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Cooperative-relaying networks have great potential for deployment in next-generation wireless communication networks. However, a cooperative-relaying network using two-dimensional multiple-input-multiple-output technology can further enhance the network performance. In this article, we propose a game theoretical framework for mobile two-dimensional multiple-input-multiple-output communication networks to achieve optimal relay selection and cooperative control. A source node, relay, and destination node can make service-selection decisions dynamically in a two-level network, based on the mobile-channel satisfaction parameters (e.g. spatial-temporal correlation and relay survivability). To model this dynamic interactive decision problem, we propose a hierarchical dynamic game framework. At the outer level, we formulate an evolutionary game to model and analyze the process of adaptive selection of relays for maximizing the multiple-input-multiple-output capacity by relay selection and power allocation. At the inner level, by aligning relays, we formulate an evolutionary game to model a self-organizing network structure for relays, to increase the capacity. A closed-loop evolutionary game equilibrium is considered to solve the dynamic game. Numerical results show that the proposed algorithm can effectively improve the quality of service for mobile two-dimensional multiple-input-multiple-output communication networks. [ABSTRACT FROM AUTHOR]