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Evolutionary Dynamics of Strategic Behavior in a Collective-Risk Dilemma

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  • Maria Abou Chakra
  • Arne Traulsen

Abstract

A collective-risk social dilemma arises when a group must cooperate to reach a common target in order to avoid the risk of collective loss while each individual is tempted to free-ride on the contributions of others. In contrast to the prisoners' dilemma or public goods games, the collective-risk dilemma encompasses the risk that all individuals lose everything. These characteristics have potential relevance for dangerous climate change and other risky social dilemmas. Cooperation is costly to the individual and it only benefits all individuals if the common target is reached. An individual thus invests without guarantee that the investment is worthwhile for anyone. If there are several subsequent stages of investment, it is not clear when individuals should contribute. For example, they could invest early, thereby signaling their willingness to cooperate in the future, constantly invest their fair share, or wait and compensate missing contributions. To investigate the strategic behavior in such situations, we have simulated the evolutionary dynamics of such collective-risk dilemmas in a finite population. Contributions depend individually on the stage of the game and on the sum of contributions made so far. Every individual takes part in many games and successful behaviors spread in the population. It turns out that constant contributors, such as constant fair sharers, quickly lose out against those who initially do not contribute, but compensate this in later stages of the game. In particular for high risks, such late contributors are favored. Author Summary: The evolution of cooperation is a fascinating topic with a wide range of applications, from microbial evolution to global cooperation of humans in the context of climate change. Motivated by the prospect of dangerous climate change, behavioral experiments of a ‘collective-risk dilemma’ were conducted, where cooperation is in vain unless a threshold is met. This game requires multilateral efforts over several rounds in order to reach a known target and avoid collective loss. We have conducted large scale computer simulations to explore the evolutionary dynamics of strategic behavior in such collective-risk dilemmas. Individuals can react to the contributions of their co-players over the course of the game and adopt their own contributions. The timing of contributions to the public good is a very important issue for long-term problems such as climate change. In this context, it is imperative to know when individuals (or countries) would naturally contribute. We show that a specific behavior, late contributions, is favored, especially when risk is high. Collective-risk dilemmas can by their very nature lead to a detrimental outcome for all involved, and, thus it is crucial to understand the behavior that is expected in such a situation.

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  • Maria Abou Chakra & Arne Traulsen, 2012. "Evolutionary Dynamics of Strategic Behavior in a Collective-Risk Dilemma," PLOS Computational Biology, Public Library of Science, vol. 8(8), pages 1-7, August.
    • Handle: RePEc:plo:pcbi00:1002652
    DOI: 10.1371/journal.pcbi.1002652
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    1. Jiang, Luo-Luo & Gao, Jian & Chen, Zhi & Li, Wen-Jing & Kurths, Jürgen, 2021. "Reducing the bystander effect via decreasing group size to solve the collective-risk social dilemma," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Chica, Manuel & Santos, Francisco C., 2023. "Seeding leading cooperators and institutions in networked climate dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Bin Wu & Lei Zhou, 2018. "Individualised aspiration dynamics: Calculation by proofs," PLOS Computational Biology, Public Library of Science, vol. 14(9), pages 1-15, September.
    4. Ding, Rui & Wang, Xianjia & Liu, Yang & Zhao, Jinhua & Gu, Cuiling, 2023. "Evolutionary games with environmental feedbacks under an external incentive mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. Chica, Manuel & Hernández, Juan M. & Santos, Francisco C., 2022. "Cooperation dynamics under pandemic risks and heterogeneous economic interdependence," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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