Multi-hop reasoning approaches over knowledge graphs infer a missing relationship between entities with a multi-hop rule, which corresponds to a chain of relationships. %Such reasoning schema enables both strong expressivity and transparency of the inference process of missing relationships. We extend existing works to consider a generalized form of multi-hop rules, where each rule is a set of relation chains. Thus a target relationship is inferred with the joint-information of the chains instead of applying each chain separately. To learn such generalized rules efficiently, we propose a two-step approach that first selects a small set of relation chains as a rule and then evaluates the confidence of the target relationship by jointly scoring the selected chains. A game-theoretical framework is proposed to this end to simultaneously optimize the rule selection and prediction steps. Empirical results show that our multi-chain multi-hop (MCMH) rules result in superior results compared to the standard single-chain approaches, justifying both our formulation of generalized rules and the effectiveness of the proposed learning framework.