Before revision:  We consider a stylized duopoly model in which two firms face the same problem instance of multi-armed bandits . Users arrive one by one and choose between the two firms, so that each firm makes progress on its bandit instance only if it is chosen.
After revision:  We consider a stylized duopoly model in which two firms face the same problem instance of multi-armed bandit problem . Users arrive one by one and choose between the two firms, so that each firm makes progress on its bandit instance only if it is chosen.