Massive MIMO is a promising technique to meet the exponential growth of mobile traffic demand. However, contrary to the current systems, energy consumption of next generation networks is required to be load adaptive as the network load varies significantly throughout the day. In this paper, we propose a load adaptive multi-cell massive MIMO system where each base station (BS) adapts the number of antennas to the daily load profile (DLP) in order to maximize the downlink energy efficiency (EE). In order to incorporate the DLP, the load at each BS is modeled as an M/G/m/m state dependent queue under the assumption that the network is dimensioned to serve a maximum number of users at the peak load. The EE maximization problem is formulated in a game theoretic framework where the number of antennas to be used by a BS is determined through best response iteration. This load adaptive system achieves around 24% higher EE and saves around 40% energy compared to a baseline system where the BSs always run with the fixed number of antennas that is most energy efficient at the peak load and that can be switched off when there is no traffic.