On the existence of pure epsilon-equilibrium
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913860501372928 |
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| author | Pradelski, Bary S. R. Tarbush, Bassel |
| author_facet | Pradelski, Bary S. R. Tarbush, Bassel |
| contents | We show that for any $ε>0$, as the number of agents gets large, the share of games that admit a pure $ε$-equilibrium converges to 1. Our result holds even for pure $ε$-equilibrium in which all agents, except for at most one, play a best response. In contrast, it is known that the share of games that admit a pure Nash equilibrium, that is, for $ε=0$, is asymptotically $1-1/e\approx 0.63$. This suggests that very small deviations from perfect rationality, captured by positive values of $ε$, suffice to ensure the general existence of stable outcomes. We also study the existence of pure $ε$-equilibrium when the number of actions gets large. Our proofs rely on the probabilistic method and on the Chen-Stein method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07585 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the existence of pure epsilon-equilibrium Pradelski, Bary S. R. Tarbush, Bassel Theoretical Economics Computer Science and Game Theory We show that for any $ε>0$, as the number of agents gets large, the share of games that admit a pure $ε$-equilibrium converges to 1. Our result holds even for pure $ε$-equilibrium in which all agents, except for at most one, play a best response. In contrast, it is known that the share of games that admit a pure Nash equilibrium, that is, for $ε=0$, is asymptotically $1-1/e\approx 0.63$. This suggests that very small deviations from perfect rationality, captured by positive values of $ε$, suffice to ensure the general existence of stable outcomes. We also study the existence of pure $ε$-equilibrium when the number of actions gets large. Our proofs rely on the probabilistic method and on the Chen-Stein method. |
| title | On the existence of pure epsilon-equilibrium |
| topic | Theoretical Economics Computer Science and Game Theory |
| url | https://arxiv.org/abs/2502.07585 |