---
_id: '15006'
abstract:
- lang: eng
text: Graphical games are a useful framework for modeling the interactions of (selfish)
agents who are connected via an underlying topology and whose behaviors influence
each other. They have wide applications ranging from computer science to economics
and biology. Yet, even though an agent’s payoff only depends on the actions of
their direct neighbors in graphical games, computing the Nash equilibria and making
statements about the convergence time of "natural" local dynamics in particular
can be highly challenging. In this work, we present a novel approach for classifying
complexity of Nash equilibria in graphical games by establishing a connection
to local graph algorithms, a subfield of distributed computing. In particular,
we make the observation that the equilibria of graphical games are equivalent
to locally verifiable labelings (LVL) in graphs; vertex labelings which are verifiable
with constant-round local algorithms. This connection allows us to derive novel
lower bounds on the convergence time to equilibrium of best-response dynamics
in graphical games. Since we establish that distributed convergence can sometimes
be provably slow, we also introduce and give bounds on an intuitive notion of
"time-constrained" inefficiency of best responses. We exemplify how our results
can be used in the implementation of mechanisms that ensure convergence of best
responses to a Nash equilibrium. Our results thus also give insight into the convergence
of strategy-proof algorithms for graphical games, which is still not well understood.
acknowledgement: This work was partially funded by the Academy of Finland, grant 314888,
the European Research Council CoG 863818 (ForM-SMArt), and the Austrian Science
Fund (FWF) project I 4800-N (ADVISE). LS was supported by the Stochastic Analysis
and Application Research Center (SAARC) under National Research Foundation of Korea
grant NRF-2019R1A5A1028324.
alternative_title:
- LIPIcs
article_number: '11'
article_processing_charge: No
arxiv: 1
author:
- first_name: Juho
full_name: Hirvonen, Juho
last_name: Hirvonen
- 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: Stefan
full_name: Schmid, Stefan
last_name: Schmid
citation:
ama: 'Hirvonen J, Schmid L, Chatterjee K, Schmid S. On the convergence time in graphical
games: A locality-sensitive approach. In: 27th International Conference on
Principles of Distributed Systems. Vol 286. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2024. doi:10.4230/LIPIcs.OPODIS.2023.11'
apa: 'Hirvonen, J., Schmid, L., Chatterjee, K., & Schmid, S. (2024). On the
convergence time in graphical games: A locality-sensitive approach. In 27th
International Conference on Principles of Distributed Systems (Vol. 286).
Tokyo, Japan: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.OPODIS.2023.11'
chicago: 'Hirvonen, Juho, Laura Schmid, Krishnendu Chatterjee, and Stefan Schmid.
“On the Convergence Time in Graphical Games: A Locality-Sensitive Approach.” In
27th International Conference on Principles of Distributed Systems, Vol.
286. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.OPODIS.2023.11.'
ieee: 'J. Hirvonen, L. Schmid, K. Chatterjee, and S. Schmid, “On the convergence
time in graphical games: A locality-sensitive approach,” in 27th International
Conference on Principles of Distributed Systems, Tokyo, Japan, 2024, vol.
286.'
ista: 'Hirvonen J, Schmid L, Chatterjee K, Schmid S. 2024. On the convergence time
in graphical games: A locality-sensitive approach. 27th International Conference
on Principles of Distributed Systems. OPODIS: Conference on Principles of Distributed
Systems, LIPIcs, vol. 286, 11.'
mla: 'Hirvonen, Juho, et al. “On the Convergence Time in Graphical Games: A Locality-Sensitive
Approach.” 27th International Conference on Principles of Distributed Systems,
vol. 286, 11, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.OPODIS.2023.11.'
short: J. Hirvonen, L. Schmid, K. Chatterjee, S. Schmid, in:, 27th International
Conference on Principles of Distributed Systems, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2024.
conference:
end_date: 2023-12-08
location: Tokyo, Japan
name: 'OPODIS: Conference on Principles of Distributed Systems'
start_date: 2023-12-06
date_created: 2024-02-18T23:01:01Z
date_published: 2024-01-18T00:00:00Z
date_updated: 2025-07-14T09:10:03Z
day: '18'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.OPODIS.2023.11
ec_funded: 1
external_id:
arxiv:
- '2102.13457'
file:
- access_level: open_access
checksum: 4fc7eea6e4ba140b904781fc7df868ec
content_type: application/pdf
creator: dernst
date_created: 2024-02-26T09:04:58Z
date_updated: 2024-02-26T09:04:58Z
file_id: '15028'
file_name: 2024_LIPICs_Hirvonen.pdf
file_size: 867363
relation: main_file
success: 1
file_date_updated: 2024-02-26T09:04:58Z
has_accepted_license: '1'
intvolume: ' 286'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: 27th International Conference on Principles of Distributed Systems
publication_identifier:
isbn:
- '9783959773089'
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'On the convergence time in graphical games: A locality-sensitive approach'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 286
year: '2024'
...
