---
_id: '2817'
abstract:
- lang: eng
  text: The basic idea of evolutionary game theory is that payoff determines reproductive
    rate. Successful individuals have a higher payoff and produce more offspring.
    But in evolutionary and ecological situations there is not only reproductive rate
    but also carrying capacity. Individuals may differ in their exposure to density
    limiting effects. Here we explore an alternative approach to evolutionary game
    theory by assuming that the payoff from the game determines the carrying capacity
    of individual phenotypes. Successful strategies are less affected by density limitation
    (crowding) and reach higher equilibrium abundance. We demonstrate similarities
    and differences between our framework and the standard replicator equation. Our
    equation is defined on the positive orthant, instead of the simplex, but has the
    same equilibrium points as the replicator equation. Linear stability analysis
    produces the classical conditions for asymptotic stability of pure strategies,
    but the stability properties of internal equilibria can differ in the two frameworks.
    For example, in a two-strategy game with an internal equilibrium that is always
    stable under the replicator equation, the corresponding equilibrium can be unstable
    in the new framework resulting in a limit cycle.
article_processing_charge: No
author:
- first_name: Sebastian
  full_name: Novak, Sebastian
  id: 461468AE-F248-11E8-B48F-1D18A9856A87
  last_name: Novak
  orcid: 0000-0002-2519-824X
- 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: Novak S, Chatterjee K, Nowak M. Density games. <i>Journal of Theoretical Biology</i>.
    2013;334:26-34. doi:<a href="https://doi.org/10.1016/j.jtbi.2013.05.029">10.1016/j.jtbi.2013.05.029</a>
  apa: Novak, S., Chatterjee, K., &#38; Nowak, M. (2013). Density games. <i>Journal
    of Theoretical Biology</i>. Elsevier. <a href="https://doi.org/10.1016/j.jtbi.2013.05.029">https://doi.org/10.1016/j.jtbi.2013.05.029</a>
  chicago: Novak, Sebastian, Krishnendu Chatterjee, and Martin Nowak. “Density Games.”
    <i>Journal of Theoretical Biology</i>. Elsevier, 2013. <a href="https://doi.org/10.1016/j.jtbi.2013.05.029">https://doi.org/10.1016/j.jtbi.2013.05.029</a>.
  ieee: S. Novak, K. Chatterjee, and M. Nowak, “Density games,” <i>Journal of Theoretical
    Biology</i>, vol. 334. Elsevier, pp. 26–34, 2013.
  ista: Novak S, Chatterjee K, Nowak M. 2013. Density games. Journal of Theoretical
    Biology. 334, 26–34.
  mla: Novak, Sebastian, et al. “Density Games.” <i>Journal of Theoretical Biology</i>,
    vol. 334, Elsevier, 2013, pp. 26–34, doi:<a href="https://doi.org/10.1016/j.jtbi.2013.05.029">10.1016/j.jtbi.2013.05.029</a>.
  short: S. Novak, K. Chatterjee, M. Nowak, Journal of Theoretical Biology 334 (2013)
    26–34.
corr_author: '1'
date_created: 2018-12-11T11:59:45Z
date_published: 2013-10-07T00:00:00Z
date_updated: 2025-09-29T13:59:11Z
day: '07'
ddc:
- '000'
department:
- _id: NiBa
- _id: KrCh
doi: 10.1016/j.jtbi.2013.05.029
ec_funded: 1
external_id:
  isi:
  - '000323629500003'
file:
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  checksum: 3c29059ab03a4b8f97a07646b817ddbb
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  creator: system
  date_created: 2018-12-12T10:14:54Z
  date_updated: 2020-07-14T12:45:49Z
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file_date_updated: 2020-07-14T12:45:49Z
fulldoi: https://doi.org/10.1016/j.jtbi.2013.05.029
has_accepted_license: '1'
intvolume: '       334'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 26 - 34
project:
- _id: 25B07788-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '250152'
  name: Limits to selection in biology and in evolutionary computation
- _id: 2584A770-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P 23499-N23
  name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: S11407
  name: Game Theory
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '279307'
  name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2587B514-B435-11E9-9278-68D0E5697425
  name: Microsoft Research Faculty Fellowship
publication: Journal of Theoretical Biology
publication_status: published
publisher: Elsevier
publist_id: '3984'
pubrep_id: '400'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Density games
tmp:
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  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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 334
year: '2013'
...