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Competitions for shareable and limited resources have long been studied withstrategic agents. In reality, agents often have to learn and maximize therewards of the resources at the same time. To design an individualizedcompeting policy, we model the competition between agents in a novelmulti-player multi-armed bandit (MPMAB) setting where players are selfish andaim to maximize their own rewards. In addition, when several players pull thesame arm, we assume that these players averagely share the arms' rewards byexpectation. Under this setting, we first analyze the Nash equilibrium whenarms' rewards are known. Subsequently, we propose a novel Selfish MPMAB withAveraging Allocation (SMAA) approach based on the equilibrium. We theoreticallydemonstrate that SMAA could achieve a good regret guarantee for each playerwhen all players follow the algorithm. Additionally, we establish that nosingle selfish player can significantly increase their rewards throughdeviation, nor can they detrimentally affect other players' rewards withoutincurring substantial losses for themselves. We finally validate theeffectiveness of the method in extensive synthetic experiments.

Competing for Shareable Arms in Multi-Player Multi-Armed Bandits