  Knowing the strategy of an opponent in a competitive environment conveys
obvious evolutionary advantages. But this information is costly, and the
benefit of being informed may not necessarily offset the additional cost. Here
we introduce social dilemmas with informed strategies, and we show that this
gives rise to two cyclically dominant triplets that form defensive alliances.
The stability of these two alliances is determined by the rotation velocity of
the strategies within each triplet. A weaker strategy in a faster rotating
triplet can thus overcome an individually stronger competitor. Fascinating
spatial patterns favor the dominance of a single defensive alliance, but enable
also the stable coexistence of both defensive alliances in very narrow regions
of the parameter space. A continuous reentrant phase transition reveals before
unseen complexity behind the stability of strategic alliances in evolutionary
social dilemmas.
