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 ...

As a generalization of the three-strategy Rock-Scissors-Paper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated, and a neutral interacting partner. Depending on their interaction topologies, all imaginable systems can be classified into four (isomorphic) groups exh...

Secure sets were introduced by Brigham, Dutton, and Hedetniemi [1] as an extension of defensive alliances in a graph. Members of a defensive alliance have agreed to come to the aid of their neighbors in the alliance for mutual protection from attack by nonmembers. Alliances can occur, for example, between nations, biological sequences, and business cartels, and also have been used to model a va...