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Role-separating ordering in social dilemmas controlled by topological frustration
Marco A Amaral1, Matjaž Perc2,3, Lucas Wardil4
1Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, CEP 30161-970, Belo Horizonte-MG, Brazil.
Physical Review. E
|April 19, 2017
Summary
Topological frustration in the snowdrift game on triangular lattices creates complex patterns. Cooperation levels directly indicate frustration, offering a new way to measure it in networks.
Area of Science:
- Statistical physics
- Evolutionary game theory
- Network science
Background:
- The "three is a crowd" proverb highlights social and physical complexities.
- Topological frustration in statistical physics models impacts system dynamics.
- Understanding social relations in triangular configurations is crucial.
Purpose of the Study:
- To investigate the effect of topological frustration on the evolutionary dynamics of the snowdrift game.
- To analyze the impact of triangular lattice topology on strategy evolution.
- To explore how frustration influences cooperation and pattern formation.
Main Methods:
- Simulations of the snowdrift game on a triangular lattice.
- Employing various strategy updating protocols.
- Utilizing mean-field approximations and Monte Carlo simulations.
- Comparing results with a square lattice (no frustration).
Main Results:
- Topological frustration on triangular lattices prevents optimal strategy anticoordination.
- Complex spatial patterns, like honeycomb structures, emerge to mitigate frustration.
- Cooperation levels correlate directly with topological frustration levels.
- Gradual transition from triangular to square lattices reveals frustration's impact.
Conclusions:
- Topological frustration significantly shapes evolutionary dynamics and spatial patterns in game theory models.
- Honeycomb-like patterns emerge as a mechanism to cope with frustration.
- Cooperation serves as a quantifiable indicator of topological frustration in networks.
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