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In this paper, we consider a multiuser multiple inputs and multiple output (MIMO) system. We study the erodogic capacity bound of the multi-access channels with channel estimation error, which has never been investigated before. Game theory is adopted to model the MIMO multi-access channels, which gives us a new understanding for the analysis of MIMO multi-access channels. Game-theoretic power allocation is used, which borrows the idea from iterative water-filling power allocation, to solve the Nash equilibrium and maximize the sum capacity of the multiuser MIMO system with channel estimation error. The effect of the channel estimation error to the capacity of multiuser MIMO multi-access channel is also studied.