---
_id: '12861'
abstract:
- lang: eng
text: The field of indirect reciprocity investigates how social norms can foster
cooperation when individuals continuously monitor and assess each other’s social
interactions. By adhering to certain social norms, cooperating individuals can
improve their reputation and, in turn, receive benefits from others. Eight social
norms, known as the “leading eight," have been shown to effectively promote the
evolution of cooperation as long as information is public and reliable. These
norms categorize group members as either ’good’ or ’bad’. In this study, we examine
a scenario where individuals instead assign nuanced reputation scores to each
other, and only cooperate with those whose reputation exceeds a certain threshold.
We find both analytically and through simulations that such quantitative assessments
are error-correcting, thus facilitating cooperation in situations where information
is private and unreliable. Moreover, our results identify four specific norms
that are robust to such conditions, and may be relevant for helping to sustain
cooperation in natural populations.
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.). L.S. received additional partial support by the Austrian Science
Fund (FWF) under grant Z211-N23 (Wittgenstein Award), and also thanks the support
by the Stochastic Analysis and Application Research Center (SAARC) under National
Research Foundation of Korea grant NRF-2019R1A5A1028324. The authors additionally
thank Stefan Schmid for providing access to his lab infrastructure at the University
of Vienna for the purpose of collecting simulation data.'
article_number: '2086'
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: Farbod
full_name: Ekbatani, Farbod
last_name: Ekbatani
- 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
citation:
ama: Schmid L, Ekbatani F, Hilbe C, Chatterjee K. Quantitative assessment can stabilize
indirect reciprocity under imperfect information. Nature Communications.
2023;14. doi:10.1038/s41467-023-37817-x
apa: Schmid, L., Ekbatani, F., Hilbe, C., & Chatterjee, K. (2023). Quantitative
assessment can stabilize indirect reciprocity under imperfect information. Nature
Communications. Springer Nature. https://doi.org/10.1038/s41467-023-37817-x
chicago: Schmid, Laura, Farbod Ekbatani, Christian Hilbe, and Krishnendu Chatterjee.
“Quantitative Assessment Can Stabilize Indirect Reciprocity under Imperfect Information.”
Nature Communications. Springer Nature, 2023. https://doi.org/10.1038/s41467-023-37817-x.
ieee: L. Schmid, F. Ekbatani, C. Hilbe, and K. Chatterjee, “Quantitative assessment
can stabilize indirect reciprocity under imperfect information,” Nature Communications,
vol. 14. Springer Nature, 2023.
ista: Schmid L, Ekbatani F, Hilbe C, Chatterjee K. 2023. Quantitative assessment
can stabilize indirect reciprocity under imperfect information. Nature Communications.
14, 2086.
mla: Schmid, Laura, et al. “Quantitative Assessment Can Stabilize Indirect Reciprocity
under Imperfect Information.” Nature Communications, vol. 14, 2086, Springer
Nature, 2023, doi:10.1038/s41467-023-37817-x.
short: L. Schmid, F. Ekbatani, C. Hilbe, K. Chatterjee, Nature Communications 14
(2023).
date_created: 2023-04-23T22:01:03Z
date_published: 2023-04-12T00:00:00Z
date_updated: 2025-07-14T09:09:52Z
day: '12'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.1038/s41467-023-37817-x
ec_funded: 1
external_id:
isi:
- '001003644100020'
pmid:
- '37045828'
file:
- access_level: open_access
checksum: a4b3b7b36fbef068cabf4fb99501fef6
content_type: application/pdf
creator: dernst
date_created: 2023-04-25T09:13:53Z
date_updated: 2023-04-25T09:13:53Z
file_id: '12868'
file_name: 2023_NatureComm_Schmid.pdf
file_size: 1786475
relation: main_file
success: 1
file_date_updated: 2023-04-25T09:13:53Z
has_accepted_license: '1'
intvolume: ' 14'
isi: 1
language:
- iso: eng
month: '04'
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: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
publication: Nature Communications
publication_identifier:
eissn:
- 2041-1723
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantitative assessment can stabilize indirect reciprocity under imperfect
information
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 14
year: '2023'
...
