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Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

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Abstract

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The "TASP" (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.

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  • Timothy N. Cason & Daniel Friedman & Ed Hopkins, 2009. "Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria," Edinburgh School of Economics Discussion Paper Series 188, Edinburgh School of Economics, University of Edinburgh.
  • Handle: RePEc:edn:esedps:188
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    1. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    2. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    3. Rutström, E. Elisabet & Wilcox, Nathaniel T., 2009. "Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test," Games and Economic Behavior, Elsevier, vol. 67(2), pages 616-632, November.
    4. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    5. 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.
    6. Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory," Levine's Bibliography 321307000000000724, UCLA Department of Economics.
    7. Anderson, Christopher M. & Plott, Charles R. & Shimomura, K.-I.Ken-Ichi & Granat, Sander, 2004. "Global instability in experimental general equilibrium: the Scarf example," Journal of Economic Theory, Elsevier, vol. 115(2), pages 209-249, April.
    8. Foster, Dean P. & Young, H. Peyton, 2003. "Learning, hypothesis testing, and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 73-96, October.
    9. Ignacio Palacios-Huerta & Oscar Volij, 2008. "Experientia Docet: Professionals Play Minimax in Laboratory Experiments," Econometrica, Econometric Society, vol. 76(1), pages 71-115, January.
    10. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
    11. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    12. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    13. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
    14. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181.
    15. Brown, James N & Rosenthal, Robert W, 1990. "Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment," Econometrica, Econometric Society, vol. 58(5), pages 1065-1081, September.
    16. Brown-Kruse, Jamie, et al, 1994. "Bertrand-Edgeworth Competition in Experimental Markets," Econometrica, Econometric Society, vol. 62(2), pages 343-372, March.
    17. Battalio, Raymond & Samuelson, Larry & Van Huyck, John, 2001. "Optimization Incentives and Coordination Failure in Laboratory Stag Hunt Games," Econometrica, Econometric Society, vol. 69(3), pages 749-764, May.
    18. Steven D. Levitt & John A. List & David H. Reiley, 2010. "What Happens in the Field Stays in the Field: Exploring Whether Professionals Play Minimax in Laboratory Experiments," Econometrica, Econometric Society, vol. 78(4), pages 1413-1434, July.
    19. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    20. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    21. Dekel, Eddie & Scotchmer, Suzanne, 1992. "On the evolution of optimizing behavior," Journal of Economic Theory, Elsevier, vol. 57(2), pages 392-406, August.
    22. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
    23. repec:feb:artefa:0094 is not listed on IDEAS
    24. Steven Levitt & John List & David Reiley, 2010. "What happens in the field stays in the field: Professionals do not play minimax in laboratory experiments," Artefactual Field Experiments 00080, The Field Experiments Website.
    25. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    26. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 395-415.
    27. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    28. 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.
    29. Charles N. Noussair & Charles R. Plott & Raymond G. Riezman, 2013. "An Experimental Investigation of the Patterns of International Trade," World Scientific Book Chapters, in: Raymond Riezman (ed.), International Trade Agreements and Political Economy, chapter 17, pages 299-328, World Scientific Publishing Co. Pte. Ltd..
    30. Cason, Timothy N. & Friedman, Daniel, 2003. "Buyer search and price dispersion: a laboratory study," Journal of Economic Theory, Elsevier, vol. 112(2), pages 232-260, October.
    31. repec:ams:ndfwpp:03-11 is not listed on IDEAS
    32. Ellison, Glenn & Fudenberg, Drew, 2000. "Learning Purified Mixed Equilibria," Journal of Economic Theory, Elsevier, vol. 90(1), pages 84-115, January.
    33. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
    34. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
    35. Wolf Ze'ev Ehrblatt & Kyle Hyndman & Erkut Y. ÄOzbay & Andrew Schotter, 2006. "Convergence: An Experimental Study," Levine's Working Paper Archive 122247000000001148, David K. Levine.
    36. Cason, Timothy N. & Friedman, Daniel & Wagener, Florian, 2005. "The dynamics of price dispersion, or Edgeworth variations," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 801-822, April.
    37. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April.
    38. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2003. "Stochastic Approximations and Differential Inclusions," Working Papers hal-00242990, HAL.
    39. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions; Part II: Applications," Working Papers hal-00242974, HAL.
    40. Tang, Fang-Fang, 2001. "Anticipatory learning in two-person games: some experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 44(2), pages 221-232, February.
    41. Offerman, Theo & Sonnemans, Joep & Schram, Arthur, 1996. "Value Orientations, Expectations and Voluntary Contributions in Public Goods," Economic Journal, Royal Economic Society, vol. 106(437), pages 817-845, July.
    42. Nathaniel T Wilcox, 2006. "Theories of Learning in Games and Heterogeneity Bias," Econometrica, Econometric Society, vol. 74(5), pages 1271-1292, September.
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    Cited by:

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    2. Christoph Kuzmics & Daniel Rodenburger, 2020. "A case of evolutionarily stable attainable equilibrium in the laboratory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 685-721, October.
    3. Bouton, Laurent & Castanheira, Micael & Llorente-Saguer, Aniol, 2016. "Divided majority and information aggregation: Theory and experiment," Journal of Public Economics, Elsevier, vol. 134(C), pages 114-128.
    4. Wang Yijia & Wang Zhijian, 2023. "Pulse in collapse: a game dynamics experiment," Papers 2302.09336, arXiv.org.
    5. Timothy N. Cason & Daniel Friedman & Ed Hopkins, 2021. "An Experimental Investigation of Price Dispersion and Cycles," Journal of Political Economy, University of Chicago Press, vol. 129(3), pages 789-841.
    6. Bouton, Laurent & Castanheira, Micael & Llorente-Saguer, Aniol, 2016. "Divided majority and information aggregation: Theory and experiment," Journal of Public Economics, Elsevier, vol. 134(C), pages 114-128.
    7. Martin Hahn, 2012. "An Evolutionary Analysis of Varian’s Model of Sales," Dynamic Games and Applications, Springer, vol. 2(1), pages 71-96, March.
    8. Antonio Cabrales & José-Ramón Uriarte, 2013. "Doubts and equilibria," Journal of Evolutionary Economics, Springer, vol. 23(4), pages 783-810, September.
    9. Wang, Yijia & Chen, Xiaojie & Wang, Zhijian, 2017. "Testability of evolutionary game dynamics based on experimental economics data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 455-464.
    10. Zhijian Wang & Qinmei Yao & Yijia Wang, 2022. "Eigen mode selection in human subject game experiment," Papers 2204.08071, arXiv.org.
    11. Zhijian Wang & Shujie Zhou & Qinmei Yao & Yijia Wang, 2022. "Dynamic Structure in Four-strategy Game: Theory and Experiment," Papers 2203.14669, arXiv.org.

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    More about this item

    Keywords

    games; experiments; TASP; learning; unstable; mixed equilibrium; fictitious play;
    All these keywords.

    JEL classification:

    • 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
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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