Massive MIMO is a promising technique to meet the exponential growth of global mobile data 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 massive MIMO system that varies the number of antennas following the daily load profile (DLP) in order to maximize the downlink energy efficiency (EE). A multi-cell system is considered where each base station (BS) is equipped with a large number of antennas to serve many single antenna users. In order to incorporate DLP, 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. For a given number of users in a cell, the optimum number of active antennas maximizing EE is derived. 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 overall 19% higher EE compared to a baseline system where the BSs always run with the fixed number of antennas that is most energy efficient at peak load and that can be switched-off when there is no traffic