Critical Phenomena and Strategy Ordering with Hub Centrality Approach in the Aspiration-based Coordination Game
arXiv:2108.10997 · doi:10.1063/5.0064406
Abstract
We study the coordination game with an aspiration-driven update rule in regular graphs and scale-free networks. We prove that the model coincides exactly with the Ising model and shows a phase transition at the critical selection noise when the aspiration level is zero. It is found that the critical selection noise decreases with clustering in random regular graphs. With a non-zero aspiration level, the model also exhibits a phase transition as long as the aspiration level is smaller than the degree of graphs. We also show that the critical exponents are independent of clustering and aspiration level to confirm that the coordination game belongs to the Ising universality class. As for scale-free networks, the effect of aspiration level on the order parameter at a low selection noise is examined. In model networks (Barabási-Albert network and Holme-Kim network), the order parameter abruptly decreases when the aspiration level is the same as the average degree of the network. In real-world networks, in contrast, the order parameter decreases gradually. We explain this difference by proposing the concepts of hub centrality and local hub. The histogram of hub centrality of real-world networks separates into two parts unlike model networks, and local hubs exist only in real-world networks. We conclude that the difference of network structures in model and real-world networks induces qualitatively different behavior in the coordination game.
9 pages, 7 figures
References in corpus (14)
- Statistical physics of social dynamics
- Evolutionary games on graphs
- Hierarchical structure and the prediction of missing links in networks
- Co-evolution of strategy and structure in complex networks with dynamical linking
- Nonequilibrium Physics in Biology
- Stochastic win-stay-lose-shift strategy with dynamic aspirations in evolutionary social dilemmas
- Prisoners' dilemma in real-world acquaintance networks: Spikes and quasi-equilibria induced by the interplay between structure and dynamics
- Effects of strategy-migration direction and noise in the evolutionary spatial prisoner's dilemma
- Ising antiferromagnet on the Archimedean lattices
- Power-law citation distributions are not scale-free
- Phase transition in the majority-vote model on the Archimedean lattices
- Spin glass properties of an Ising antiferromagnet on the Archimedean (3,12^2) lattice
- Reference to Global State and Social Contagion Dynamics
- Highly Clustered Complex Networks in the Configuration Model: Random Regular Small-World Network