IDEAS home Printed from https://ideas.repec.org/a/jas/jasssj/2007-11-2.html
   My bibliography  Save this article

Reinforcement Learning Dynamics in Social Dilemmas

Author

Abstract

In this paper we replicate and advance Macy and Flache's (2002; Proc. Natl. Acad. Sci. USA, 99, 7229–7236) work on the dynamics of reinforcement learning in 2×2 (2-player 2-strategy) social dilemmas. In particular, we provide further insight into the solution concepts that they describe, illustrate some recent analytical results on the dynamics of their model, and discuss the robustness of such results to occasional mistakes made by players in choosing their actions (i.e. trembling hands). It is shown here that the dynamics of their model are strongly dependent on the speed at which players learn. With high learning rates the system quickly reaches its asymptotic behaviour; on the other hand, when learning rates are low, two distinctively different transient regimes can be clearly observed. It is shown that the inclusion of small quantities of randomness in players' decisions can change the dynamics of the model dramatically.

Suggested Citation

  • Segismundo S. Izquierdo & Luis R. Izquierdo & Nicholas M. Gotts, 2008. "Reinforcement Learning Dynamics in Social Dilemmas," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 11(2), pages 1-1.
    • Handle: RePEc:jas:jasssj:2007-11-2
    as

    Download full text from publisher

    File URL: https://www.jasss.org/11/2/1/1.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Karandikar, Rajeeva & Mookherjee, Dilip & Ray, Debraj & Vega-Redondo, Fernando, 1998. "Evolving Aspirations and Cooperation," Journal of Economic Theory, Elsevier, vol. 80(2), pages 292-331, June.
    2. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 17-45.
    3. Fernando Vega-Redondo & Frédéric Palomino, 1999. "Convergence of aspirations and (partial) cooperation in the prisoner's dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 465-488.
    4. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    5. Mookherjee Dilip & Sopher Barry, 1994. "Learning Behavior in an Experimental Matching Pennies Game," Games and Economic Behavior, Elsevier, vol. 7(1), pages 62-91, July.
    6. Margaret Edwards & Sylvie Huet & François Goreaud & Guillaume Deffuant, 2003. "Comparing an Individual-Based Model of Behaviour Diffusion with Its Mean Field Aggregate Approximation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 6(4), pages 1-9.
    7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    8. Binmore, K. & Samuelson, L., 1993. "An Economist's Perspective on the Evolution of Norms," Working papers 9323, Wisconsin Madison - Social Systems.
    9. Mookherjee, Dilip & Sopher, Barry, 1997. "Learning and Decision Costs in Experimental Constant Sum Games," Games and Economic Behavior, Elsevier, vol. 19(1), pages 97-132, April.
    10. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    11. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    12. J. Gareth Polhill & Luis R. Izquierdo, 2005. "Lessons Learned from Converting the Artificial Stock Market to Interval Arithmetic," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 8(2), pages 1-2.
    13. José Manuel Galán & Luis R. Izquierdo, 2005. "Appearances Can Be Deceiving: Lessons Learned Re-Implementing Axelrod's 'Evolutionary Approach to Norms'," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 8(3), pages 1-2.
    14. Binmore Kenneth G. & Samuelson Larry & Vaughan Richard, 1995. "Musical Chairs: Modeling Noisy Evolution," Games and Economic Behavior, Elsevier, vol. 11(1), pages 1-35, October.
    15. Yan Chen & Fang-Fang Tang, 1998. "Learning and Incentive-Compatible Mechanisms for Public Goods Provision: An Experimental Study," Journal of Political Economy, University of Chicago Press, vol. 106(3), pages 633-662, June.
    16. Luis R. Izquierdo & J. Gareth Polhill, 2006. "Is Your Model Susceptible to Floating-Point Errors?," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 9(4), pages 1-4.
    17. Youngse Kim, 1999. "Satisficing and optimality in 2þ2 common interest games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 365-375.
    18. Leigh Tesfatsion & Kenneth L. Judd (ed.), 2006. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 2, number 2.
    19. Duffy, John, 2006. "Agent-Based Models and Human Subject Experiments," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 19, pages 949-1011, Elsevier.
    20. Sylvie Huet & Margaret Edwards & Guillaume Deffuant, 2007. "Taking into Account the Variations of Neighbourhood Sizes in the Mean-Field Approximation of the Threshold Model on a Random Network," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(1), pages 1-10.
    21. Erev, Ido & Bereby-Meyer, Yoella & Roth, Alvin E., 1999. "The effect of adding a constant to all payoffs: experimental investigation, and implications for reinforcement learning models," Journal of Economic Behavior & Organization, Elsevier, vol. 39(1), pages 111-128, May.
    22. Andreas Flache & Michael W. Macy, 2002. "Stochastic Collusion and the Power Law of Learning," Journal of Conflict Resolution, Peace Science Society (International), vol. 46(5), pages 629-653, October.
    23. Michael W. Macy, 1989. "Walking out of Social Traps," Rationality and Society, , vol. 1(2), pages 197-219, October.
    24. John G. Cross, 1973. "A Stochastic Learning Model of Economic Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(2), pages 239-266.
    25. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Gotts, Nicholas M. & Polhill, J. Gary, 2007. "Transient and asymptotic dynamics of reinforcement learning in games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 259-276, November.
    26. Bendor Jonathan & Mookherjee Dilip & Ray Debraj, 2001. "Reinforcement Learning in Repeated Interaction Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, March.
    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. Cheng, Yuan & Zheng, Xiaoping, 2018. "Emergence of cooperation during an emergency evacuation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 485-494.
    2. Jia, Danyang & Li, Tong & Zhao, Yang & Zhang, Xiaoqin & Wang, Zhen, 2022. "Empty nodes affect conditional cooperation under reinforcement learning," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    3. Li Zhenpeng & Tang Xijin, 2021. "Stimuli strategy and learning dynamics promote the wisdom of crowds," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(12), pages 1-8, December.
    4. Dan Miodownik & Britt Cartrite & Ravi Bhavnani, 2010. "Between Replication and Docking: "Adaptive Agents, Political Institutions, and Civic Traditions" Revisited," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 13(3), pages 1-1.
    5. Ding, Zhen-Wei & Zhang, Ji-Qiang & Zheng, Guo-Zhong & Cai, Wei-Ran & Cai, Chao-Ran & Chen, Li & Wang, Xu-Ming, 2024. "Emergence of anti-coordinated patterns in snowdrift game by reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    6. José Manuel Galán & Luis R. Izquierdo & Segismundo S. Izquierdo & José Ignacio Santos & Ricardo del Olmo & Adolfo López-Paredes & Bruce Edmonds, 2009. "Errors and Artefacts in Agent-Based Modelling," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-1.
    7. John W. Straka & Brenda C. Straka, 2020. "Reframe policymaking dysfunction through bipartisan-inclusion leadership," Policy Sciences, Springer;Society of Policy Sciences, vol. 53(4), pages 779-802, December.
    8. Luis R. Izquierdo & Segismundo S. Izquierdo & José Manuel Galán & José Ignacio Santos, 2009. "Techniques to Understand Computer Simulations: Markov Chain Analysis," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-6.
    9. Han, Zhen & Wu, Wenning & Song, Qun & Zhu, Peican, 2024. "Analysis of payoff expectation in evolutionary game based on Bush–Mosteller model," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).

