To support machine-type communications in an LTE system, we propose a contention control method that regulates the number of devices competing simultaneously for the random-access channel in a distributed manner. We modeled the decision problem of a device-whether to participate in a random-access contention-as the minority game. Using inductive reasoning from observing the collective behavior of all devices, a device adapts access strategies so as to increase the probability of access success. We analyze the average number of successfully decoded preambles by deriving the average number of devices competing simultaneously. Through simulation studies, we also show that our method reduces the probability of random-access failure, the access delay, and the energy consumption of a device compared with other conventional methods.