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

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.Comment: 6 two-column pages, 5 figures; accepted for publication in Europhysics Letter

Emerging solutions from the battle of defensive alliances

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.Comment: 11 pages, 8 figures, accepted for publication in Scientific Report

2010-2011, University of Memphis bulletin

University of Memphis bulletin containing the graduate catalog for 2010-2011.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1430/thumbnail.jp

2009-2010, University of Memphis bulletin

University of Memphis bulletin containing the graduate catalog for 2009-2010.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1429/thumbnail.jp

University of Minnesota-Morris Bulletin 1981-1983

https://digitalcommons.morris.umn.edu/catalog/1024/thumbnail.jp

2012-2013, University of Memphis bulletin

University of Memphis bulletin containing the graduate catalog for 2012-2013.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1432/thumbnail.jp

2006-2007, University of Memphis bulletin

University of Memphis bulletin containing the graduate catalog for 2006-2007.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1426/thumbnail.jp

2011-2012, University of Memphis bulletin

University of Memphis bulletin containing the graduate catalog for 2011-2012.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1431/thumbnail.jp

2001-2003, University of Memphis bulletin

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