---
_id: '12280'
abstract:
- lang: eng
text: 'In repeated interactions, players can use strategies that respond to the
outcome of previous rounds. Much of the existing literature on direct reciprocity
assumes that all competing individuals use the same strategy space. Here, we study
both learning and evolutionary dynamics of players that differ in the strategy
space they explore. We focus on the infinitely repeated donation game and compare
three natural strategy spaces: memory-1 strategies, which consider the last moves
of both players, reactive strategies, which respond to the last move of the co-player,
and unconditional strategies. These three strategy spaces differ in the memory
capacity that is needed. We compute the long term average payoff that is achieved
in a pairwise learning process. We find that smaller strategy spaces can dominate
larger ones. For weak selection, unconditional players dominate both reactive
and memory-1 players. For intermediate selection, reactive players dominate memory-1
players. Only for strong selection and low cost-to-benefit ratio, memory-1 players
dominate the others. We observe that the supergame between strategy spaces can
be a social dilemma: maximum payoff is achieved if both players explore a larger
strategy space, but smaller strategy spaces dominate.'
acknowledgement: "This work was supported by the European Research Council (https://erc.europa.eu/)\r\nCoG
863818 (ForM-SMArt) (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_number: e1010149
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: 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: Martin
full_name: Nowak, Martin
last_name: Nowak
citation:
ama: Schmid L, Hilbe C, Chatterjee K, Nowak M. Direct reciprocity between individuals
that use different strategy spaces. PLOS Computational Biology. 2022;18(6).
doi:10.1371/journal.pcbi.1010149
apa: Schmid, L., Hilbe, C., Chatterjee, K., & Nowak, M. (2022). Direct reciprocity
between individuals that use different strategy spaces. PLOS Computational
Biology. Public Library of Science. https://doi.org/10.1371/journal.pcbi.1010149
chicago: Schmid, Laura, Christian Hilbe, Krishnendu Chatterjee, and Martin Nowak.
“Direct Reciprocity between Individuals That Use Different Strategy Spaces.” PLOS
Computational Biology. Public Library of Science, 2022. https://doi.org/10.1371/journal.pcbi.1010149.
ieee: L. Schmid, C. Hilbe, K. Chatterjee, and M. Nowak, “Direct reciprocity between
individuals that use different strategy spaces,” PLOS Computational Biology,
vol. 18, no. 6. Public Library of Science, 2022.
ista: Schmid L, Hilbe C, Chatterjee K, Nowak M. 2022. Direct reciprocity between
individuals that use different strategy spaces. PLOS Computational Biology. 18(6),
e1010149.
mla: Schmid, Laura, et al. “Direct Reciprocity between Individuals That Use Different
Strategy Spaces.” PLOS Computational Biology, vol. 18, no. 6, e1010149,
Public Library of Science, 2022, doi:10.1371/journal.pcbi.1010149.
short: L. Schmid, C. Hilbe, K. Chatterjee, M. Nowak, PLOS Computational Biology
18 (2022).
date_created: 2023-01-16T10:02:51Z
date_published: 2022-06-14T00:00:00Z
date_updated: 2025-07-14T09:09:49Z
day: '14'
ddc:
- '000'
- '570'
department:
- _id: KrCh
doi: 10.1371/journal.pcbi.1010149
ec_funded: 1
external_id:
isi:
- '000843626800031'
pmid:
- '35700167'
file:
- access_level: open_access
checksum: 31b6b311b6731f1658277a9dfff6632c
content_type: application/pdf
creator: dernst
date_created: 2023-01-30T11:28:13Z
date_updated: 2023-01-30T11:28:13Z
file_id: '12460'
file_name: 2022_PlosCompBio_Schmid.pdf
file_size: 3143222
relation: main_file
success: 1
file_date_updated: 2023-01-30T11:28:13Z
has_accepted_license: '1'
intvolume: ' 18'
isi: 1
issue: '6'
keyword:
- Computational Theory and Mathematics
- Cellular and Molecular Neuroscience
- Genetics
- Molecular Biology
- Ecology
- Modeling and Simulation
- Ecology
- Evolution
- Behavior and Systematics
language:
- iso: eng
month: '06'
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'
publication: PLOS Computational Biology
publication_identifier:
eissn:
- 1553-7358
publication_status: published
publisher: Public Library of Science
quality_controlled: '1'
scopus_import: '1'
status: public
title: Direct reciprocity between individuals that use different strategy spaces
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 18
year: '2022'
...
