IDEAS home Printed from https://ideas.repec.org/a/plo/pcbi00/1004232.html
   My bibliography  Save this article

The Effect of Incentives and Meta-incentives on the Evolution of Cooperation

Author

Listed:
  • Isamu Okada
  • Hitoshi Yamamoto
  • Fujio Toriumi
  • Tatsuya Sasaki

Abstract

Although positive incentives for cooperators and/or negative incentives for free-riders in social dilemmas play an important role in maintaining cooperation, there is still the outstanding issue of who should pay the cost of incentives. The second-order free-rider problem, in which players who do not provide the incentives dominate in a game, is a well-known academic challenge. In order to meet this challenge, we devise and analyze a meta-incentive game that integrates positive incentives (rewards) and negative incentives (punishments) with second-order incentives, which are incentives for other players’ incentives. The critical assumption of our model is that players who tend to provide incentives to other players for their cooperative or non-cooperative behavior also tend to provide incentives to their incentive behaviors. In this paper, we solve the replicator dynamics for a simple version of the game and analytically categorize the game types into four groups. We find that the second-order free-rider problem is completely resolved without any third-order or higher (meta) incentive under the assumption. To do so, a second-order costly incentive, which is given individually (peer-to-peer) after playing donation games, is needed. The paper concludes that (1) second-order incentives for first-order reward are necessary for cooperative regimes, (2) a system without first-order rewards cannot maintain a cooperative regime, (3) a system with first-order rewards and no incentives for rewards is the worst because it never reaches cooperation, and (4) a system with rewards for incentives is more likely to be a cooperative regime than a system with punishments for incentives when the cost-effect ratio of incentives is sufficiently large. This solution is general and strong in the sense that the game does not need any centralized institution or proactive system for incentives.Author Summary: Although social dilemmas can be resolved if punishing non-cooperators or rewarding cooperators works, such rewards and punishments, i.e., external incentives, entail certain expenses. As a result, a cooperative player who shirks his or her duty to provide an incentive to other players will emerge, and he or she will be more advantageous than an incentive-provider. In fact, the problem of excluding such cooperative incentive-non-providers, or second-order free-riders, is a well-known academic challenge. In order to meet this challenge, we devise and analyze a meta-incentive game that integrates positive incentives (rewards) and negative incentives (punishments) with second-order incentives, which are incentives for other players’ incentives. In this paper, we solve the replicator dynamics for a simple version of the game and analytically categorize the game types into four groups. We show that second-order incentives for first-order reward are necessary for cooperative regimes. This solution is general and strong in the sense that the game does not need any centralized institution or proactive system for incentives.

Suggested Citation

  • Isamu Okada & Hitoshi Yamamoto & Fujio Toriumi & Tatsuya Sasaki, 2015. "The Effect of Incentives and Meta-incentives on the Evolution of Cooperation," PLOS Computational Biology, Public Library of Science, vol. 11(5), pages 1-17, May.
    • Handle: RePEc:plo:pcbi00:1004232
    DOI: 10.1371/journal.pcbi.1004232
    as