    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. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Gotts, Nicholas M. & Polhill, J. Gary, 2007. "Transient and asymptotic dynamics of reinforcement learning in games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 259-276, November.
    2. Schuster, Stephan, 2012. "Applications in Agent-Based Computational Economics," MPRA Paper 47201, University Library of Munich, Germany.
    3. Duffy, John, 2006. "Agent-Based Models and Human Subject Experiments," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 19, pages 949-1011, Elsevier.
    4. Napel, Stefan, 2003. "Aspiration adaptation in the ultimatum minigame," Games and Economic Behavior, Elsevier, vol. 43(1), pages 86-106, April.
    5. Schuster, Stephan, 2010. "Network Formation with Adaptive Agents," MPRA Paper 27388, University Library of Munich, Germany.
    6. José Manuel Galán & Luis R. Izquierdo & Segismundo S. Izquierdo & José Ignacio Santos & Ricardo del Olmo & Adolfo López-Paredes & Bruce Edmonds, 2009. "Errors and Artefacts in Agent-Based Modelling," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-1.
    7. Mitropoulos, Atanasios, 2001. "Learning under minimal information: An experiment on mutual fate control," Journal of Economic Psychology, Elsevier, vol. 22(4), pages 523-557, August.
    8. Ianni, A., 2002. "Reinforcement learning and the power law of practice: some analytical results," Discussion Paper Series In Economics And Econometrics 203, Economics Division, School of Social Sciences, University of Southampton.
    9. Dziubiński, Marcin & Roy, Jaideep, 2012. "Popularity of reinforcement-based and belief-based learning models: An evolutionary approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 433-454.
    10. Ponti, Giovanni, 2000. "Continuous-time evolutionary dynamics: theory and practice," Research in Economics, Elsevier, vol. 54(2), pages 187-214, June.
    11. repec:wyi:journl:002151 is not listed on IDEAS
    12. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    13. Atanasios Mitropoulos, 2001. "Learning Under Little Information: An Experiment on Mutual Fate Control," Game Theory and Information 0110003, University Library of Munich, Germany.
    14. Shachat, Jason & Swarthout, J. Todd, 2012. "Learning about learning in games through experimental control of strategic interdependence," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 383-402.
    15. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    16. Ianni, Antonella, 2014. "Learning strict Nash equilibria through reinforcement," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 148-155.
    17. Osili, Una Okonkwo & Paulson, Anna, 2014. "Crises and confidence: Systemic banking crises and depositor behavior," Journal of Financial Economics, Elsevier, vol. 111(3), pages 646-660.
    18. Oyarzun, Carlos & Sarin, Rajiv, 2013. "Learning and risk aversion," Journal of Economic Theory, Elsevier, vol. 148(1), pages 196-225.
    19. Chen, Yan & Khoroshilov, Yuri, 2003. "Learning under limited information," Games and Economic Behavior, Elsevier, vol. 44(1), pages 1-25, July.
    20. Tassos Patokos, 2014. "Introducing Disappointment Dynamics and Comparing Behaviors in Evolutionary Games: Some Simulation Results," Games, MDPI, vol. 5(1), pages 1-25, January.
    21. Yu Zhang & Jason Leezer, 2010. "Simulating human-like decisions in a memory-based agent model," Computational and Mathematical Organization Theory, Springer, vol. 16(4), pages 373-399, December.

    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:jas:jasssj:2007-11-2. 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: Francesco Renzini (email available below). General contact details of provider: .

    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.