---
APC_amount: 3003,56 EUR
OA_place: publisher
OA_type: hybrid
_id: '20857'
abstract:
- lang: eng
  text: 'Evolutionary games provide a flexible mathematical framework for many problems
    in biology and social evolution. Prisoners’ dilemma, and in particular, the important
    special case of donation games, represents social dilemmas where cooperation is
    mutually beneficial, yet defection is preferred by selfish agents. In evolutionary
    games on networks, the agents interact over a population structure. The existence
    of population structures that promote cooperative behavior is a fascinating and
    active research topic. Previous research establishes structures promoting cooperation
    in the limit of weak selection where the benefit-to-cost ratio β exceeds 1.5.
    The existence of such structures for medium and strong selection for 1 < ß < 2
    and for weak selection for 1 < ß < 1.5 has been a long-standing open question.
    First, we answer the open questions in the affirmative: For every selection strength
    and every ß > 1, we construct networks promoting cooperation. Second, we present
    a robustness result with respect to β and selection strength: Our structures promote
    cooperation for a range of these parameter values rather than specific parameter
    values. Finally, we supplement our theoretical results with simulation results
    on small population structures that show the effectiveness of our construction
    over well-studied population structures.'
acknowledgement: J.S. and K.C. were supported by the European Research Council CoG
  863818 (ForM-SMArt) and Austrian Science Fund (FWF) 10.55776/COE12.
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Jakub
  full_name: Svoboda, Jakub
  id: 130759D2-D7DD-11E9-87D2-DE0DE6697425
  last_name: Svoboda
  orcid: 0000-0002-1419-3267
- first_name: Krishnendu
  full_name: Chatterjee, Krishnendu
  id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
  last_name: Chatterjee
  orcid: 0000-0002-4561-241X
citation:
  ama: Svoboda J, Chatterjee K. Promoters of cooperation in evolutionary games. <i>Proceedings
    of the National Academy of Sciences</i>. 2025;122(51):e2524109122. doi:<a href="https://doi.org/10.1073/pnas.2524109122">10.1073/pnas.2524109122</a>
  apa: Svoboda, J., &#38; Chatterjee, K. (2025). Promoters of cooperation in evolutionary
    games. <i>Proceedings of the National Academy of Sciences</i>. National Academy
    of Sciences. <a href="https://doi.org/10.1073/pnas.2524109122">https://doi.org/10.1073/pnas.2524109122</a>
  chicago: Svoboda, Jakub, and Krishnendu Chatterjee. “Promoters of Cooperation in
    Evolutionary Games.” <i>Proceedings of the National Academy of Sciences</i>. National
    Academy of Sciences, 2025. <a href="https://doi.org/10.1073/pnas.2524109122">https://doi.org/10.1073/pnas.2524109122</a>.
  ieee: J. Svoboda and K. Chatterjee, “Promoters of cooperation in evolutionary games,”
    <i>Proceedings of the National Academy of Sciences</i>, vol. 122, no. 51. National
    Academy of Sciences, p. e2524109122, 2025.
  ista: Svoboda J, Chatterjee K. 2025. Promoters of cooperation in evolutionary games.
    Proceedings of the National Academy of Sciences. 122(51), e2524109122.
  mla: Svoboda, Jakub, and Krishnendu Chatterjee. “Promoters of Cooperation in Evolutionary
    Games.” <i>Proceedings of the National Academy of Sciences</i>, vol. 122, no.
    51, National Academy of Sciences, 2025, p. e2524109122, doi:<a href="https://doi.org/10.1073/pnas.2524109122">10.1073/pnas.2524109122</a>.
  short: J. Svoboda, K. Chatterjee, Proceedings of the National Academy of Sciences
    122 (2025) e2524109122.
corr_author: '1'
date_created: 2025-12-28T23:01:26Z
date_published: 2025-12-15T00:00:00Z
date_updated: 2026-05-20T08:13:17Z
day: '15'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.1073/pnas.2524109122
ec_funded: 1
external_id:
  pmid:
  - '41397136'
file:
- access_level: open_access
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  creator: dernst
  date_created: 2025-12-29T09:36:50Z
  date_updated: 2025-12-29T09:36:50Z
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  file_name: 2025_PNAS_Svoboda.pdf
  file_size: 2308124
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file_date_updated: 2025-12-29T09:36:50Z
has_accepted_license: '1'
intvolume: '       122'
issue: '51'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: e2524109122
pmid: 1
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
  call_identifier: H2020
  grant_number: '863818'
  name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: Proceedings of the National Academy of Sciences
publication_identifier:
  eissn:
  - 1091-6490
publication_status: published
publisher: National Academy of Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Promoters of cooperation in evolutionary games
tmp:
  image: /images/cc_by_nc_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
    (CC BY-NC-ND 4.0)
  short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 122
year: '2025'
...