    Download full text from publisher

    File URL: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004232
    Download Restriction: no
    File URL: https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1004232&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pcbi.1004232?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    2. Rick L. Riolo & Michael D. Cohen & Robert Axelrod, 2001. "Evolution of cooperation without reciprocity," Nature, Nature, vol. 414(6862), pages 441-443, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiaojie Chen & Attila Szolnoki, 2018. "Punishment and inspection for governing the commons in a feedback-evolving game," PLOS Computational Biology, Public Library of Science, vol. 14(7), pages 1-15, July.
    2. Satoshi Uchida & Hitoshi Yamamoto & Isamu Okada & Tatsuya Sasaki, 2019. "Evolution of Cooperation with Peer Punishment under Prospect Theory," Games, MDPI, vol. 10(1), pages 1-13, February.
    3. Isamu Okada, 2020. "A Review of Theoretical Studies on Indirect Reciprocity," Games, MDPI, vol. 11(3), pages 1-17, July.
    4. Saptarshi Pal & Christian Hilbe, 2022. "Reputation effects drive the joint evolution of cooperation and social rewarding," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    5. Hitoshi Yamamoto & Takahisa Suzuki, 2018. "Effects of beliefs about sanctions on promoting cooperation in a public goods game," Palgrave Communications, Palgrave Macmillan, vol. 4(1), pages 1-6, December.
    6. Yutaro Usui & Fujio Toriumi & Toshiharu Sugawara, 2023. "User behaviors in consumer-generated media under monetary reward schemes," Journal of Computational Social Science, Springer, vol. 6(1), pages 389-409, April.
    7. Liu, Linjie & Chen, Xiaojie, 2022. "Effects of interconnections among corruption, institutional punishment, and economic factors on the evolution of cooperation," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    8. Zhang, Boyu & An, Xinmiao & Dong, Yali, 2021. "Conditional cooperator enhances institutional punishment in public goods game," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    9. Tatsuya Sasaki & Isamu Okada & Satoshi Uchida & Xiaojie Chen, 2015. "Commitment to Cooperation and Peer Punishment: Its Evolution," Games, MDPI, vol. 6(4), pages 1-14, November.
    10. Fujio Toriumi & Hitoshi Yamamoto & Isamu Okada, 2020. "A belief in rewards accelerates cooperation on consumer-generated media," Journal of Computational Social Science, Springer, vol. 3(1), pages 19-31, April.
    11. Yamamoto, Hitoshi & Okada, Isamu, 2016. "How to keep punishment to maintain cooperation: Introducing social vaccine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 526-536.
    12. Xie Nenggang & Bao Wei & Ye Ye & Wang Meng, 2020. "A New Type of Evolutionary Strategy Based on a Multi-player Iterated Prisoner’s Dilemma Game," Journal of Systems Science and Information, De Gruyter, vol. 8(1), pages 67-81, February.
    13. Misato Inaba & Nobuyuki Takahashi, 2019. "Linkage Based on the Kandori Norm Successfully Sustains Cooperation in Social Dilemmas," Games, MDPI, vol. 10(1), pages 1-15, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dimitris Iliopoulos & Arend Hintze & Christoph Adami, 2010. "Critical Dynamics in the Evolution of Stochastic Strategies for the Iterated Prisoner's Dilemma," PLOS Computational Biology, Public Library of Science, vol. 6(10), pages 1-8, October.
    2. Isamu Okada, 2020. "A Review of Theoretical Studies on Indirect Reciprocity," Games, MDPI, vol. 11(3), pages 1-17, July.
    3. Caterina Cruciani & Anna Moretti & Paolo Pellizzari, 2012. "Does sharing values lead to cooperation? A similarity-based investigation," Working Papers 1, Department of Management, Università Ca' Foscari Venezia.
    4. Guofang Liu & Chongde Lin & Ziqiang Xin, 2014. "The Effects of Within- and Between-Group Competition on Trust and Trustworthiness among Acquaintances," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-5, July.
    5. Tetsushi Ohdaira & Takao Terano, 2009. "Cooperation in the Prisoner's Dilemma Game Based on the Second-Best Decision," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(4), pages 1-7.
    6. Su, Qi & Li, Aming & Wang, Long, 2017. "Spatial structure favors cooperative behavior in the snowdrift game with multiple interactive dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 299-306.
    7. Zhang, Yifan & Shu, Gang & Li, Ya, 2017. "Strategy-updating depending on local environment enhances cooperation in prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 224-232.
    8. Chen, Wei & Wu, Te & Li, Zhiwu & Wang, Long, 2016. "Friendship-based partner switching promotes cooperation in heterogeneous populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 192-199.
    9. Shade T. Shutters, 2009. "Strong reciprocity, social structure, and the evolution of fair allocations in a simulated ultimatum game," Computational and Mathematical Organization Theory, Springer, vol. 15(2), pages 64-77, June.
    10. Guan, Kaixuan & Chen, Yuyou & Zheng, Wanjun & Zeng, Lulu & Ye, Hang, 2022. "Costly signals can facilitate cooperation and punishment in the prisoner’s dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    11. Jian, Qing & Li, Xiaopeng & Wang, Juan & Xia, Chengyi, 2021. "Impact of reputation assortment on tag-mediated altruistic behaviors in the spatial lattice," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    12. Yamamoto, Hitoshi & Okada, Isamu, 2016. "How to keep punishment to maintain cooperation: Introducing social vaccine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 526-536.
    13. Shafi, Kamran & Bender, Axel & Zhong, Weicai & Abbass, Hussein A., 2012. "Spatio-temporal dynamics of security investments in an interdependent risk environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 5004-5017.
    14. Faqi Du & Feng Fu, 2011. "Partner Selection Shapes the Strategic and Topological Evolution of Cooperation," Dynamic Games and Applications, Springer, vol. 1(3), pages 354-369, September.
    15. Xiaojie Chen & Alana Schick & Michael Doebeli & Alistair Blachford & Long Wang, 2012. "Reputation-Based Conditional Interaction Supports Cooperation in Well-Mixed Prisoner’s Dilemmas," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-7, May.
    16. Mengyuan Zhou, 2022. "Does the Source of Inheritance Matter in Bequest Attitudes? Evidence from Japan," Journal of Family and Economic Issues, Springer, vol. 43(4), pages 867-887, December.
    17. Wendelin Schnedler & Nina Lucia Stephan, 2020. "Revisiting a Remedy Against Chains of Unkindness," Schmalenbach Business Review, Springer;Schmalenbach-Gesellschaft, vol. 72(3), pages 347-364, July.
    18. Mengyuan Zhou, 2019. "The Effect of the Source of Inheritance on Bequest Attitudes: Evidence from Japan," Keio-IES Discussion Paper Series 2019-018, Institute for Economics Studies, Keio University.
    19. Alós-Ferrer, Carlos & Garagnani, Michele, 2020. "The cognitive foundations of cooperation," Journal of Economic Behavior & Organization, Elsevier, vol. 175(C), pages 71-85.
    20. Cinzia Di Novi & Rowena Jacobs & Matteo Migheli, 2013. "The quality of life of female informal caregivers: from Scandinavia to the Mediterranean Sea," Working Papers 084cherp, Centre for Health Economics, University of York.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pcbi00:1004232. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ploscompbiol (email available below). General contact details of provider: https://journals.plos.org/ploscompbiol/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.