Active-Absorbing Phase Transitions in the Parallel Minority Game
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arXiv
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| Format: | Preprint |
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2025
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| author | Tyagi, Aryan Biswas, Soumyajyoti Chakraborti, Anirban |
| author_facet | Tyagi, Aryan Biswas, Soumyajyoti Chakraborti, Anirban |
| contents | The Parallel Minority Game (PMG) is a synchronous adaptive multi-agent model that exhibits active-absorbing transitions characteristic of non-equilibrium statistical systems. We perform a comprehensive numerical study of the PMG under two families of microscopic decision rules: (i) agents update their choices based on instantaneous population in their alternative choices, and (ii) threshold-based activation that activates agents movement only after overcrowding density crossing a threshold. We measure time-dependent and steady state limits of activity $A(t)$, overcrowding fraction $F(t)$ as functions of the control parameter $g=N/D$, where $N$ is the number of agents and $D$ is the total number of sites. Instantaneous rules display mean-field directed-percolation (MF-DP) scaling with $β\approx1.00$, $δ\approx0.5$, and $ν_{\parallel}\approx2.0$. Threshold rules, however, produce a distinct non-mean-field universality class with $β\approx0.75$ and a systematic failure of dynamical scaling. We show that thresholding acts as a relevant perturbation to the critical behavior of the model. The results highlight how minimal cognitive features at the agent level fundamentally alter large-scale critical behavior in socio-economic and active systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22826 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Active-Absorbing Phase Transitions in the Parallel Minority Game Tyagi, Aryan Biswas, Soumyajyoti Chakraborti, Anirban Statistical Mechanics Computational Physics Physics and Society The Parallel Minority Game (PMG) is a synchronous adaptive multi-agent model that exhibits active-absorbing transitions characteristic of non-equilibrium statistical systems. We perform a comprehensive numerical study of the PMG under two families of microscopic decision rules: (i) agents update their choices based on instantaneous population in their alternative choices, and (ii) threshold-based activation that activates agents movement only after overcrowding density crossing a threshold. We measure time-dependent and steady state limits of activity $A(t)$, overcrowding fraction $F(t)$ as functions of the control parameter $g=N/D$, where $N$ is the number of agents and $D$ is the total number of sites. Instantaneous rules display mean-field directed-percolation (MF-DP) scaling with $β\approx1.00$, $δ\approx0.5$, and $ν_{\parallel}\approx2.0$. Threshold rules, however, produce a distinct non-mean-field universality class with $β\approx0.75$ and a systematic failure of dynamical scaling. We show that thresholding acts as a relevant perturbation to the critical behavior of the model. The results highlight how minimal cognitive features at the agent level fundamentally alter large-scale critical behavior in socio-economic and active systems. |
| title | Active-Absorbing Phase Transitions in the Parallel Minority Game |
| topic | Statistical Mechanics Computational Physics Physics and Society |
| url | https://arxiv.org/abs/2512.22826 |