---
_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. Nature Human Behaviour. 2021;5(10):1292–1302. doi:10.1038/s41562-021-01114-8
apa: Schmid, L., Chatterjee, K., Hilbe, C., & Nowak, M. A. (2021). A unified
framework of direct and indirect reciprocity. Nature Human Behaviour. Springer
Nature. https://doi.org/10.1038/s41562-021-01114-8
chicago: Schmid, Laura, Krishnendu Chatterjee, Christian Hilbe, and Martin A. Nowak.
“A Unified Framework of Direct and Indirect Reciprocity.” Nature Human Behaviour.
Springer Nature, 2021. https://doi.org/10.1038/s41562-021-01114-8.
ieee: L. Schmid, K. Chatterjee, C. Hilbe, and M. A. Nowak, “A unified framework
of direct and indirect reciprocity,” Nature Human Behaviour, 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.”
Nature Human Behaviour, vol. 5, no. 10, Springer Nature, 2021, pp. 1292–1302,
doi:10.1038/s41562-021-01114-8.
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'
...
---
_id: '9403'
abstract:
- lang: eng
text: Optimal decision making requires individuals to know their available options
and to anticipate correctly what consequences these options have. In many social
interactions, however, we refrain from gathering all relevant information, even
if this information would help us make better decisions and is costless to obtain.
This chapter examines several examples of “deliberate ignorance.” Two simple models
are proposed to illustrate how ignorance can evolve among self-interested and
payoff - maximizing individuals, and open problems are highlighted that lie ahead
for future research to explore.
article_processing_charge: No
author:
- first_name: Laura
full_name: Schmid, Laura
id: 38B437DE-F248-11E8-B48F-1D18A9856A87
last_name: Schmid
orcid: 0000-0002-6978-7329
- first_name: Christian
full_name: Hilbe, Christian
last_name: Hilbe
citation:
ama: 'Schmid L, Hilbe C. The evolution of strategic ignorance in strategic interaction.
In: Hertwig R, Engel C, eds. Deliberate Ignorance: Choosing Not To Know.
Vol 29. Strüngmann Forum Reports. MIT Press; 2021:139-152.'
apa: 'Schmid, L., & Hilbe, C. (2021). The evolution of strategic ignorance in
strategic interaction. In R. Hertwig & C. Engel (Eds.), Deliberate Ignorance:
Choosing Not To Know (Vol. 29, pp. 139–152). MIT Press.'
chicago: 'Schmid, Laura, and Christian Hilbe. “The Evolution of Strategic Ignorance
in Strategic Interaction.” In Deliberate Ignorance: Choosing Not To Know,
edited by Ralph Hertwig and Christoph Engel, 29:139–52. Strüngmann Forum Reports.
MIT Press, 2021.'
ieee: 'L. Schmid and C. Hilbe, “The evolution of strategic ignorance in strategic
interaction,” in Deliberate Ignorance: Choosing Not To Know, vol. 29, R.
Hertwig and C. Engel, Eds. MIT Press, 2021, pp. 139–152.'
ista: 'Schmid L, Hilbe C. 2021.The evolution of strategic ignorance in strategic
interaction. In: Deliberate Ignorance: Choosing Not To Know. vol. 29, 139–152.'
mla: 'Schmid, Laura, and Christian Hilbe. “The Evolution of Strategic Ignorance
in Strategic Interaction.” Deliberate Ignorance: Choosing Not To Know,
edited by Ralph Hertwig and Christoph Engel, vol. 29, MIT Press, 2021, pp. 139–52.'
short: 'L. Schmid, C. Hilbe, in:, R. Hertwig, C. Engel (Eds.), Deliberate Ignorance:
Choosing Not To Know, MIT Press, 2021, pp. 139–152.'
date_created: 2021-05-19T12:25:42Z
date_published: 2021-03-01T00:00:00Z
date_updated: 2023-02-23T13:57:04Z
day: '01'
department:
- _id: GradSch
- _id: KrCh
editor:
- first_name: Ralph
full_name: Hertwig, Ralph
last_name: Hertwig
- first_name: Christoph
full_name: Engel, Christoph
last_name: Engel
intvolume: ' 29'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://esforum.de/publications/PDFs/sfr29/SFR29_09_Hilbe%20and%20Schmid.pdf
month: '03'
oa: 1
oa_version: Published Version
page: 139-152
publication: 'Deliberate Ignorance: Choosing Not To Know'
publication_identifier:
isbn:
- 978-0-262-04559-9
publisher: MIT Press
quality_controlled: '1'
series_title: Strüngmann Forum Reports
status: public
title: The evolution of strategic ignorance in strategic interaction
type: book_chapter
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 29
year: '2021'
...
