  We introduce a "high probability" framework for repeated games with
incomplete information. In our non-equilibrium setting, players aim to
guarantee a certain payoff with high probability, rather than in expected
value. We provide a high probability counterpart of the classical result of
Mertens and Zamir for the zero-sum repeated games. Any payoff that can be
guaranteed with high probability can be guaranteed in expectation, but the
reverse is not true. Hence, unlike the average payoff case where the payoff
guaranteed by each player is the negative of the payoff by the other player,
the two guaranteed payoffs would differ in the high probability framework. One
motivation for this framework comes from information transmission systems,
where it is customary to formulate problems in terms of asymptotically
vanishing probability of error. An application of our results to a class of
compound arbitrarily varying channels is given.
