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Strategizing against No-regret Learners
Yuan Deng · Jon Schneider · Balasubramanian Sivan

Wed Dec 04:25 PM -- 04:40 PM PST @ West Exhibition Hall A

How should a player who repeatedly plays a game against a no-regret learner strategize to maximize his utility? We study this question and show that under some mild assumptions, the player can always guarantee himself a utility of at least what he would get in a Stackelberg equilibrium. When the no-regret learner has only two actions, we show that the player cannot get any higher utility than the Stackelberg equilibrium utility. But when the no-regret learner has more than two actions and plays a mean-based no-regret strategy, we show that the player can get strictly higher than the Stackelberg equilibrium utility. We construct the optimal game-play for the player against a mean-based no-regret learner who has three actions. When the no-regret learner's strategy also guarantees him a no-swap regret, we show that the player cannot get anything higher than a Stackelberg equilibrium utility.

Author Information

Yuan Deng (Duke University)
Jon Schneider (Google Research)
Balasubramanian Sivan (Google Research)

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