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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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Zhang, Boyu & An, Xinmiao & Dong, Yali, 2021. "Conditional cooperator enhances institutional punishment in public goods game," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    2. Shen, Yong & Ma, Yujie & Kang, Hongwei & Sun, Xingping & Chen, Qingyi, 2024. "Learning and propagation: Evolutionary dynamics in spatial public goods games through combined Q-learning and Fermi rule," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    3. 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.
    4. 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.
    5. 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.
    6. Xie Nenggang & Ye Ye & Bao Wei & 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.
    7. 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.
    8. Zhang, Yao & Hao, Qing-Yi & Qian, Jia-Li & Wu, Chao-Yun & Bi, Yan, 2024. "The influence of the heterogeneities of social institutions and individuals’ tendency to establish social institutions on cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    9. 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.
    10. Isamu Okada, 2020. "A Review of Theoretical Studies on Indirect Reciprocity," Games, MDPI, vol. 11(3), pages 1-17, July.
    11. Geng, Yini & Lu, Yikang & Hong, Lijun & Shi, Lei, 2025. "Evolution of cooperation with asymmetric rewards," Applied Mathematics and Computation, Elsevier, vol. 487(C).
    12. 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.
    13. 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.
    14. 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.
    15. 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).
    16. 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.

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