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Reinforcement Learning Dynamics in Social Dilemmas

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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.

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  • 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
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    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.
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    Cited by:

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    5. 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).
    6. 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.
    7. 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.

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