In this paper we consider one-to-many matching problems where the preferences of the agents involved are represented by … matching to a matching of maximum total reward, one can always provide a compensation schedule that will be ex-post stable in … uses the fact that the core of an associated compensation matching game with constraints is nonempty. …

We examine recent claims that a particular Q-learning algorithm used by competitors 'autonomously' and systematically … detailed analysis of the inner workings of this algorithm reveals that there is no immediate reason for alarm. We set out what … is needed to demonstrate the existence of a colluding price algorithm that does form a threat to competition. …