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Symmetric solution of the Bellman optimality equation for repeated harmony game — arXiv:2609.16289

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.16289
License (as archived): CC0-1.0
Archived: 2026-10-15T18:32:48.817Z
SHA-256 of the archived text: 0c87d8ca7caeaf888379cc408a5d9ff497dd37b68eac0108a0805669b43d1f6d
Stable URL of this page: https://metraipolis.com/documento/dc_00a45cc3cfda

How to cite

Symmetric solution of the Bellman optimality equation for repeated harmony game — arXiv:2609.16289 — arXiv (en), https://arxiv.org/abs/2609.16289 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_00a45cc3cfda (Metraipolis archive dc_00a45cc3cfda, sha256 0c87d8ca7caeaf888379cc408a5d9ff497dd37b68eac0108a0805669b43d1f6d)

BibTeX

@misc{dc00a45cc3cfda,
  title = {Symmetric solution of the Bellman optimality equation for repeated harmony game — arXiv:2609.16289},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.16289},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_00a45cc3cfda; sha256 0c87d8ca7caeaf888379cc408a5d9ff497dd37b68eac0108a0805669b43d1f6d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.16289. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In social dilemma games, additional rewards or punishments have been studied as means of promoting cooperation. Therefore, it is important to investigate the ideal situation, in which such an additional payoff would change the game. In this study, we investigated the symmetric solution of the Bellman optimality equation for a repeated harmony game. The calculations showed that three types of symmetric solutions exist. One of them corresponds to the trivial All-C strategy, and another to the Win-stay Lose-shift strategy of the prisoners dilemma game. The nontrivial behavior of the strategy corresponding to the last solution is also discussed in detail. In addition, we numerically investigated which strategy the agents actually learn by the reinforcement learning algorithm.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-16 in cs.AI).
Categorie arXiv: Computer Science and Game Theory (cs.GT) ; Artificial Intelligence (cs.AI); Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.16289 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T18:03:09.609Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-09-16?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).