Title: Representation Interference Suppression via Non-linear Value Factorization for Indecomposable Markov Games. Abstract: Value factorization is an efficient approach for centralized training with decentralized execution in cooperative multi-agent reinforcement learning tasks. As the simplest implementation of value factorization, Linear Value Factorization (LVF) attracts wide attention. In this paper, firstly, we investigate the applicable conditions of LVF, which is important but usually neglected by previous works. We prove that due to the representation limitation, LVF is only perfectly applicable to an extremely narrow class of tasks, which we define as the decomposable Markov game. Secondly, to handle the indecomposable Markov game where the LVF is inapplicable, we turn to value factorization with complete representation capability (CRC) and explore the general form of the value factorization function that satisfies both Independent Global Max (IGM) and CRC conditions. A common problem of these value factorization functions is the representation interference among true Q values with shared local Q value functions. As a result, the policy could be trapped in local optimums due to the representation interference on the optimal true Q values. Thirdly, to address the problem, we propose a novel value factorization method, namely Q Factorization with Representation Interference Suppression (QFRIS).  QFRIS adaptively reduces the gradients of the local Q value functions contributed by the non-optimal true Q values. Our method is evaluated on various benchmarks. Experimental results demonstrate the good convergence of QFIRS.