Emerging solutions from the battle of defensive alliances

Abstract

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.

11 pages, 8 figures, accepted for publication in Scientific Reports

References in corpus (23)

• Cyclic dominance in evolutionary games: A review
• Competition of tolerant strategies in the spatial public goods game
• Dynamically generated cyclic dominance in spatial prisoner's dilemma games
• Zealots tame oscillations in the spatial rock-paper-scissors game
• Pattern formations driven by cyclic interactions: a brief review of recent developments
• Reentrant phase transitions and defensive alliances in social dilemmas with informed strategies
• Segregation process and phase transition in cyclic predator-prey models with even number of species
• Biodiversity in models of cyclic dominance is preserved by heterogeneity in site-specific invasion rates
• Phase transitions induced by variation of invasion rates in spatial cyclic predator-prey models with four or six species
• Costly hide and seek pays: Unexpected consequences of deceit in a social dilemma
• Early exclusion leads to cyclical cooperation in repeated group interactions
• Strategy dependent learning activity in cyclic dominant systems
• The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games
• The effect of habitats and fitness on species coexistence in systems with cyclic dominance
• Non-Hermitian topology in rock-paper-scissors games
• Dynamically generated hierarchies in games of competition
• Competition of alliances in a cyclically dominant eight-species population
• Risk and interaction aversion: screening mechanisms in the Prisoner's Dilemma game
• Performance of weak species in the simplest generalization of the rock-paper-scissors model to four species
• Weak species in rock-paper-scissors models
• How multiple weak species jeopardise biodiversity in spatial rock-paper-scissors models
• Stabilizing spiral structures in the asymmetric May-Leonard model
• Competition among alliances of different sizes

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