---
_id: '9402'
abstract:
- lang: eng
  text: Direct and indirect reciprocity are key mechanisms for the evolution of cooperation.
    Direct reciprocity means that individuals use their own experience to decide whether
    to cooperate with another person. Indirect reciprocity means that they also consider
    the experiences of others. Although these two mechanisms are intertwined, they
    are typically studied in isolation. Here, we introduce a mathematical framework
    that allows us to explore both kinds of reciprocity simultaneously. We show that
    the well-known ‘generous tit-for-tat’ strategy of direct reciprocity has a natural
    analogue in indirect reciprocity, which we call ‘generous scoring’. Using an equilibrium
    analysis, we characterize under which conditions either of the two strategies
    can maintain cooperation. With simulations, we additionally explore which kind
    of reciprocity evolves when members of a population engage in social learning
    to adapt to their environment. Our results draw unexpected connections between
    direct and indirect reciprocity while highlighting important differences regarding
    their evolvability.
acknowledgement: 'This work was supported by the European Research Council CoG 863818
  (ForM-SMArt) (to K.C.), the European Research Council Start Grant 279307: Graph
  Games (to K.C.), and the European Research Council Starting Grant 850529: E-DIRECT
  (to C.H.). The funders had no role in study design, data collection and analysis,
  decision to publish or preparation of the manuscript.'
article_processing_charge: No
article_type: original
author:
- first_name: Laura
  full_name: Schmid, Laura
  id: 38B437DE-F248-11E8-B48F-1D18A9856A87
  last_name: Schmid
  orcid: 0000-0002-6978-7329
- first_name: Krishnendu
  full_name: Chatterjee, Krishnendu
  id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
  last_name: Chatterjee
  orcid: 0000-0002-4561-241X
- first_name: Christian
  full_name: Hilbe, Christian
  id: 2FDF8F3C-F248-11E8-B48F-1D18A9856A87
  last_name: Hilbe
  orcid: 0000-0001-5116-955X
- first_name: Martin A.
  full_name: Nowak, Martin A.
  last_name: Nowak
citation:
  ama: Schmid L, Chatterjee K, Hilbe C, Nowak MA. A unified framework of direct and
    indirect reciprocity. <i>Nature Human Behaviour</i>. 2021;5(10):1292–1302. doi:<a
    href="https://doi.org/10.1038/s41562-021-01114-8">10.1038/s41562-021-01114-8</a>
  apa: Schmid, L., Chatterjee, K., Hilbe, C., &#38; Nowak, M. A. (2021). A unified
    framework of direct and indirect reciprocity. <i>Nature Human Behaviour</i>. Springer
    Nature. <a href="https://doi.org/10.1038/s41562-021-01114-8">https://doi.org/10.1038/s41562-021-01114-8</a>
  chicago: Schmid, Laura, Krishnendu Chatterjee, Christian Hilbe, and Martin A. Nowak.
    “A Unified Framework of Direct and Indirect Reciprocity.” <i>Nature Human Behaviour</i>.
    Springer Nature, 2021. <a href="https://doi.org/10.1038/s41562-021-01114-8">https://doi.org/10.1038/s41562-021-01114-8</a>.
  ieee: L. Schmid, K. Chatterjee, C. Hilbe, and M. A. Nowak, “A unified framework
    of direct and indirect reciprocity,” <i>Nature Human Behaviour</i>, vol. 5, no.
    10. Springer Nature, pp. 1292–1302, 2021.
  ista: Schmid L, Chatterjee K, Hilbe C, Nowak MA. 2021. A unified framework of direct
    and indirect reciprocity. Nature Human Behaviour. 5(10), 1292–1302.
  mla: Schmid, Laura, et al. “A Unified Framework of Direct and Indirect Reciprocity.”
    <i>Nature Human Behaviour</i>, vol. 5, no. 10, Springer Nature, 2021, pp. 1292–1302,
    doi:<a href="https://doi.org/10.1038/s41562-021-01114-8">10.1038/s41562-021-01114-8</a>.
  short: L. Schmid, K. Chatterjee, C. Hilbe, M.A. Nowak, Nature Human Behaviour 5
    (2021) 1292–1302.
date_created: 2021-05-18T16:56:57Z
date_published: 2021-05-13T00:00:00Z
date_updated: 2025-07-14T09:10:09Z
day: '13'
ddc:
- '000'
department:
- _id: KrCh
- _id: GradSch
doi: 10.1038/s41562-021-01114-8
ec_funded: 1
external_id:
  isi:
  - '000650304000002'
  pmid:
  - '33986519'
file:
- access_level: open_access
  checksum: 34f55e173f90dc1dab731063458ac780
  content_type: application/pdf
  creator: dernst
  date_created: 2023-11-07T08:27:23Z
  date_updated: 2023-11-07T08:27:23Z
  file_id: '14496'
  file_name: 2021_NatureHumanBehaviour_Schmid_accepted.pdf
  file_size: 5232761
  relation: main_file
  success: 1
file_date_updated: 2023-11-07T08:27:23Z
has_accepted_license: '1'
intvolume: '         5'
isi: 1
issue: '10'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Submitted Version
page: 1292–1302
pmid: 1
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
  call_identifier: H2020
  grant_number: '863818'
  name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '279307'
  name: 'Quantitative Graph Games: Theory and Applications'
publication: Nature Human Behaviour
publication_identifier:
  eissn:
  - 2397-3374
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  link:
  - description: News on IST Homepage
    relation: press_release
    url: https://ist.ac.at/en/news/the-emergence-of-cooperation/
  record:
  - id: '10293'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: A unified framework of direct and indirect reciprocity
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 5
year: '2021'
...