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Nash welfare rule — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Nash_welfare_rule
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T11:27:28.592Z
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Nash welfare rule — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Nash_welfare_rule (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_ea22d083fe43 (Metraipolis archive dc_ea22d083fe43, sha256 5d196735c86783df916dcc4583b26aad348995b096877a607a07e95494b361a1)

BibTeX

@misc{dcea22d083fe43,
  title = {Nash welfare rule — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Nash_welfare_rule},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_ea22d083fe43; sha256 5d196735c86783df916dcc4583b26aad348995b096877a607a07e95494b361a1},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Nash_welfare_rule. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In social choice and operations research, the Nash welfare rule (also called the max-product rule, the Nash-optimal rule or maximum Nash welfare, often abbreviated MNW) is a rule saying that, among all possible alternatives, society should pick the alternative which maximizes the product of the utilities of all individuals in society. The product of utilities is called the Nash social welfare, after John Forbes Nash Jr., whose solution to the cooperative bargaining problem selects the utility profile maximizing the product of the agents' gains. The corresponding social welfare function was axiomatized by Kaneko and Nakamura. The Nash welfare rule is often described as a compromise between the utilitarian rule, which maximizes the sum of utilities and emphasizes aggregate efficiency, and the egalitarian rule, which maximizes the minimum utility and emphasizes the worst-off individual. Because the logarithm of the Nash welfare equals the sum of the logarithms of the utilities, maximizing the Nash welfare rewards increases in the utility of an agent in inverse proportion to that agent's current utility level: raising a poor agent's utility from 1 to 2 doubles the product, whereas raising a rich agent's utility from 10 to 11 increases it by only ten percent. The rule is closely related to the proportional-fair rule used in the analysis of communication networks.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Mathematical optimization»).
Fonte: Wikipedia in inglese, voce «Nash welfare rule» — https://en.wikipedia.org/wiki/Nash_welfare_rule
Wikidata Q141273414 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q141273414
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Nash_welfare_rule?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1374717114, consultata il 2026-10-07T11:16:48.004Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 09c810ca1e9acdace4491c9822ad1a7cf36e195a56fd2a2fc6dec078b452b65c