IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-00754481.html
   My bibliography  Save this paper

Ising model versus normal form game

Author

Listed:
  • Serge Galam

    (CREA - Centre de recherche en épistémologie appliquée - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Bernard Walliser

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

The 2-spin Ising model in statistical mechanics and the 2×2 normal form game in game theory are compared. All configurations allowed by the second are recovered by the first when the only concern is about Nash equilibria. But it holds no longer when Pareto optimum considerations are introduced as in the prisoner's dilemma. This gap can nevertheless be filled by adding a new coupling term to the Ising model, even if that term has up to now no physical meaning. An individual complete bilinear objective function is thus found to be sufficient to reproduce all possible configurations of a 2×2 game. Using this one-to-one mapping new perspectives for future research in both fields can be envisioned.

Suggested Citation

  • Serge Galam & Bernard Walliser, 2010. "Ising model versus normal form game," Post-Print halshs-00754481, HAL.
    • Handle: RePEc:hal:journl:halshs-00754481
    DOI: 10.1016/j.physa.2009.09.029
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    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. Bernard Walliser, 2006. "Justifications of Game Theoretic Equilibrium Notions," Chapters, in: Richard Arena & Agnès Festré (ed.), Knowledge, Beliefs and Economics, chapter 5, Edward Elgar Publishing.
    3. Richard Arena & Agnès Festré, 2006. "Knowledge, Beliefs and Economics," Post-Print halshs-00271316, HAL.
    4. Serge Galam, 2008. "Sociophysics: A Review Of Galam Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 409-440.
    5. Harjoat Singh Bhamra, 2000. "Imitation In Financial Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 473-478.
    6. Bernard Walliser, 2006. "Justifications of game equilibrium notions," Post-Print halshs-00754735, HAL.
    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. Leonidov, Andrey & Vasilyeva, Ekaterina, 2022. "Strategic stiffening/cooling in the Ising game," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Sarkar, Shubhayan & Benjamin, Colin, 2019. "Entanglement renders free riding redundant in the thermodynamic limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 607-613.
    3. Király, Balázs, 2023. "A tensor renormalization group analysis of the Blume–Capel model inspired by game theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    4. Szabó, György & Hódsági, Kristóf, 2016. "The role of mixed strategies in spatial evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 198-206.
    5. Zimmaro, Filippo & Galam, Serge & Javarone, Marco Alberto, 2024. "Asymmetric games on networks: Mapping to Ising models and bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    6. Paolo Pellizzari & Elena Sartori & Marco Tolotti, 2015. "Optimal Policies In Two-Step Binary Games Under Social Pressure And Limited Resources," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 18(05n06), pages 1-16, August.
    7. Barreira da Silva Rocha, André, 2013. "Evolutionary dynamics of nationalism and migration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3183-3197.
    8. Marco Alberto Javarone, 2016. "Modeling Poker Challenges by Evolutionary Game Theory," Games, MDPI, vol. 7(4), pages 1-10, December.
    9. Colin Benjamin & Arjun Krishnan U.M., 2023. "Nash equilibrium mapping vs. Hamiltonian dynamics vs. Darwinian evolution for some social dilemma games in the thermodynamic limit," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(7), pages 1-16, 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. Matjaž Steinbacher & Mitja Steinbacher, 2019. "Opinion Formation with Imperfect Agents as an Evolutionary Process," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 479-505, February.
    2. Stephanie Blankenburg, 2011. "On Sraffa, post-Keynesian theories of pricing and capitalist competition: Some observations," European Journal of Economics and Economic Policies: Intervention, Edward Elgar Publishing, vol. 8(1), pages 183-200.
    3. Falk Armin & Kosfeld Michael, 2012. "It's all about Connections: Evidence on Network Formation," Review of Network Economics, De Gruyter, vol. 11(3), pages 1-36, September.
    4. Szabó, György & Borsos, István & Szombati, Edit, 2019. "Games, graphs and Kirchhoff laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 416-423.
    5. 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.
    6. Steven N. Durlauf & Yannis M. Ioannides, 2010. "Social Interactions," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 451-478, September.
    7. Sanjeev Goyal & Fernando Vega-Redondo, 2000. "Learning, Network Formation and Coordination," Econometric Society World Congress 2000 Contributed Papers 0113, Econometric Society.
    8. Steven N. Durlauf, 1996. "Statistical Mechanics Approaches to Socioeconomic Behavior," NBER Technical Working Papers 0203, National Bureau of Economic Research, Inc.
    9. Christian Hilbe & Moshe Hoffman & Martin A. Nowak, 2015. "Cooperate without Looking in a Non-Repeated Game," Games, MDPI, vol. 6(4), pages 1-15, September.
    10. repec:ebl:ecbull:v:3:y:2007:i:19:p:1-8 is not listed on IDEAS
    11. Zhang, Boyu & Hofbauer, Josef, 2016. "Quantal response methods for equilibrium selection in 2×2 coordination games," Games and Economic Behavior, Elsevier, vol. 97(C), pages 19-31.
    12. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.
    13. Hutzler, S. & Sommer, C. & Richmond, P., 2016. "On the relationship between income, fertility rates and the state of democracy in society," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 9-18.
    14. Floriana Gargiulo & José J Ramasco, 2012. "Influence of Opinion Dynamics on the Evolution of Games," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-7, November.
    15. Venkatasubramanian, Venkat & Luo, Yu & Sethuraman, Jay, 2015. "How much inequality in income is fair? A microeconomic game theoretic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 120-138.
    16. Célestin Coquidé & José Lages & Dima Shepelyansky, 2024. "Opinion Formation in the World Trade Network," Post-Print hal-04461784, HAL.
    17. Denis Phan, 2006. "Discrete Choices under Social Influence:Generic Properties," Post-Print halshs-00105857, HAL.
    18. Fan Zou & Yupeng Li & Jiahuan Huang, 2022. "Group interaction and evolution of customer reviews based on opinion dynamics towards product redesign," Electronic Commerce Research, Springer, vol. 22(4), pages 1131-1151, December.
    19. Lawrence E. Blume, 1995. "Evolutionary Equilibrium with Forward-Looking Players," Game Theory and Information 9509001, University Library of Munich, Germany.
    20. Roland Pongou & Roberto Serrano, 2009. "A dynamic theory of fidelity networks with an application to the spread of HIV/AIDS," Working Papers 2009-03, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    21. Sheri M. Markose, 2005. "Computability and Evolutionary Complexity: Markets as Complex Adaptive Systems (CAS)," Economic Journal, Royal Economic Society, vol. 115(504), pages 159-192, 06.

    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:hal:journl:halshs-00754481. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.