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Learning in Networks—An Experimental Study Using Stationary Concepts

Author

Listed:
  • Siegfried K. Berninghaus

    () (Institute of Economics, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, Karlsruhe D-76049, Germany)

  • Thomas Neumann

    () (Otto-von-Guericke University Magdeburg, Faculty of Economics and Management, P.O. Box 4120, Magdeburg 39016, Germany)

  • Bodo Vogt

    () (Otto-von-Guericke University Magdeburg, Faculty of Economics and Management, P.O. Box 4120, Magdeburg 39016, Germany)

Abstract

Our study analyzes theories of learning for strategic interactions in networks. Participants played two of the 2 × 2 games used by Selten and Chmura [1]. Every participant played against four neighbors. As a distinct aspect our experimental design allows players to choose different strategies against each different neighbor. The games were played in two network structures: a lattice and a circle. We analyze our results with respect to three aspects. We first compare our results with the predictions of five different equilibrium concepts (Nash equilibrium, quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium, and impulse balance equilibrium) which represent the long-run equilibrium of a learning process. Secondly, we relate our results to four different learning models (impulse-matching learning, action-sampling learning, self-tuning EWA, and reinforcement learning) which are based on the (behavioral) round-by-round learning process. At last, we compare the data with the experimental results of Selten and Chmura [1]. One main result is that the majority of players choose the same strategy against each neighbor. As other results, we observe an order of predictive success for the equilibrium concepts that is different from the order shown by Selten and Chmura and an order of predictive success for the learning models that is only slightly different from the order shown in a recent paper by Chmura, Goerg and Selten [2].

Suggested Citation

  • Siegfried K. Berninghaus & Thomas Neumann & Bodo Vogt, 2014. "Learning in Networks—An Experimental Study Using Stationary Concepts," Games, MDPI, Open Access Journal, vol. 5(3), pages 1-20, July.
  • Handle: RePEc:gam:jgames:v:5:y:2014:i:3:p:140-159:d:38757
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    References listed on IDEAS

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    1. 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, pages 848-881.
    2. Cassar, Alessandra, 2007. "Coordination and cooperation in local, random and small world networks: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 58(2), pages 209-230, February.
    3. Kirchkamp, Oliver & Nagel, Rosemarie, 2005. "Learning and cooperation in network experiments," Sonderforschungsbereich 504 Publications 05-27, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    4. Berninghaus, Siegfried K. & Ehrhart, Karl-Martin & Keser, Claudia, 2002. "Conventions and Local Interaction Structures: Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 39(2), pages 177-205, May.
    5. Reinhard Selten & Thorsten Chmura & Sebastian J. Goerg, 2011. "Stationary Concepts for Experimental 2 X 2 Games: Reply," American Economic Review, American Economic Association, pages 1041-1044.
    6. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    7. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    8. Ben Greiner, 2004. "The Online Recruitment System ORSEE 2.0 - A Guide for the Organization of Experiments in Economics," Working Paper Series in Economics 10, University of Cologne, Department of Economics.
    9. Reinhard Selten & Klaus Abbink & Ricarda Cox, 2005. "Learning Direction Theory and the Winner’s Curse," Experimental Economics, Springer;Economic Science Association, vol. 8(1), pages 5-20, April.
    10. Ho, Teck H. & Camerer, Colin F. & Chong, Juin-Kuan, 2007. "Self-tuning experience weighted attraction learning in games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 177-198, March.
    11. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
    12. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, pages 938-966.
    13. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, pages 834-847.
    14. Kirchkamp, Oliver & Nagel, Rosemarie, 2007. "Naive learning and cooperation in network experiments," Games and Economic Behavior, Elsevier, vol. 58(2), pages 269-292, February.
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    Cited by:

    1. Edward Cartwright & Anna Stepanova, 2017. "Efficiency in a forced contribution threshold public good game," International Journal of Game Theory, Springer;Game Theory Society, pages 1163-1191.

    More about this item

    Keywords

    stationary concepts; networks; learning; experimental economics;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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