  In this paper, we solve the constant-payoff conjecture formulated by Sorin,
Venel and Vigeral (2010), for absorbing games with an arbitrary evaluation of
the stage rewards. That is, the existence of a pair of asymptotically optimal
strategies, indexed by the evaluation of the stage rewards, so that the average
rewards are constant on any fraction of the game. That the constant-payoff
conjecture holds for stochastic games with an arbitrary evaluation is still
open.
