---
OA_place: publisher
OA_type: hybrid
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abstract:
- lang: eng
  text: 'The public goods game is among the most studied metaphors of cooperation
    in groups. In this game, individuals can use their endowments to make contributions
    towards a good that benefits everyone. Each individual, however, is tempted to
    free-ride on the contributions of others. Herein, we study repeated public goods
    games among asymmetric players. Previous work has explored to which extent asymmetry
    allows for full cooperation, such that players contribute their full endowment
    each round. However, by design that work focusses on equilibria where individuals
    make the same contribution each round. Instead, here we consider players whose
    contributions along the equilibrium path can change from one round to the next.
    We do so for three different models – one without any budget constraints, one
    with endowment constraints, and one in which individuals can save their current
    endowment to be used in subsequent rounds. In each case, we explore two key quantities:
    the welfare and the resource efficiency that can be achieved in equilibrium. Welfare
    corresponds to the sum of all players’ payoffs. Resource efficiency relates this
    welfare to the total contributions made by the players. Compared to constant contribution
    sequences, we find that time-dependent contributions can improve resource efficiency
    across all three models. Moreover, they can improve the players’ welfare in the
    model with savings.'
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 programme
  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),
  and ARC SRIEAS Grant SR200100005 Securing Antarctica’s Environmental Future (to
  M.K.). Open access funding provided by Institute of Science and Technology (IST
  Austria).'
article_processing_charge: Yes (via OA deal)
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: Christian
  full_name: Hilbe, Christian
  id: 2FDF8F3C-F248-11E8-B48F-1D18A9856A87
  last_name: Hilbe
  orcid: 0000-0001-5116-955X
- first_name: Manuel
  full_name: Staab, Manuel
  last_name: Staab
- first_name: Maria
  full_name: Kleshnina, Maria
  id: 4E21749C-F248-11E8-B48F-1D18A9856A87
  last_name: Kleshnina
  orcid: 0000-0002-5518-8317
- first_name: Krishnendu
  full_name: Chatterjee, Krishnendu
  id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
  last_name: Chatterjee
  orcid: 0000-0002-4561-241X
citation:
  ama: Hübner V, Hilbe C, Staab M, Kleshnina M, Chatterjee K. Time-dependent strategies
    in repeated asymmetric public goods games. <i>Dynamic Games and Applications</i>.
    2025;15:1617-1645. doi:<a href="https://doi.org/10.1007/s13235-025-00627-5">10.1007/s13235-025-00627-5</a>
  apa: Hübner, V., Hilbe, C., Staab, M., Kleshnina, M., &#38; Chatterjee, K. (2025).
    Time-dependent strategies in repeated asymmetric public goods games. <i>Dynamic
    Games and Applications</i>. Springer Nature. <a href="https://doi.org/10.1007/s13235-025-00627-5">https://doi.org/10.1007/s13235-025-00627-5</a>
  chicago: Hübner, Valentin, Christian Hilbe, Manuel Staab, Maria Kleshnina, and Krishnendu
    Chatterjee. “Time-Dependent Strategies in Repeated Asymmetric Public Goods Games.”
    <i>Dynamic Games and Applications</i>. Springer Nature, 2025. <a href="https://doi.org/10.1007/s13235-025-00627-5">https://doi.org/10.1007/s13235-025-00627-5</a>.
  ieee: V. Hübner, C. Hilbe, M. Staab, M. Kleshnina, and K. Chatterjee, “Time-dependent
    strategies in repeated asymmetric public goods games,” <i>Dynamic Games and Applications</i>,
    vol. 15. Springer Nature, pp. 1617–1645, 2025.
  ista: Hübner V, Hilbe C, Staab M, Kleshnina M, Chatterjee K. 2025. Time-dependent
    strategies in repeated asymmetric public goods games. Dynamic Games and Applications.
    15, 1617–1645.
  mla: Hübner, Valentin, et al. “Time-Dependent Strategies in Repeated Asymmetric
    Public Goods Games.” <i>Dynamic Games and Applications</i>, vol. 15, Springer
    Nature, 2025, pp. 1617–45, doi:<a href="https://doi.org/10.1007/s13235-025-00627-5">10.1007/s13235-025-00627-5</a>.
  short: V. Hübner, C. Hilbe, M. Staab, M. Kleshnina, K. Chatterjee, Dynamic Games
    and Applications 15 (2025) 1617–1645.
