Reputation with one-sided monitoring: Ignorance as a commitment device

•Repeated Games with one-sided monitoring and two long-run player.•Two-sided Incomplete Information.•Reputation result: player with no monitoring device can secure a payoff close to her Stackelberg Payoff.

I analyze a repeated two-sided incomplete information game with two long-run players in which only one of them can observe the history of the game. Using standard reputation arguments, I prove that if players are sufficiently patient, then the player with no monitoring device can secure a payoff arbitrarily close to her Stackelberg payoff; providing a novel form of equilibrium selection.