In this paper we introduce incomplete information à la global games into a max-min two-group contest with binary actions and we characterize the set of equilibria. Depending on whether the complete information assumption is relaxed on the value of the prize or on the cost of providing effort, we obtain different results in terms of equilibrium selection: in the first case, there exists both an equilibrium in (monotonic) switching strategies and an equilibrium robust to incomplete information in the sense of Kajii and Morris [1997], in which no player exerts effort in both groups, whereas in the second one there exists a unique equilibrium in (monotonic) switching-strategies.