In this paper, we present two approaches for min-max economic model predictive control (MPC). The first is based on the standard approach for robust min-max stabilizing MPC which is well known from literature and transferred to the case of non-definite cost functions. The second is based on ideas from robust tube-based MPC. In contrast to an exact prediction of the error, invariant error sets are considered in the optimization. While this setup is in general more conservative, it can lead to optimization problems which are computationally more appealing. We provide a priori bounds on the asymptotic average performance for both approaches and discuss and compare them in detail.