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This paper considers repeated games in which one player has more informationabout the game than the other players. In particular, we investigate repeatedtwo-player zero-sum games where only the column player knows the payoff matrixA of the game. Suppose that while repeatedly playing this game, the row playerchooses her strategy at each round by using a no-regret algorithm to minimizeher (pseudo) regret. We develop a no-instant-regret algorithm for the columnplayer to exhibit last round convergence to a minimax equilibrium. We show thatour algorithm is efficient against a large set of popular no-regret algorithmsof the row player, including the multiplicative weight update algorithm, theonline mirror descent method/follow-the-regularized-leader, the linearmultiplicative weight update algorithm, and the optimistic multiplicativeweight update.

Last Round Convergence and No-Instant Regret in Repeated Games with Asymmetric Information