  Mean-payoff games are important quantitative models for open reactive
systems. They have been widely studied as games of full observation. In this
paper we investigate the algorithmic properties of several sub-classes of
mean-payoff games where the players have asymmetric information about the state
of the game. These games are in general undecidable and not determined
according to the classical definition. We show that such games are determined
under a more general notion of winning strategy. We also consider mean-payoff
games where the winner can be determined by the winner of a finite
cycle-forming game. This yields several decidable classes of mean-payoff games
of asymmetric information that require only finite-memory strategies, including
a generalization of full-observation games where positional strategies are
sufficient. We give an exponential time algorithm for determining the winner of
the latter.
