ReLExS: Reinforcement Learning Explanations for Stackelberg No-Regret Learners
This addresses theoretical guarantees for equilibrium convergence in Stackelberg games with no-regret learners, which is incremental to existing game theory research.
The paper tackles the problem of whether players in a two-player Stackelberg game can reach Stackelberg equilibrium under a no-regret constraint for the follower, showing that they can achieve this equilibrium and providing a strict upper bound on the follower's utility difference.
With the constraint of a no regret follower, will the players in a two-player Stackelberg game still reach Stackelberg equilibrium? We first show when the follower strategy is either reward-average or transform-reward-average, the two players can always get the Stackelberg Equilibrium. Then, we extend that the players can achieve the Stackelberg equilibrium in the two-player game under the no regret constraint. Also, we show a strict upper bound of the follower's utility difference between with and without no regret constraint. Moreover, in constant-sum two-player Stackelberg games with non-regret action sequences, we ensure the total optimal utility of the game remains also bounded.