corr_author: '1'
date_created: 2025-02-23T23:01:57Z
date_published: 2025-11-01T00:00:00Z
date_updated: 2026-09-16T06:58:23Z
day: '01'
ddc:
- '000'
department:
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doi: 10.1007/s13235-025-00627-5
ec_funded: 1
external_id:
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  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Dynamic Games and Applications
publication_identifier:
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  issn:
  - 2153-0785
publication_status: published
publisher: Springer Nature
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title: Time-dependent strategies in repeated asymmetric public goods games
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '19508'
abstract:
- lang: eng
  text: We consider random two-player zero-sum dynamic games with perfect information
    on a class of infinite directed graphs. Starting from a fixed vertex, the players
    take turns to move a token along the edges of the graph. Every vertex is assigned
    a payoff known in advance by both players. Every time the token visits a vertex,
    Player 2 pays Player 1 the corresponding payoff. We consider a distribution over
    such games by assigning i.i.d. payoffs to the vertices. On the one hand, for acyclic
    directed graphs of bounded degree and sub-exponential expansion, we show that,
    when the duration of the game tends to infinity, the value converges almost surely
    to a constant at an exponential rate dominated in terms of the expansion. On the
    other hand, for the infinite d-ary tree (that does not fall into the previous
    class of graphs), we show convergence at a double-exponential rate.
acknowledgement: Open access funding provided by Institute of Science and Technology
  (IST Austria). This work was supported by the French Agence Nationale de la Recherche
  (ANR) under references ANR-21-CE40-0020 (CONVERGENCE project) and ANR-20-CE40-0002
  (GrHyDy), by Fondecyt grant 1220174, by ANID Chile grant ACT210005, and by the ERC
  CoG 863818 (ForM-SMArt) grant. This collaboration was mainly conducted during a
  1-year visit of Bruno Ziliotto to the Center for Mathematical Modeling (CMM) at
  University of Chile in 2023, under the IRL program of CNRS. This work was supported
  by Fondation CFM pour la Recherche. This paper has also been funded by the Agence
  Nationale de la Recherche under grant ANR-17-EURE-0010 (Investissements d’Avenir
  program).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Luc
  full_name: Attia, Luc
  last_name: Attia
- first_name: Lyuben
  full_name: Lichev, Lyuben
  id: 9aa8388e-d003-11ee-8458-c4c1d7447977
  last_name: Lichev
- first_name: Dieter
  full_name: Mitsche, Dieter
  last_name: Mitsche
- first_name: Raimundo J
  full_name: Saona Urmeneta, Raimundo J
  id: BD1DF4C4-D767-11E9-B658-BC13E6697425
  last_name: Saona Urmeneta
  orcid: 0000-0001-5103-038X
- first_name: Bruno
  full_name: Ziliotto, Bruno
  last_name: Ziliotto
citation:
  ama: Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. Random zero-sum
    dynamic games on infinite directed graphs. <i>Dynamic Games and Applications</i>.
    2025;15:1517-1535. doi:<a href="https://doi.org/10.1007/s13235-025-00636-4">10.1007/s13235-025-00636-4</a>
  apa: Attia, L., Lichev, L., Mitsche, D., Saona Urmeneta, R. J., &#38; Ziliotto,
    B. (2025). Random zero-sum dynamic games on infinite directed graphs. <i>Dynamic
    Games and Applications</i>. Springer Nature. <a href="https://doi.org/10.1007/s13235-025-00636-4">https://doi.org/10.1007/s13235-025-00636-4</a>
  chicago: Attia, Luc, Lyuben Lichev, Dieter Mitsche, Raimundo J Saona Urmeneta, and
    Bruno Ziliotto. “Random Zero-Sum Dynamic Games on Infinite Directed Graphs.” <i>Dynamic
    Games and Applications</i>. Springer Nature, 2025. <a href="https://doi.org/10.1007/s13235-025-00636-4">https://doi.org/10.1007/s13235-025-00636-4</a>.
  ieee: L. Attia, L. Lichev, D. Mitsche, R. J. Saona Urmeneta, and B. Ziliotto, “Random
    zero-sum dynamic games on infinite directed graphs,” <i>Dynamic Games and Applications</i>,
    vol. 15. Springer Nature, pp. 1517–1535, 2025.
  ista: Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. 2025. Random
    zero-sum dynamic games on infinite directed graphs. Dynamic Games and Applications.
    15, 1517–1535.
  mla: Attia, Luc, et al. “Random Zero-Sum Dynamic Games on Infinite Directed Graphs.”
