We consider a multi-armed bandit problem in which a set of arms is registered by each agent, and the agent receives reward when its arm is selected. An agent might strategically submit more arms with replications, which can bring more reward by abusing the bandit algorithm's exploration-exploitation balance. Our analysis reveals that a standard algorithm indeed fails at preventing replication and suffers from linear regret in time $T$. We aim to design a bandit algorithm which demotivates replications and also achieves a small cumulative regret. We devise Hierarchical UCB (H-UCB) of replication-proof, which has $O(\ln T)$-regret under any equilibrium. We further propose Robust Hierarchical UCB (RH-UCB) which has a sublinear regret even in a realistic scenario with irrational agents replicating careless. We verify our theoretical findings through numerical experiments.

翻译：我们的分析表明,标准算法在防止复制方面确实失败,在时间上遭受线性遗憾$T美元。我们的目标是设计一种使复制活动失去动力并取得少量累积遗憾的土匪算法。我们设计了防复制的等级性UCB(H-UCB)系统,在任何平衡下都拥有$(n)T(regret)值。我们进一步提议使用强势高射级UCB(RH-UCB)系统(RH-UCB)系统(RH-UCB)系统(UCB-UCB)系统,该系统在现实情况下甚至与不理性的代理进行复制时,也会产生亚线性遗憾。我们通过数字实验来验证我们的理论结论。