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Phase transitions for rock-scissors-paper game on different networks
Attila Szolnoki1, György Szabó
1Research Institute for Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
Summary
This study explores phase transitions in the rock-scissors-paper game using Monte Carlo simulations. Results show universal critical behavior in phase transitions, independent of network clustering.
Area of Science:
- Complex Systems
- Statistical Physics
- Network Science
Background:
- The rock-scissors-paper game is a classic model for studying cyclic dynamics and evolutionary game theory.
- Understanding phase transitions in game dynamics on complex networks is crucial for predicting emergent behaviors.
Purpose of the Study:
- To investigate phase transitions in the rock-scissors-paper game on various host networks with simultaneous quenched and annealed randomness.
- To identify stationary states and analyze the influence of network topology on game dynamics.
Main Methods:
- Utilized Monte Carlo simulations and dynamical mean-field approximations.
- Studied the game on host networks derived from lattices with introduced randomness.
Main Results:
- Identified three distinct stationary states across all network structures.
- Found that the clustering coefficient has no significant impact on the emergence of a global oscillating phase.
- Observed universal critical behavior in phase transitions, describable by consistent exponents.
Conclusions:
- Network clustering is not a determining factor for global oscillations in this game model.
- The phase transitions exhibit universal characteristics, suggesting a fundamental dynamic underlying the system's behavior.