  Competing strategies in an evolutionary game model, or species in a
biosystem, can easily form a larger unit which protects them from the invasion
of an external actor. Such a defensive alliance may have two, three, four or
even more members. But how effective can be such formation against an
alternative group composed by other competitors? To address this question we
study a minimal model where a two-member and a four-member alliances fight in a
symmetric and balanced way. By presenting representative phase diagrams, we
systematically explore the whole parameter range which characterizes the inner
dynamics of the alliances and the intensity of their interactions. The group
formed by a pair, who can exchange their neighboring positions, prevail in the
majority of the parameter region. The rival quartet can only win if their inner
cyclic invasion rate is significant while the mixing rate of the pair is
extremely low. At specific parameter values, when neither of the alliances is
strong enough, new four-member solutions emerge where a
rock-paper-scissors-like trio is extended by the other member of the pair.
These new solutions coexist hence all six competitors can survive. The
evolutionary process is accompanied by serious finite-size effects which can be
mitigated by appropriately chosen prepared initial states.
