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Cycles and Instability in a Rock--Paper--Scissors Population Game: A Continuous Time Experiment

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  • Timothy N. Cason
  • Daniel Friedman
  • ED Hopkins

Abstract

We report laboratory experiments that use new, visually oriented software to explore the dynamics of 3x3 games with intransitive best responses. Each moment, each player is matched against the entire population, here 8 human subjects. A "heat map" offers instantaneous feedback on current profit opportunities. In the continuous slow adjustment treatment, we see distinct cycles in the population mix. The cycle amplitude, frequency and direction are consistent with the standard learning models. Cycles are more erratic and higher frequency in the instantaneous adjustment treatment. Control treatments (using simultaneous matching in discrete time) replicate previous results that exhibit weak or no cycles. Average play is approximated fairly well by Nash equilibrium, and an alternative point prediction, "TASP" (Time Average of the Shapley Polygon), captures some regularities that Nash equilibrium misses. Copyright 2014, Oxford University Press.

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  • Timothy N. Cason & Daniel Friedman & ED Hopkins, 2014. "Cycles and Instability in a Rock--Paper--Scissors Population Game: A Continuous Time Experiment," Review of Economic Studies, Oxford University Press, vol. 81(1), pages 112-136.
  • Handle: RePEc:oup:restud:v:81:y:2014:i:1:p:112-136
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    File URL: http://hdl.handle.net/10.1093/restud/rdt023
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    References listed on IDEAS

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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. Cason, Timothy N. & Friedman, Daniel & Hopkins, Ed, 2010. "Testing the TASP: An experimental investigation of learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2309-2331, November.
    3. Hommes, Cars H. & Ochea, Marius I., 2012. "Multiple equilibria and limit cycles in evolutionary games with Logit Dynamics," Games and Economic Behavior, Elsevier, vol. 74(1), pages 434-441.
    4. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    5. Dan Friedman, 2010. "Equilibrium in Evolutionary Games: Some Experimental Results," Levine's Working Paper Archive 393, David K. Levine.
    6. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
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    Cited by:

    1. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 195-208.
    2. Benndorf, Volker & Martínez-Martínez, Ismael, 2017. "Perturbed best response dynamics in a hawk–dove game," Economics Letters, Elsevier, vol. 153(C), pages 61-64.
    3. Zhijian Wang & Bin Xu, 2014. "Cycling in stochastic general equilibrium," Papers 1410.8432, arXiv.org.
    4. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," LSE Research Online Documents on Economics 65422, London School of Economics and Political Science, LSE Library.
    5. Heller, Yuval & Mohlin, Erik, 2015. "Unique Stationary Behavior," MPRA Paper 66179, University Library of Munich, Germany.
    6. repec:eee:phsmap:v:486:y:2017:i:c:p:455-464 is not listed on IDEAS
    7. Wang, Zhijian & Zhu, Siqian & Xu, Bin, 2013. "A Comment on "Cycles and Instability in a Rock-Paper-Scissors Population Game: A Continuous Time Experiment"," MPRA Paper 51691, University Library of Munich, Germany.
    8. Benndorf, Volker & Martínez-Martínez, Ismael & Normann, Hans-Theo, 2016. "Equilibrium selection with coupled populations in hawk–dove games: Theory and experiment in continuous time," Journal of Economic Theory, Elsevier, vol. 165(C), pages 472-486.
    9. Xu, Bin & Zhou, Hai-Jun & Wang, Zhijian, 2013. "Cycle frequency in standard Rock–Paper–Scissors games: Evidence from experimental economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4997-5005.

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