---
_id: '10293'
abstract:
- lang: eng
text: "Indirect reciprocity in evolutionary game theory is a prominent mechanism
for explaining the evolution of cooperation among unrelated individuals. In contrast
to direct reciprocity, which is based on individuals meeting repeatedly, and conditionally
cooperating by using their own experiences, indirect reciprocity is based on individuals’
reputations. If a player helps another, this increases the helper’s public standing,
benefitting them in the future. This lets cooperation in the population emerge
without individuals having to meet more than once. While the two modes of reciprocity
are intertwined, they are difficult to compare. Thus, they are usually studied
in isolation. Direct reciprocity can maintain cooperation with simple strategies,
and is robust against noise even when players do not remember more\r\nthan their
partner’s last action. Meanwhile, indirect reciprocity requires its successful
strategies, or social norms, to be more complex. Exhaustive search previously
identified eight such norms, called the “leading eight”, which excel at maintaining
cooperation. However, as the first result of this thesis, we show that the leading
eight break down once we remove the fundamental assumption that information is
synchronized and public, such that everyone agrees on reputations. Once we consider
a more realistic scenario of imperfect information, where reputations are private,
and individuals occasionally misinterpret or miss observations, the leading eight
do not promote cooperation anymore. Instead, minor initial disagreements can proliferate,
fragmenting populations into subgroups. In a next step, we consider ways to mitigate
this issue. We first explore whether introducing “generosity” can stabilize cooperation
when players use the leading eight strategies in noisy environments. This approach
of modifying strategies to include probabilistic elements for coping with errors
is known to work well in direct reciprocity. However, as we show here, it fails
for the more complex norms of indirect reciprocity. Imperfect information still
prevents cooperation from evolving. On the other hand, we succeeded to show in
this thesis that modifying the leading eight to use “quantitative assessment”,
i.e. tracking reputation scores on a scale beyond good and bad, and making overall
judgments of others based on a threshold, is highly successful, even when noise
increases in the environment. Cooperation can flourish when reputations\r\nare
more nuanced, and players have a broader understanding what it means to be “good.”
Finally, we present a single theoretical framework that unites the two modes of
reciprocity despite their differences. Within this framework, we identify a novel
simple and successful strategy for indirect reciprocity, which can cope with noisy
environments and has an analogue in direct reciprocity. We can also analyze decision
making when different sources of information are available. Our results help highlight
that for sustaining cooperation, already the most simple rules of reciprocity
can be sufficient."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Laura
full_name: Schmid, Laura
id: 38B437DE-F248-11E8-B48F-1D18A9856A87
last_name: Schmid
orcid: 0000-0002-6978-7329
citation:
ama: Schmid L. Evolution of cooperation via (in)direct reciprocity under imperfect
information. 2021. doi:10.15479/at:ista:10293
apa: Schmid, L. (2021). Evolution of cooperation via (in)direct reciprocity under
imperfect information. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10293
chicago: Schmid, Laura. “Evolution of Cooperation via (in)Direct Reciprocity under
Imperfect Information.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:10293.
ieee: L. Schmid, “Evolution of cooperation via (in)direct reciprocity under imperfect
information,” Institute of Science and Technology Austria, 2021.
ista: Schmid L. 2021. Evolution of cooperation via (in)direct reciprocity under
imperfect information. Institute of Science and Technology Austria.
mla: Schmid, Laura. Evolution of Cooperation via (in)Direct Reciprocity under
Imperfect Information. Institute of Science and Technology Austria, 2021,
doi:10.15479/at:ista:10293.
short: L. Schmid, Evolution of Cooperation via (in)Direct Reciprocity under Imperfect
Information, Institute of Science and Technology Austria, 2021.
date_created: 2021-11-15T17:12:57Z
date_published: 2021-11-17T00:00:00Z
date_updated: 2025-07-14T09:10:09Z
day: '17'
ddc:
- '519'
- '576'
degree_awarded: PhD
department:
- _id: GradSch
- _id: KrCh
doi: 10.15479/at:ista:10293
ec_funded: 1
file:
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checksum: 86a05b430756ca12ae8107b6e6f3c1e5
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language:
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month: '11'
oa: 1
oa_version: Published Version
page: '171'
project:
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '9997'
relation: part_of_dissertation
status: public
- id: '2'
relation: part_of_dissertation
status: public
- id: '9402'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
title: Evolution of cooperation via (in)direct reciprocity under imperfect information
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_id: '9997'
abstract:
- lang: eng
text: Indirect reciprocity is a mechanism for the evolution of cooperation based
on social norms. This mechanism requires that individuals in a population observe
and judge each other’s behaviors. Individuals with a good reputation are more
likely to receive help from others. Previous work suggests that indirect reciprocity
is only effective when all relevant information is reliable and publicly available.
