---
APC_amount: 3041,76 EUR
OA_place: publisher
OA_type: hybrid
_id: '15083'
abstract:
- lang: eng
text: 'Direct reciprocity is a powerful mechanism for cooperation in social dilemmas.
The very logic of reciprocity, however, seems to require that individuals are
symmetric, and that everyone has the same means to influence each others’ payoffs.
Yet in many applications, individuals are asymmetric. Herein, we study the effect
of asymmetry in linear public good games. Individuals may differ in their endowments
(their ability to contribute to a public good) and in their productivities (how
effective their contributions are). Given the individuals’ productivities, we
ask which allocation of endowments is optimal for cooperation. To this end, we
consider two notions of optimality. The first notion focuses on the resilience
of cooperation. The respective endowment distribution ensures that full cooperation
is feasible even under the most adverse conditions. The second notion focuses
on efficiency. The corresponding endowment distribution maximizes group welfare.
Using analytical methods, we fully characterize these two endowment distributions.
This analysis reveals that both optimality notions favor some endowment inequality:
More productive players ought to get higher endowments. Yet the two notions disagree
on how unequal endowments are supposed to be. A focus on resilience results in
less inequality. With additional simulations, we show that the optimal endowment
allocation needs to account for both the resilience and the efficiency of cooperation.'
acknowledgement: 'This work was supported by the European Research Council CoG 863818
(ForM-SMArt) (to K.C.) and the European Research Council Starting Grant 850529:
E-DIRECT (to C.H.), the European Union’s Horizon 2020 research and innovation program
under the Marie Skłodowska-Curie Grant Agreement #754411 and the French Agence Nationale
de la Recherche (under the Investissement d’Avenir Programme, ANR-17-EURE-0010)
(to M.K.).'
article_number: e2315558121
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Valentin
full_name: Hübner, Valentin
id: 2c8aa207-dc7d-11ea-9b2f-f22972ecd910
last_name: Hübner
orcid: 0009-0001-5009-4987
- first_name: Manuel
full_name: Staab, Manuel
last_name: Staab
- first_name: Christian
full_name: Hilbe, Christian
id: 2FDF8F3C-F248-11E8-B48F-1D18A9856A87
last_name: Hilbe
orcid: 0000-0001-5116-955X
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Maria
full_name: Kleshnina, Maria
last_name: Kleshnina
citation:
ama: Hübner V, Staab M, Hilbe C, Chatterjee K, Kleshnina M. Efficiency and resilience
of cooperation in asymmetric social dilemmas. Proceedings of the National Academy
of Sciences of the United States of America. 2024;121(10). doi:10.1073/pnas.2315558121
apa: Hübner, V., Staab, M., Hilbe, C., Chatterjee, K., & Kleshnina, M. (2024).
Efficiency and resilience of cooperation in asymmetric social dilemmas. Proceedings
of the National Academy of Sciences of the United States of America. National
Academy of Sciences. https://doi.org/10.1073/pnas.2315558121
chicago: Hübner, Valentin, Manuel Staab, Christian Hilbe, Krishnendu Chatterjee,
and Maria Kleshnina. “Efficiency and Resilience of Cooperation in Asymmetric Social
Dilemmas.” Proceedings of the National Academy of Sciences of the United States
of America. National Academy of Sciences, 2024. https://doi.org/10.1073/pnas.2315558121.
ieee: V. Hübner, M. Staab, C. Hilbe, K. Chatterjee, and M. Kleshnina, “Efficiency
and resilience of cooperation in asymmetric social dilemmas,” Proceedings of
the National Academy of Sciences of the United States of America, vol. 121,
no. 10. National Academy of Sciences, 2024.
ista: Hübner V, Staab M, Hilbe C, Chatterjee K, Kleshnina M. 2024. Efficiency and
resilience of cooperation in asymmetric social dilemmas. Proceedings of the National
Academy of Sciences of the United States of America. 121(10), e2315558121.
mla: Hübner, Valentin, et al. “Efficiency and Resilience of Cooperation in Asymmetric
Social Dilemmas.” Proceedings of the National Academy of Sciences of the United
States of America, vol. 121, no. 10, e2315558121, National Academy of Sciences,
2024, doi:10.1073/pnas.2315558121.
short: V. Hübner, M. Staab, C. Hilbe, K. Chatterjee, M. Kleshnina, Proceedings of
the National Academy of Sciences of the United States of America 121 (2024).
corr_author: '1'
date_created: 2024-03-05T09:18:49Z
date_published: 2024-03-05T00:00:00Z
date_updated: 2026-04-07T12:30:56Z
day: '05'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.1073/pnas.2315558121
ec_funded: 1
external_id:
isi:
- '001207786500004'
pmid:
- '38408249'
file:
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creator: dernst
date_created: 2024-03-12T13:12:22Z
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intvolume: ' 121'
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language:
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month: '03'
oa: 1
oa_version: Published Version
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: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Proceedings of the National Academy of Sciences of the United States
of America
publication_identifier:
eissn:
- 1091-6490
issn:
- 0027-8424
publication_status: published
publisher: National Academy of Sciences
quality_controlled: '1'
related_material:
link:
- description: News on ISTA Website
relation: press_release
url: https://ista.ac.at/en/news/what-math-tells-us-about-social-dilemmas/
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scopus_import: '1'
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title: Efficiency and resilience of cooperation in asymmetric social dilemmas
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