Zero-Error Nash Equilibrium: Harnessing Nonlocal Correlation in Incomplete Information Games
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arXiv
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| Format: | Preprint |
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2025
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| author | Ambuj Tushar Pandey, Siddharth R. Patra, Ram Krishna Bhowmik, Anandamay Das Som, Kuntal Mukherjee, Amit |
| author_facet | Ambuj Tushar Pandey, Siddharth R. Patra, Ram Krishna Bhowmik, Anandamay Das Som, Kuntal Mukherjee, Amit |
| contents | Claude Shannon's zero-error communication paradigm reshaped our understanding of fault-tolerant information transfer. Here, we adapt this notion into game theory with incomplete information. We ask: can players with private information coordinate on a Nash equilibrium with zero probability of error? We identify Bayesian games in which such coordination is impossible classically, yet achievable by harnessing Bell nonlocal correlations. We formalize this requirement as zero-error Nash equilibrium coordination, establishing a new bridge between information theory, game theory, and quantum nonlocality. Furthermore, we construct a tripartite Bayesian game that admits zero-error Nash equilibrium coordination with genuine entanglement, and a two-player game where a stronger notion of coordination can be achieved using every two-qubit pure entangled state except the maximally one. Crucially, the advantage persists under experimentally relevant noise, demonstrating nonlocality as a robust resource for near-zero error decision-making under uncertainty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zero-Error Nash Equilibrium: Harnessing Nonlocal Correlation in Incomplete Information Games Ambuj Tushar Pandey, Siddharth R. Patra, Ram Krishna Bhowmik, Anandamay Das Som, Kuntal Mukherjee, Amit Quantum Physics Computer Science and Game Theory Claude Shannon's zero-error communication paradigm reshaped our understanding of fault-tolerant information transfer. Here, we adapt this notion into game theory with incomplete information. We ask: can players with private information coordinate on a Nash equilibrium with zero probability of error? We identify Bayesian games in which such coordination is impossible classically, yet achievable by harnessing Bell nonlocal correlations. We formalize this requirement as zero-error Nash equilibrium coordination, establishing a new bridge between information theory, game theory, and quantum nonlocality. Furthermore, we construct a tripartite Bayesian game that admits zero-error Nash equilibrium coordination with genuine entanglement, and a two-player game where a stronger notion of coordination can be achieved using every two-qubit pure entangled state except the maximally one. Crucially, the advantage persists under experimentally relevant noise, demonstrating nonlocality as a robust resource for near-zero error decision-making under uncertainty. |
| title | Zero-Error Nash Equilibrium: Harnessing Nonlocal Correlation in Incomplete Information Games |
| topic | Quantum Physics Computer Science and Game Theory |
| url | https://arxiv.org/abs/2509.02947 |