Otherwise, individuals may disagree on how to assess others, even if they all
apply the same social norm. Such disagreements can lead to a breakdown of cooperation.
Here we explore whether the predominantly studied ‘leading eight’ social norms
of indirect reciprocity can be made more robust by equipping them with an element
of generosity. To this end, we distinguish between two kinds of generosity. According
to assessment generosity, individuals occasionally assign a good reputation to
group members who would usually be regarded as bad. According to action generosity,
individuals occasionally cooperate with group members with whom they would usually
defect. Using individual-based simulations, we show that the two kinds of generosity
have a very different effect on the resulting reputation dynamics. Assessment
generosity tends to add to the overall noise and allows defectors to invade. In
contrast, a limited amount of action generosity can be beneficial in a few cases.
However, even when action generosity is beneficial, the respective simulations
do not result in full cooperation. Our results suggest that while generosity can
favor cooperation when individuals use the most simple strategies of reciprocity,
it is disadvantageous when individuals use more complex social norms.
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.). L.S. received additional partial support by the Austrian Science
Fund (FWF) under Grant Z211-N23 (Wittgenstein Award).'
article_number: '17443'
article_processing_charge: Yes
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: Pouya
full_name: Shati, Pouya
last_name: Shati
- first_name: Christian
full_name: Hilbe, Christian
last_name: Hilbe
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
citation:
ama: Schmid L, Shati P, Hilbe C, Chatterjee K. The evolution of indirect reciprocity
under action and assessment generosity. Scientific Reports. 2021;11(1).
doi:10.1038/s41598-021-96932-1
apa: Schmid, L., Shati, P., Hilbe, C., & Chatterjee, K. (2021). The evolution
of indirect reciprocity under action and assessment generosity. Scientific
Reports. Springer Nature. https://doi.org/10.1038/s41598-021-96932-1
chicago: Schmid, Laura, Pouya Shati, Christian Hilbe, and Krishnendu Chatterjee.
“The Evolution of Indirect Reciprocity under Action and Assessment Generosity.”
Scientific Reports. Springer Nature, 2021. https://doi.org/10.1038/s41598-021-96932-1.
ieee: L. Schmid, P. Shati, C. Hilbe, and K. Chatterjee, “The evolution of indirect
reciprocity under action and assessment generosity,” Scientific Reports,
vol. 11, no. 1. Springer Nature, 2021.
ista: Schmid L, Shati P, Hilbe C, Chatterjee K. 2021. The evolution of indirect
reciprocity under action and assessment generosity. Scientific Reports. 11(1),
17443.
mla: Schmid, Laura, et al. “The Evolution of Indirect Reciprocity under Action and
Assessment Generosity.” Scientific Reports, vol. 11, no. 1, 17443, Springer
Nature, 2021, doi:10.1038/s41598-021-96932-1.
short: L. Schmid, P. Shati, C. Hilbe, K. Chatterjee, Scientific Reports 11 (2021).
date_created: 2021-09-11T16:22:02Z
date_published: 2021-08-31T00:00:00Z
date_updated: 2025-07-14T09:10:09Z
day: '31'
ddc:
- '003'
department:
- _id: GradSch
- _id: KrCh
doi: 10.1038/s41598-021-96932-1
ec_funded: 1
external_id:
isi:
- '000692406400018'
pmid:
- '34465830'
file:
- access_level: open_access
checksum: 19df8816cf958b272b85841565c73182
content_type: application/pdf
creator: cchlebak
date_created: 2021-09-13T10:31:21Z
date_updated: 2021-09-13T10:31:21Z
file_id: '10006'
file_name: 2021_ScientificReports_Schmid.pdf
file_size: 2424943
relation: main_file
success: 1
file_date_updated: 2021-09-13T10:31:21Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
issue: '1'
keyword:
- Multidisciplinary
language:
- iso: eng
month: '08'
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: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
publication: Scientific Reports
publication_identifier:
eissn:
- 2045-2322
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '10293'
relation: dissertation_contains
status: public
status: public
title: The evolution of indirect reciprocity under action and assessment generosity
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 11
year: '2021'
...
---
_id: '7346'
abstract:
- lang: eng
text: 'The Price of Anarchy (PoA) is a well-established game-theoretic concept to
shed light on coordination issues arising in open distributed systems. Leaving
agents to selfishly optimize comes with the risk of ending up in sub-optimal states
(in terms of performance and/or costs), compared to a centralized system design.
