---
_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. <i>PLOS Computational Biology</i>. 2022;18(6).
    doi:<a href="https://doi.org/10.1371/journal.pcbi.1010149">10.1371/journal.pcbi.1010149</a>
  apa: Schmid, L., Hilbe, C., Chatterjee, K., &#38; Nowak, M. (2022). Direct reciprocity
    between individuals that use different strategy spaces. <i>PLOS Computational
    Biology</i>. Public Library of Science. <a href="https://doi.org/10.1371/journal.pcbi.1010149">https://doi.org/10.1371/journal.pcbi.1010149</a>
  chicago: Schmid, Laura, Christian Hilbe, Krishnendu Chatterjee, and Martin Nowak.
    “Direct Reciprocity between Individuals That Use Different Strategy Spaces.” <i>PLOS
    Computational Biology</i>. Public Library of Science, 2022. <a href="https://doi.org/10.1371/journal.pcbi.1010149">https://doi.org/10.1371/journal.pcbi.1010149</a>.
  ieee: L. Schmid, C. Hilbe, K. Chatterjee, and M. Nowak, “Direct reciprocity between
    individuals that use different strategy spaces,” <i>PLOS Computational Biology</i>,
    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.” <i>PLOS Computational Biology</i>, vol. 18, no. 6, e1010149,
    Public Library of Science, 2022, doi:<a href="https://doi.org/10.1371/journal.pcbi.1010149">10.1371/journal.pcbi.1010149</a>.
  short: L. Schmid, C. Hilbe, K. Chatterjee, M. Nowak, PLOS Computational Biology
    18 (2022).
corr_author: '1'
date_created: 2023-01-16T10:02:51Z
date_published: 2022-06-14T00:00:00Z
date_updated: 2025-04-14T07:52:47Z
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
fulldoi: https://doi.org/10.1371/journal.pcbi.1010149
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'
...