IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v515y2019icp102-111.html
   My bibliography  Save this article

Cooperation risk and Nash equilibrium: Quantitative description for realistic players

Author

Listed:
  • Nakamura, G.M.
  • Contesini, G.S.
  • Martinez, A.S.

Abstract

The emergence of cooperation figures among the main goal of game theory in competitive-cooperative environments. Potential games have long been hinted as viable alternatives to study realistic player behavior. Here, we expand the potential games approach by taking into account the inherent risks of cooperation. We show the Public Goods game reduce to a Hamiltonian with one-body operators, with the correct Nash Equilibrium as the ground state. The inclusion of punishments to the Public Goods game reduces cooperation risks, creating two-body interactions with a rich phase diagram, in which phase transitions segregates cooperative from competitive regimes.

Suggested Citation

  • Nakamura, G.M. & Contesini, G.S. & Martinez, A.S., 2019. "Cooperation risk and Nash equilibrium: Quantitative description for realistic players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 102-111.
    • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:102-111
    DOI: 10.1016/j.physa.2018.09.194
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118313268
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.09.194?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    2. Rand, David Gertler & Dreber, Anna & Fudenberg, Drew & Ellingson, Tore & Nowak, Martin A., 2009. "Positive Interactions Promote Public Cooperation," Scholarly Articles 3804483, Harvard University Department of Economics.
    3. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    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. Changping Zhao & Xiya Xie & Jun Song, 2021. "Complex Network Game Model Simulation of Arctic Sustainable Fishery Trade Cooperation under COVID-19," Sustainability, MDPI, vol. 13(14), pages 1-17, July.

    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. Du, Faqi & Fu, Feng, 2013. "Quantifying the impact of noise on macroscopic organization of cooperation in spatial games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 35-44.
    2. Kurz, Konstantin & Bock, Carolin & Knodt, Michèle & Stöckl, Anna, 2022. "A Friend in Need Is a Friend Indeed? Analysis of the Willingness to Share Self-Produced Electricity During a Long-lasting Power Outage," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 136773, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    3. Konstantin Kurz & Carolin Bock & Michèle Knodt & Anna Stöckl, 2022. "A Friend in Need Is a Friend Indeed? Analysis of the Willingness to Share Self-Produced Electricity During a Long-lasting Power Outage," Schmalenbach Journal of Business Research, Springer, vol. 74(4), pages 727-761, December.
    4. 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.
    5. E Lance Howe & James J Murphy & Drew Gerkey & Colin Thor West, 2016. "Indirect Reciprocity, Resource Sharing, and Environmental Risk: Evidence from Field Experiments in Siberia," PLOS ONE, Public Library of Science, vol. 11(7), pages 1-17, July.
    6. Min, Yong & Du, Yuchen & Jin, Cheng, 2018. "The effect of link rewiring on a coevolutionary common pool resource game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 935-944.
    7. Bin Wu & Da Zhou & Feng Fu & Qingjun Luo & Long Wang & Arne Traulsen, 2010. "Evolution of Cooperation on Stochastic Dynamical Networks," PLOS ONE, Public Library of Science, vol. 5(6), pages 1-7, June.
    8. Christian Hilbe & Maria Kleshnina & Kateřina Staňková, 2023. "Evolutionary Games and Applications: Fifty Years of ‘The Logic of Animal Conflict’," Dynamic Games and Applications, Springer, vol. 13(4), pages 1035-1048, December.
    9. Danilo Liuzzi & Aymeric Vié, 2022. "Staring at the Abyss: a neurocognitive grounded agent-based model of collective-risk social dilemma under the threat of environmental disaster," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(2), pages 613-637, April.
    10. Deng, Kuiying & Li, Zhuozheng & Kurokawa, Shun & Chu, Tianguang, 2012. "Rare but severe concerted punishment that favors cooperation," Theoretical Population Biology, Elsevier, vol. 81(4), pages 284-291.
    11. 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.
    12. Chen, Qiao & Chen, Tong & Wang, Yongjie, 2016. "How the expanded crowd-funding mechanism of some southern rural areas in China affects cooperative behaviors in threshold public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 649-655.
    13. 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.
    14. Elisabeth Gsottbauer & Jeroen den Bergh, 2013. "Bounded rationality and social interaction in negotiating a climate agreement," International Environmental Agreements: Politics, Law and Economics, Springer, vol. 13(3), pages 225-249, September.
    15. Hong Ding & Lin Cao & Yizhi Ren & Kim-Kwang Raymond Choo & Benyun Shi, 2016. "Reputation-Based Investment Helps to Optimize Group Behaviors in Spatial Lattice Networks," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-17, September.
    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. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 321-339.
    19. Carattini, Stefano & Gillingham, Kenneth & Meng, Xiangyu & Yoeli, Erez, 2024. "Peer-to-peer solar and social rewards: Evidence from a field experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 219(C), pages 340-370.
    20. Steven N. Durlauf, 1996. "Statistical Mechanics Approaches to Socioeconomic Behavior," NBER Technical Working Papers 0203, National Bureau of Economic Research, Inc.

    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:eee:phsmap:v:515:y:2019:i:c:p:102-111. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.