    <i>Dynamic Games and Applications</i>, vol. 15, Springer Nature, 2025, pp. 1517–35,
    doi:<a href="https://doi.org/10.1007/s13235-025-00636-4">10.1007/s13235-025-00636-4</a>.
  short: L. Attia, L. Lichev, D. Mitsche, R.J. Saona Urmeneta, B. Ziliotto, Dynamic
    Games and Applications 15 (2025) 1517–1535.
corr_author: '1'
date_created: 2025-04-06T22:01:32Z
date_published: 2025-11-01T00:00:00Z
date_updated: 2026-09-16T07:00:33Z
day: '01'
ddc:
- '000'
department:
- _id: MaKw
- _id: KrCh
doi: 10.1007/s13235-025-00636-4
ec_funded: 1
external_id:
  isi:
  - '001449708900001'
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publication: Dynamic Games and Applications
publication_identifier:
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  issn:
  - 2153-0785
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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title: Random zero-sum dynamic games on infinite directed graphs
tmp:
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2025'
...
---
_id: '10770'
abstract:
- lang: eng
  text: Mathematical models often aim to describe a complicated mechanism in a cohesive
    and simple manner. However, reaching perfect balance between being simple enough
    or overly simplistic is a challenging task. Frequently, game-theoretic models
    have an underlying assumption that players, whenever they choose to execute a
    specific action, do so perfectly. In fact, it is rare that action execution perfectly
    coincides with intentions of individuals, giving rise to behavioural mistakes.
    The concept of incompetence of players was suggested to address this issue in
    game-theoretic settings. Under the assumption of incompetence, players have non-zero
    probabilities of executing a different strategy from the one they chose, leading
    to stochastic outcomes of the interactions. In this article, we survey results
    related to the concept of incompetence in classic as well as evolutionary game
    theory and provide several new results. We also suggest future extensions of the
    model and argue why it is important to take into account behavioural mistakes
    when analysing interactions among players in both economic and biological settings.
acknowledgement: "The authors would like to acknowledge stimulating email discussions
  with Dr Wayne Lobb of W.A. Lobb LLC on the topic of evolutionary games. We also
  thank Dr Thomas Taimre for his input to the material in Sect. 3.\r\nThe authors
  would like to acknowledge partial support from the Australian Research Council under
  the Discovery grant DP180101602 and support by the European Union’s Horizon 2020
  research and innovation program under the Marie Sklodowska-Curie Grant Agreement
  #754411."
article_processing_charge: No
article_type: original
author:
- first_name: Thomas
  full_name: Graham, Thomas
  last_name: Graham
- first_name: Maria
  full_name: Kleshnina, Maria
  id: 4E21749C-F248-11E8-B48F-1D18A9856A87
  last_name: Kleshnina
- first_name: Jerzy A.
  full_name: Filar, Jerzy A.
  last_name: Filar
citation:
  ama: Graham T, Kleshnina M, Filar JA. Where do mistakes lead? A survey of games
    with incompetent players. <i>Dynamic Games and Applications</i>. 2023;13:231-264.
    doi:<a href="https://doi.org/10.1007/s13235-022-00425-3">10.1007/s13235-022-00425-3</a>
  apa: Graham, T., Kleshnina, M., &#38; Filar, J. A. (2023). Where do mistakes lead?
    A survey of games with incompetent players. <i>Dynamic Games and Applications</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s13235-022-00425-3">https://doi.org/10.1007/s13235-022-00425-3</a>
  chicago: Graham, Thomas, Maria Kleshnina, and Jerzy A. Filar. “Where Do Mistakes
    Lead? A Survey of Games with Incompetent Players.” <i>Dynamic Games and Applications</i>.
    Springer Nature, 2023. <a href="https://doi.org/10.1007/s13235-022-00425-3">https://doi.org/10.1007/s13235-022-00425-3</a>.
  ieee: T. Graham, M. Kleshnina, and J. A. Filar, “Where do mistakes lead? A survey
    of games with incompetent players,” <i>Dynamic Games and Applications</i>, vol.
    13. Springer Nature, pp. 231–264, 2023.
  ista: Graham T, Kleshnina M, Filar JA. 2023. Where do mistakes lead? A survey of
    games with incompetent players. Dynamic Games and Applications. 13, 231–264.
  mla: Graham, Thomas, et al. “Where Do Mistakes Lead? A Survey of Games with Incompetent
    Players.” <i>Dynamic Games and Applications</i>, vol. 13, Springer Nature, 2023,
    pp. 231–64, doi:<a href="https://doi.org/10.1007/s13235-022-00425-3">10.1007/s13235-022-00425-3</a>.
  short: T. Graham, M. Kleshnina, J.A. Filar, Dynamic Games and Applications 13 (2023)
    231–264.
date_created: 2022-02-20T23:01:32Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2025-04-14T07:43:48Z
day: '01'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.1007/s13235-022-00425-3
ec_funded: 1
external_id:
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isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 231-264
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Dynamic Games and Applications
publication_identifier:
  eissn:
  - 2153-0793
  issn:
  - 2153-0785
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Where do mistakes lead? A survey of games with incompetent players
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  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 13
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...