In existing systems of mobile routers, the frequency band is shared in uplinks from wireless terminals to mobile routers, and carrier sense multiple access with collision avoidance (CSMA/CA) is generally used as the medium access control protocol. To use the frequency band effectively, adaptive control is one promising approach. In this paper, a decentralized access control protocol in which mobile routers adaptively select the minimum contention window size is proposed. However, because of their mobility, which is one of the main difference between mobile routers and fixed access points, individual local area networks (LANs) consisting of the mobile routers and wireless terminals randomly interact with each other, and such random interactions can cause instability. To analyze the stability of the proposed control, evolutionary game theory is introduced because a system with random interactions between numerous decision-making entities can be analyzed by using evolutionary game theory. Using evolutionary game theory, the condition for existence of a convergence point is obtained. In addition, to implement the decentralized access control, a learning rule is proposed. In the proposed learning rule, each mobile router selects a strategy based on the result of past trials. From the simulation result, it is confirmed that the decentralized access control converges to a point closed to the stable state derived through evolutionary game theory.