On repeated games with incomplete information played by non-Bayesian players

Unlike in the traditional theory of games of incomplete information, the players here arenot Bayesian, i.e. a player does not necessarily have any prior probability distribution as to what game is being played. The game is infinitely repeated. A player may be absolutely uninformed, i.e. he may know only how many strategies he has. However, after each play the player is informed about his payoff and, moreover, he has perfect recall. A strategy is described, that with probability unity guarantees (in the sense of the liminf of the average payoff) in any game, whatever the player could guarantee if he had complete knowledge of the game.