Spin Glass Mapping of the Parallel Minority Game
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916037225611264 |
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| author | Tyagi, Aryan Das, Soumyaditya Biswas, Soumyajyoti Chakraborti, Anirban |
| author_facet | Tyagi, Aryan Das, Soumyaditya Biswas, Soumyajyoti Chakraborti, Anirban |
| contents | The parallel minority game (PMG) extends the classical minority game to many choices, with each agent restricted to two predetermined alternatives. In this condition, minimizing the population variance across all choices is a complex combinatorial optimization problem. We show that this minimization is exactly equivalent to finding the ground state of an Ising spin glass in the mean-field limit, i.e., the Sherrington-Kirkpatrick model. By encoding the agent choices as spin variables, the variance becomes a quadratic Hamiltonian with quenched random couplings $J_{ij}$ and random fields $h_i$. This mapping reveals inherent frustration and connects the PMG to the well developed theory of spin glasses, providing a new perspective on the frozen, sub-optimal configurations observed in stochastic strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spin Glass Mapping of the Parallel Minority Game Tyagi, Aryan Das, Soumyaditya Biswas, Soumyajyoti Chakraborti, Anirban Disordered Systems and Neural Networks Statistical Mechanics The parallel minority game (PMG) extends the classical minority game to many choices, with each agent restricted to two predetermined alternatives. In this condition, minimizing the population variance across all choices is a complex combinatorial optimization problem. We show that this minimization is exactly equivalent to finding the ground state of an Ising spin glass in the mean-field limit, i.e., the Sherrington-Kirkpatrick model. By encoding the agent choices as spin variables, the variance becomes a quadratic Hamiltonian with quenched random couplings $J_{ij}$ and random fields $h_i$. This mapping reveals inherent frustration and connects the PMG to the well developed theory of spin glasses, providing a new perspective on the frozen, sub-optimal configurations observed in stochastic strategies. |
| title | Spin Glass Mapping of the Parallel Minority Game |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2605.22764 |