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Knowing the strategy of an opponent in a competitive environment conveysobvious evolutionary advantages. But this information is costly, and thebenefit of being informed may not necessarily offset the additional cost. Herewe introduce social dilemmas with informed strategies, and we show that thisgives rise to two cyclically dominant triplets that form defensive alliances.The stability of these two alliances is determined by the rotation velocity ofthe strategies within each triplet. A weaker strategy in a faster rotatingtriplet can thus overcome an individually stronger competitor. Fascinatingspatial patterns favor the dominance of a single defensive alliance, but enablealso the stable coexistence of both defensive alliances in very narrow regionsof the parameter space. A continuous reentrant phase transition reveals beforeunseen complexity behind the stability of strategic alliances in evolutionarysocial dilemmas.

Reentrant phase transitions and defensive alliances in social dilemmas with informed strategies