solutions of the normalized parabolic $p$-Laplace equation.
