  Game dynamics in which three or more strategies are cyclically competitive,
as represented by the rock-scissors-paper game, have attracted practical and
theoretical interests. In evolutionary dynamics, cyclic competition results in
oscillatory dynamics of densities of individual strategists. In finite-size
populations, it is known that oscillations blow up until all but one strategies
are eradicated if without mutation. In the present paper, we formalize
replicator dynamics with players that have different adaptation rates. We show
analytically and numerically that the heterogeneous adaptation rate suppresses
the oscillation amplitude. In social dilemma games with cyclically competing
strategies and homogeneous adaptation rates, altruistic strategies are often
relatively weak and cannot survive in finite-size populations. In such
situations, heterogeneous adaptation rates save coexistence of different
strategies and hence promote altruism. When one strategy dominates the others
without cyclic competition, fast adaptors earn more than slow adaptors. When
not, mixture of fast and slow adaptors stabilizes population dynamics, and slow
adaptation does not imply inefficiency for a player.
