For homogeneous agents in multi-agent linear bandits the regret-based TU game is convex with non-empty core containing the Shapley value; for heterogeneous agents a simple regret-based payout lies in the core and satisfies three Shapley axioms.
Lower Bound.It is also known that any bandit algorithm can not perform better than a certain level, i.e., the algorithm will have to incur some minimum rate of (expected) regret
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Creator Incentives in Recommender Systems: A Cooperative Game-Theoretic Approach for Stable and Fair Collaboration in Multi-Agent Bandits
For homogeneous agents in multi-agent linear bandits the regret-based TU game is convex with non-empty core containing the Shapley value; for heterogeneous agents a simple regret-based payout lies in the core and satisfies three Shapley axioms.