However, the PoA relies on strong assumptions about agents'' rationality (e.g.,
resources and information) and interactions, whereas in many distributed systems
agents interact locally with bounded resources. They do so repeatedly over time
(in contrast to "one-shot games"), and their strategies may evolve. Using a more
realistic evolutionary game model, this paper introduces a realized evolutionary
Price of Anarchy (ePoA). The ePoA allows an exploration of equilibrium selection
in dynamic distributed systems with multiple equilibria, based on local interactions
of simple memoryless agents. Considering a fundamental game related to virus propagation
on networks, we present analytical bounds on the ePoA in basic network topologies
and for different strategy update dynamics. In particular, deriving stationary
distributions of the stochastic evolutionary process, we find that the Nash equilibria
are not always the most abundant states, and that different processes can feature
significant off-equilibrium behavior, leading to a significantly higher ePoA compared
to the PoA studied traditionally in the literature. '
alternative_title:
- LIPIcs
article_number: '21'
article_processing_charge: No
arxiv: 1
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: Stefan
full_name: Schmid, Stefan
last_name: Schmid
citation:
ama: 'Schmid L, Chatterjee K, Schmid S. The evolutionary price of anarchy: Locally
bounded agents in a dynamic virus game. In: Proceedings of the 23rd International
Conference on Principles of Distributed Systems. Vol 153. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.OPODIS.2019.21'
apa: 'Schmid, L., Chatterjee, K., & Schmid, S. (2020). The evolutionary price
of anarchy: Locally bounded agents in a dynamic virus game. In Proceedings
of the 23rd International Conference on Principles of Distributed Systems
(Vol. 153). Neuchâtel, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.OPODIS.2019.21'
chicago: 'Schmid, Laura, Krishnendu Chatterjee, and Stefan Schmid. “The Evolutionary
Price of Anarchy: Locally Bounded Agents in a Dynamic Virus Game.” In Proceedings
of the 23rd International Conference on Principles of Distributed Systems,
Vol. 153. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.OPODIS.2019.21.'
ieee: 'L. Schmid, K. Chatterjee, and S. Schmid, “The evolutionary price of anarchy:
Locally bounded agents in a dynamic virus game,” in Proceedings of the 23rd
International Conference on Principles of Distributed Systems, Neuchâtel,
Switzerland, 2020, vol. 153.'
ista: 'Schmid L, Chatterjee K, Schmid S. 2020. The evolutionary price of anarchy:
Locally bounded agents in a dynamic virus game. Proceedings of the 23rd International
Conference on Principles of Distributed Systems. OPODIS: International Conference
on Principles of Distributed Systems, LIPIcs, vol. 153, 21.'
mla: 'Schmid, Laura, et al. “The Evolutionary Price of Anarchy: Locally Bounded
Agents in a Dynamic Virus Game.” Proceedings of the 23rd International Conference
on Principles of Distributed Systems, vol. 153, 21, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2020, doi:10.4230/LIPIcs.OPODIS.2019.21.'
short: L. Schmid, K. Chatterjee, S. Schmid, in:, Proceedings of the 23rd International
Conference on Principles of Distributed Systems, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2020.
conference:
end_date: 2019-12-19
location: Neuchâtel, Switzerland
name: 'OPODIS: International Conference on Principles of Distributed Systems'
start_date: 2019-12-17
date_created: 2020-01-21T16:00:26Z
date_published: 2020-02-10T00:00:00Z
date_updated: 2023-02-23T13:05:49Z
day: '10'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.OPODIS.2019.21
external_id:
arxiv:
- '1906.00110'
file:
- access_level: open_access
checksum: 9a91916ac2c21ab42458fcda39ef0b8d
content_type: application/pdf
creator: dernst
date_created: 2020-03-23T09:14:06Z
date_updated: 2020-07-14T12:47:56Z
file_id: '7608'
file_name: 2019_LIPIcS_Schmid.pdf
file_size: 630752
relation: main_file
file_date_updated: 2020-07-14T12:47:56Z
has_accepted_license: '1'
intvolume: ' 153'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
publication: Proceedings of the 23rd International Conference on Principles of Distributed
Systems
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The evolutionary price of anarchy: Locally bounded agents in a dynamic virus
game'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 153
year: '2020'
...
