Predators may attack isolated or grouped preys in a cooperative, collective way. Whether a gregarious behavior is advantageous to each species depends on several conditions and game theory is a useful tool to deal with such a problem. We here extend the Lett-Auger-Gaillard model [Theor. Pop. Biol. 65, 263 (2004)] to spatially distributed groups and compare the resulting behavior with their mean field predictions for the coevolving densities of predator and prey strategies. We show that the coexistence phase in which both strategies for each group are present is stable because of an effective, cyclic dominance behavior similar to a well studied generalizations of the Rock-Paper-Scissors game with four species (without neutral pairs), a further example of how ubiquitous this mechanism is. In addition, inside the coexistence phase (but interestingly, only for finite size systems) there is a realization of the survival of the weakest effect that is triggered by a percolation crossover.