---
_id: '2'
abstract:
- lang: eng
text: Indirect reciprocity explores how humans act when their reputation is at stake,
and which social norms they use to assess the actions of others. A crucial question
in indirect reciprocity is which social norms can maintain stable cooperation
in a society. Past research has highlighted eight such norms, called “leading-eight”
strategies. This past research, however, is based on the assumption that all relevant
information about other population members is publicly available and that everyone
agrees on who is good or bad. Instead, here we explore the reputation dynamics
when information is private and noisy. We show that under these conditions, most
leading-eight strategies fail to evolve. Those leading-eight strategies that do
evolve are unable to sustain full cooperation.Indirect reciprocity is a mechanism
for cooperation based on shared moral systems and individual reputations. It assumes
that members of a community routinely observe and assess each other and that they
use this information to decide who is good or bad, and who deserves cooperation.
When information is transmitted publicly, such that all community members agree
on each other’s reputation, previous research has highlighted eight crucial moral
systems. These “leading-eight” strategies can maintain cooperation and resist
invasion by defectors. However, in real populations individuals often hold their
own private views of others. Once two individuals disagree about their opinion
of some third party, they may also see its subsequent actions in a different light.
Their opinions may further diverge over time. Herein, we explore indirect reciprocity
when information transmission is private and noisy. We find that in the presence
of perception errors, most leading-eight strategies cease to be stable. Even if
a leading-eight strategy evolves, cooperation rates may drop considerably when
errors are common. Our research highlights the role of reliable information and
synchronized reputations to maintain stable moral systems.
article_processing_charge: No
author:
- first_name: Christian
full_name: Hilbe, Christian
id: 2FDF8F3C-F248-11E8-B48F-1D18A9856A87
last_name: Hilbe
orcid: 0000-0001-5116-955X
- first_name: Laura
full_name: Schmid, Laura
id: 38B437DE-F248-11E8-B48F-1D18A9856A87
last_name: Schmid
orcid: 0000-0002-6978-7329
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Martin
full_name: Nowak, Martin
last_name: Nowak
citation:
ama: Hilbe C, Schmid L, Tkadlec J, Chatterjee K, Nowak M. Indirect reciprocity with
private, noisy, and incomplete information. PNAS. 2018;115(48):12241-12246.
doi:10.1073/pnas.1810565115
apa: Hilbe, C., Schmid, L., Tkadlec, J., Chatterjee, K., & Nowak, M. (2018).
Indirect reciprocity with private, noisy, and incomplete information. PNAS.
National Academy of Sciences. https://doi.org/10.1073/pnas.1810565115
chicago: Hilbe, Christian, Laura Schmid, Josef Tkadlec, Krishnendu Chatterjee, and
Martin Nowak. “Indirect Reciprocity with Private, Noisy, and Incomplete Information.”
PNAS. National Academy of Sciences, 2018. https://doi.org/10.1073/pnas.1810565115.
ieee: C. Hilbe, L. Schmid, J. Tkadlec, K. Chatterjee, and M. Nowak, “Indirect reciprocity
with private, noisy, and incomplete information,” PNAS, vol. 115, no. 48.
National Academy of Sciences, pp. 12241–12246, 2018.
ista: Hilbe C, Schmid L, Tkadlec J, Chatterjee K, Nowak M. 2018. Indirect reciprocity
with private, noisy, and incomplete information. PNAS. 115(48), 12241–12246.
mla: Hilbe, Christian, et al. “Indirect Reciprocity with Private, Noisy, and Incomplete
Information.” PNAS, vol. 115, no. 48, National Academy of Sciences, 2018,
pp. 12241–46, doi:10.1073/pnas.1810565115.
short: C. Hilbe, L. Schmid, J. Tkadlec, K. Chatterjee, M. Nowak, PNAS 115 (2018)
12241–12246.
date_created: 2018-12-11T11:44:05Z
date_published: 2018-11-27T00:00:00Z
date_updated: 2025-07-14T09:10:09Z
day: '27'
department:
- _id: KrCh
doi: 10.1073/pnas.1810565115
ec_funded: 1
external_id:
isi:
- '000451351000063'
pmid:
- '30429320'
intvolume: ' 115'
isi: 1
issue: '48'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.ncbi.nlm.nih.gov/pubmed/30429320
month: '11'
oa: 1
oa_version: Submitted Version
page: 12241-12246
pmid: 1
project:
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: PNAS
publication_status: published
publisher: National Academy of Sciences
quality_controlled: '1'
related_material:
link:
- description: News on IST Homepage
relation: press_release
url: https://ist.ac.at/en/news/no-cooperation-without-open-communication/
record:
- id: '10293'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Indirect reciprocity with private, noisy, and incomplete information
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 115
year: '2018'
...